B&O Tech: Native or not?

#62 in a series of articles about the technology behind Bang & Olufsen products

Over the past year or so, I’ve had lots of discussions and interviews with lots of people (customers, installers, and journalists) about Bang & Olufsen’s loudspeakers – BeoLab 90 in particular. One of the questions that comes up when the chat gets more technical is whether our loudspeakers use native sampling rates or sampling rate conversion – and why. So, this posting is an attempt to answer this – even if you’re not as geeky as the people who asked the question in the first place.

There are advantages and disadvantages to choosing one of those two strategies – but before we get to talk about some of them, we have to back up and cover some basics about digital audio in general. Feel free to skip this first section if you already know this stuff.

A very quick primer in digital audio

An audio signal in real life is a change in air pressure over time. As the pressure increases above the current barometric pressure, the air molecules are squeezed closer together than normal. If those molecules are sitting in your ear canal, then they will push your eardrum inwards. As the pressure decreases, the molecules move further apart, and your eardrum is pulled outwards. This back-and-forth movement of your eardrum starts a chain reaction that ends with an electrical signal in your brain.

If we take your head out of the way and replace it with a microphone, then it’s the diaphragm of the mic that moves inwards and outwards instead of your eardrum. This causes a chain reaction that results in a change in electrical voltage over time that is analogous to the movement of the diaphragm. In other words, as the diaphragm moves inwards (because the air pressure is higher), the voltage goes higher. As the diaphragm moves outwards (because the air pressure is lower) the voltage goes lower. So, if you were to plot the change in voltage over time, the shape of the plot would be similar to the change in air pressure over time.

We can do different things with that changing voltage – we could send it directly to a loudspeaker (maybe with a little boosting in between) to make a P.A. system for a rock concert. We could send it to a storage device like a little wiggling needle digging a groove in a cylinder made of wax. Or we could measure it repeatedly…

That last one is where we’re headed. Basically speaking, a continuous, analogue (because it’s analogous to the pressure signal) audio signal is converted into a digital audio signal by making instantaneous measurements of it repeatedly, and very quickly. It’s a little bit like the way a movie works: you move your hand and take a movie – the camera takes a bunch of still photographs in such quick succession that, if you play back the photos quickly, it looks like movement to our slow eyes. Of course, I’m leaving out a bunch of details, but that’s the basic concept.

So, a digital audio signal is a series of measurements of an electrical voltage (which was changing over time) that are transmitted or stored as numbers somehow, somewhere.

Figure 1:
Figure 1: A plot showing the change in voltage over time by an arbitrary signal (which happens to look very much like a sine wave, because you always use sine waves when you’re doing science).


Figure 2:
Figure 2: A plot showing the same waveform after it has been converted to a digital representation. Notice that it’s the same shape, only the values on the y-axis have changed. Note as well that these values are arbitrary. In this case, I’ve done the conversion such that an analogue signal of 1 V at the input corresponds to a value of 32768 in the digital representation. It doesn’t matter why I picked this scaling.


Figure 3:
Figure 3: If we zoom in on a small section of Figure 2, it would look like this. Notice that the wave is not really a continuous line – it’s a series of discrete measurements (represented here by a bunch of circles on sticks – or poorly-drawn lollipops, depending on your point of view.)

Figure 3 shows a small slice of time from Figure 2, which is, itself a small slice of time that normally is considered to extend infinitely into the past and the future. If we want to get really pedantic about this, I can tell you the actual values represented in the plot in Figure 3. These are as follows:


  • -21115
  • -19634
  • -17757
  • -15522
  • -12975
  • -10167
  • -7153
  • -3996
  • -758
  • 2495
  • 5698
  • 8786
  • 11697
  • 14373
  • 16759
  • 18807
  • 20477

The actual values that I listed there really aren’t important. What is important is the concept that this list of numbers can be used to re-construct the signal. If I take that list and plot them, it would look like Figure 4.

Figure 3:
Figure 4: A plot of the values listed above. Notice that this looks exactly like the plot in Figure 3 (because it is…)

So, in order to transmit or store an audio signal that has been converted from an analogue signal into a digital signal, all I need to do is to transmit or store the numbers in the right order. Then, if I want to play them back (say, out of loudspeaker) I just need to convert the numbers back to voltages in the right order at the right rate (just like a movie is played back at the same frame rate that the photos were take in – otherwise you get things moving too fast or too slowly).

One last piece of information that you’ll need before we move on is that, in a digital audio system, the audio signal can only contain reliable information below the frequency that is one-half of the “sampling rate” (which is the rate at which you are grabbing those measurements of the voltages – each of those measurements is called a “sample”, since it’s taking an instantaneous sample of the current state of the system). It’s just like taking a blood sample or a water sample – you use it as a measurement of one portion of one thing right now. This means that if you want to record and play back audio up to 20,000 Hz (or 20,000 cycles per second – which is what textbooks say that we can hear) you will need to be making more than 40,000 measurements per second. If we use a CD as an example, the sampling rate is 44,100 samples per second – also known as a sampling rate of 44.1 kHz. This is very fast.

Sidebar: Please don’t jump to conclusions about what I have said thus far. I am not saying that “digital audio is perfect” (or even “perfect-er or worse-er than analogue”) or that “this is all you need to understand how digital audio works”. And, if you are the type of person who worships at “The Church of Our Lady of Perpetual Jitter” or “The Temple of Inflationary Bitrates” please don’t email me with abuse. All I’m trying to do here is to set the scene for the discussion to follow. Anyone really interested in how digital audio really works should read the collected writings of Harry Nyquist, Claude Shannon, John Watkinson, Jamie Angus, Stanley Lipshitz, and John Vanderkooy and send them emails instead.  (Also, if you’re one of the people that I just mentioned there, please don’t get mad at me for the deluge of spam you’re about to receive…)


Filtering an audio signal

Most loudspeakers contain a filter of some kind. Even in the simplest passive two-way loudspeaker, there is very likely a small circuit called a “crossover” that divides the analogue electrical audio signal so that the low frequencies go to the big driver (the woofer) and the higher frequencies go to the little driver (the tweeter). This circuit contains “filters” that have an input and an output – the output is a modified (or filtered) version of the input. For example, in a low-pass filter, the low frequencies are allowed to pass through it, and the higher frequencies are reduced in level (which makes it useful for sending signals to the woofer).

Once again over-simplifying, this is accomplished in an electrical circuit by playing with something called electrical impedance – a measure of how much the circuit impedes the flow of current to the next device. Some circuits will impede the flow of current if it’s alternating quickly (a high frequency) other circuits might impede the flow of current if it’s alternating slowly (a low frequency). Other circuits will do something else…

It is also possible to filter an audio signal when it is in the digital domain instead. We have the series of numbers (like the one above) and we can send these to a mathematical function which will change the values into other numbers to produce the desired characteristics (like a low-pass filter, for example).

As a simple example, if we take all of the values in the list above, and multiply them by 0.5 before converting them back to voltages, then the output level will be quieter. In other words, we’ve made a volume knob in the digital domain. Of course, it’s not a very good knob, since it’s stuck at one setting… but this isn’t a course in advanced DSP…

If you want to make something more exciting than a volume knob, the typical way of making an audio filter in the digital world is to use delays to mix the signal with delayed copies of itself. This can get very complicated, but let’s make a simple filter to illustrate…

Fig 5.
Figure 5. A very simple digital audio low pass filter


Figure 5 shows a very simple low pass filter for digital audio. Let’s think though what will happen when we send a signal through it.

If you have a very low frequency, then the current sample goes into the input and heads in two directions. Let’s ignore the top path for now and follow the lower path. The sample goes into a delay and comes out on the other side 1 sample later (in the case of a CD, this is 1/44100-th of a second later).  When that sample comes out of the delay, the one that followed it (which is now “now” at the input) meets it at the block on the right with the “+” sign in it. This adds the two samples together and spits out of the result. In other words, the filter above adds the current audio sample to the previous audio sample and delivers the result as the current output.

What will this do to the audio signal?

If the frequency of the audio signal is very low, then the two samples (the current one, and the previous one) are very similar in level, as can be seen in the plot in Figures 6 and 7, below. This means, basically, that the output of the filter will be very, very similar to the output, just twice as loud (because it’s the signal plus itself). Another way to think of this is that the current sample of the audio signal and the previous sample of the same signal are essentially “in phase” – and any two audio signals that are “in phase” and added together will give you twice the output.

However, as the frequency of the audio signal gets higher, the relative levels of those two adjacent samples becomes more and more different (because the sampling rate doesn’t change).  One of them will be closer to “0” than the other – and increasingly so as the frequency increases .  So, the higher the audio frequency, the lower the level of the output (since it will not go higher than the signal plus itself, as we saw in the low frequency example…) If we’re thinking of this in terms of phase, the higher the frequency of the audio signal, the greater the phase difference between the adjacent samples that are summed, so the lower the output…

That output level keeps dropping as the audio frequency goes up until we hit a frequency where the audio signal’s frequency is exactly one half of the sampling rate. At that “magic point”, the two samples are so far apart (in terms of the audio signal’s waveform) that they have opposite polarity values (because they’re 180 degrees out-of-phase with each other). So, if you add those two samples together, you get no output – because they are equal, but opposite.


Figure 6:
Figure 6: Portions of three sine waves – one at 10 Hz (red), one at 100 Hz (blue) and one at 22050 Hz (black), sampled at 44.1 kHz.


Let’s zoom in on the plot in Figure 6 to see the individual samples. We’ll take a slice of time around the 500-sample mark. This is shown below in Figure 7.


Figure 7:
Figure 7: a portion of Figure 6, zooming in around the 500-sample mark. Note that the vertical scales of the three plots are different – just to make things more clear visually.

As you can see in Figure 7, any two adjacent samples for a low frequency (the red plot) are almost identical. The middle frequency (the blue plot) shows that two adjacent samples are more different than they are for this low frequency. For the “magic frequency” of “sampling rate divided by 2” (in this case, 22050 Hz) two adjacent samples are equal and opposite in polarity.

Now that you know this, we are able to “connect the dots” and plot the output levels for the filter in Figure 5 for a range of frequencies from very low to very high. This is shown in Figures 8 and 9, below.

Figure 8:
Figure 8: A plot of the output level of the filter we’re talking about, as a multiple of the level of its input. Note the output is twice as loud as the input in the low frequency region (hence the “2” on the Y-axis) and that that we have no output (or a level of 0) at 22050 Hz.
Figure 9:
Figure 9: The same information plotted in Figure 8, shown on a decibel scale. The last point (at 22050 Hz) is not shown because it’s at -infinity dB, so showing this this would require that you buy a bigger screen for your computer.

Normalised frequency

Now we have to step up the coefficient of geekiness…

So far, we have been thinking with a fixed sampling rate of 44.1 kHz – just like that which is used for a CD. However, audio recordings that you can buy online are available at different sampling rates – not just 44.1 kHz. So, how does this affect our understanding so far?

Well, things don’t change that much – we just have to change gears a little by making our frequency scales vary with sampling rate.

So, without using actual examples or numbers, we already know that an audio signal with a low frequency going through the filter above will come out louder than the input. We also know that the higher the frequency, the lower the output until we get to the point where the audio signal’s frequency is one half the sampling rate, where we get no output. This is true, regardless of the sampling rate – the only change is that, by changing the sampling rate, we change the actual frequencies that we’re talking about in the audio signal.

So, if the sampling rate is 44.1 kHz, we get no output at 22050 Hz. However, if the sampling rate were 96 kHz, we wouldn’t reach our “no output” frequency until the audio signal gets to 48 kHz (half of 96 kHz). If the sampling rate were 176.4 kHz, we would get something out of our filter up to 88.2 kHz.

So, the filter generally behaves the same – we’re just moving the frequency scale around.

So, instead of plotting the magnitude response of our filter with respect to the actual frequency of the audio signal out here in the real world, we can plot it with respect to the sampling rate, where we can get all the way up to 0.5 (half of the sampling rate) since this is as high as we’re allowed to go. So, I’ve re-plotted Figures 8 and 9 below using what is called a “normalised frequency” scale – where the frequency of the audio signal is expressed as a fraction of the sampling rate.

Figure 8a:
Figure 8a: The same plot as Figure 8, but shown on a Normalised Frequency scale.
Figure 9a:
Figure 9a: The same plot as Figure 9, but shown on a Normalised Frequency scale.


These last sentences are VERY IMPORTANT! So, if you didn’t understand everything I said in the previous 6 paragraphs, go back and read them again. If you still don’t understand it, please email me or put a comment in below, because it means that I didn’t explain it well enough. ..


Note that there are two conventions for “normalised frequency” just to confuse everyone. Some people say that it’s “audio frequency relative to the sampling rate” (like I’ve done here). Some other people say that it’s “audio frequency relative to half of the sampling rate”. Now you’ve been warned.

Designing an audio filter

In the example above, I made a basic audio filter, and then we looked at its output. Of course, if we’re making a loudspeaker with digital signal processing, we do the opposite. We have a target response that we want at the output, and we build a filter that delivers that result.

For example, let’s say that I wanted to make a filter that has a similar response to the one shown above, but I want it to roll off less in the high frequencies. How could I do this? One option is shown below in Figure 10:

Fig. 10.
Fig. 10. A modified version of our first low pass filter shown in Figure 5.

Notice that I added a multiplier on the output of the delay block. This means that if the frequency is low, I’ll add the current sample to half the value of the previous one, so I’ll get a maximum output of 1.5 times the input (instead of 2 like we had before). When we get to one half the sampling rate, we won’t cancel completely, so the high end won’t drop off as much. The resulting magnitude response is shown in Figures 11 and 12, below.

Figure 11:
Figure 11: The magnitude response, plotted on a Normalised Frequency scale, of the filter shown in Figure 10.
Figure 12:
Figure 12: The same information as is shown in Figure 11, on a decibel scale.

So, we can decide on a response for the filter, and we can design a filter that delivers that response. Part of the design of that filter is the values of the “coefficients” inside it. In the case of digital filters, “coefficient” is a fancy term meaning “number” – in the case of the filter in Figure 10, it has one coefficient – the “0.5” that is multiplied by the output of the delay. For example, if we wanted less of a roll-off in the high end, we could set that coefficient to 0.1, and we would get less cancellation at half the sampling rate (and less output in the low end….)

Putting some pieces together

So, now we see that a digital filter’s magnitude response (and phase response, and other things) is dependent on three things:

  • its design (e.g. how many delays and additions)
  • the sampling rate
  • the coefficients inside it

If we change one of these three things, the magnitude response of the filter will change. This means that, if we want to change one of these things and keep the magnitude response, we’ll have to change at least one of the other things.

For example, if we want to change the sampling rate, but keep the design of the filter, in order to get the same sampling rate, we’re going to have to change the coefficients.

Again, those last two paragraphs were important… Read’em again if you didn’t get it.

So what?

Let’s now take this information into the real world.

In order for BeoLab 90 to work, we had to put a LOT of digital filters into it – and some of those filters contain thousands of coefficients… For example, when you’re changing from “Narrow” mode to “Wide” mode, you have to change a very large filter for each of loudspeaker driver (that’s thousands of coefficients times 18 drivers) – among other things… This has at least four implications:

  • there has to be enough computing power inside the BeoLab 90 to make all those multiplications at the sampling rate (which, we’ve already seen above, is very fast)
  • there has to be enough computer memory to handle all of the delays that are necessary to build the filters
  •  there has to be enough memory to store all of those coefficients (remember that they’re not numbers like 1 or 17 – they’re very precise numbers with a lot of digits like 0.010383285748578423049 (in case you’re wondering, that’s not an actual coefficient from one of the filters in a loudspeaker – I just randomly tapped on a bunch of keys on my keyboard until I got a long number… I’m just trying to make an intuitive point here…))
  • You have to be able to move those coefficients from the memory where they’re stored into the calculator (the DSP) quickly because people don’t want to wait for a long time when you’re changing modes

This is why (for now, at least) when you switch between “Narrow” and “Wide” mode, there is a small “break” in the audio signal to give the processor time to load all the coefficients and get the signal going again.

One sneaky thing in the design of the system is that, internally, the processor is always running at the same sampling rate. So, if you have a source that is playing back audio files from your hard drive, one of them ripped from a CD (and therefore at 44.1 kHz) and the next one from www.theflybynighthighresaudiodownloadcompany.com (at 192 kHz), internally at the DSP, the BeoLab 90 will not change.

Why not? Well, if it did, we would have to load a whole new set of coefficients for all of the filters every time your player changes sampling rates, which, in a worst case, is happening for every song, but which you probably don’t even realise is happening – nor should you have to worry about it…

So, instead of storing a complete set of coefficients for each possible sampling rate – and loading a new set into the processor every time you switch to the next track (which, if you’re like my kids, happens after listening to the current song for no more than 5 seconds…) we keep the internal sampling rate constant.

There is a price to pay for this – we have to ensure that the conversion from the sampling rate of the source to the internal sampling rate of the BeoLab 90 is NOT the weakest link in the chain. This is why we chose a particular component (specifically the Texas Instruments SRC4392 – which is a chip that you can buy at your local sampling rate converter store) to do the job. It has very good specifications with respect to passband ripple, signal-to-noise ratio, and distortion to ensure that the conversion is clean. One cost of this choice was that its highest input sampling rate is 216 kHz – which is not as high as the “DXD” standard for audio (which runs at 384 kHz).

So, in the development meetings for BeoLab 90, we decided three things that are linked to each other.

  1. we would maintain a fixed internal sampling rate for the DSP, ADC’s and DAC’s.
  2. This meant that we would need a very good sampling rate converter for the digital inputs.
  3. The choice of component for #2 meant that BeoLab 90’s hardware does not support DXD at its digital inputs.

One of the added benefits to using a good sampling rate converter is that it also helps to attenuate artefacts caused by jitter originating at the audio source – but that discussion is outside the scope of this posting (since I’ve already said far too much…) However, if you’re curious about this, I can recommend a bunch of good reading material that has the added benefit of curing insomnia… Not unlike everything I’ve written here…


B&O Tech: Headphone signal flows

#54 in a series of articles about the technology behind Bang & Olufsen products

Someone recently asked a question on this posting regarding headphone loudness. Specifically, the question was:

“There is still a big volume difference between H8 on Bluetooth and cable. Why is that?”

I thought that this would make a good topic for a whole posting, rather than just a quick answer to a comment – so here goes…

Introduction – the building blocks

To begin, let’s take a quick look at all the blocks that we’re going to assemble in a chain later. It’s relatively important to understand one or two small details about each block.

Two start:

  • I’ve used red lines for digital signals and blue lines for analogue signals. I’ve assumed that the digital signal contains 2 audio channels, and that the analogue connections are one channel each.
  • My signal flow goes from left to right
  • I use the word “telephone” not because I’m old-fashioned (although I am that…) but because if I say “phone”, I could be mistaken for someone talking about headphones. However, the source does not have to be a telephone, it could be anything that fits the descriptions below.
  • The blocks in my signal flows should be taken as basic examples. I have not reverse-engineered a particular telephone or computer or pair of headphones. I’m just describing basic concepts here…
Fig 1: A Digital to Analogue converter.
Fig 1: A Digital to Analogue converter.

Figure 1, above, shows a 2-channel audio DAC – a Digital to Analogue Converter. This is a device (these days, it’s usually just a chip) that receives a 2-channel digital audio signal as a stream of bits at its input and outputs an analogue signal that is essentially a voltage that varies appropriately over time.

One important thing to remember here is that different DAC’s have different output levels. So, if you send a Full Scale sine wave (say, a 997 Hz, 0 dB FS) into the input of one DAC, you might get 1 V RMS out. If you sent exactly the same input into another DAC (meaning another brand or model) you might get 2 V RMS out.

You’ll find a DAC, for example, inside your telephone, since the data inside it (your MP3 and .wav files) have to be converted to an analogue signal at some point in the chain in order to move the drivers in a pair of headphones connected to the minijack output.

Fig 2: An Analogue to Digital converter.
Fig 2: An Analogue to Digital converter.

Figure 2, above, shows a 2-channel ADC – and Analogue to Digital Converter. This does the opposite of a DAC – it receives two analogue audio channels, each one a voltage that varies in time, and converts that to a 2-channel digital representation at its output.

One important thing to remember here is the sensitivity of the input of the ADC. When you make (or use) an ADC, one way to help maximise your signal-to-noise ratio (how much louder the music is than the background noise of the device itself) is to make the highest analogue signal level produce a full-scale representation at the digital output. However, different ADC’s have different sensitivities. One ADC might be designed so that 2.0 V RMS signal at its input results in a 0 dB FS (full scale) output. Another ADC might be designed so that a 0.5 V RMS signal at its input results in a 0 dB FS output. If you send 0.5 V RMS to the first ADC (expecting a max of 2 V RMS) then you’ll get an output of approximately -12 dB FS. If you send 2 V RMS to the second ADC (which expects a maximum of only 0.5 V RMS) then you’ll clip the signal.

Fig 3: A Digital Signal Processor.
Fig 3: A Digital Signal Processor.

Figure 3, above, shows a Digital Signal Processor or DSP. This is just the component that does the calculations on the audio signals. The word “calculations” here can mean a lot of different things: it might be a simple volume control, it could be the filtering for a bass or treble control, or, in an extreme case, it might be doing fancy things like compression, upmixing, bass management, processing of headphone signals to make things sound like they’re outside your head, dynamic control of signals to make sure you don’t melt your woofers – anything…

Fig 4: A two-channel analogue amplifier block.
Fig 4: A two-channel analogue amplifier block.

Figure 4, above, shows a two-channel analogue amplifier block. This is typically somewhere in the audio chain because the output of the DAC that is used to drive the headphones either can’t provide a high-enough voltage or current (or both) to drive the headphones. So, the amplifier is there to make the voltage higher, or to be able to provide enough current to the headphones to make them loud enough so that the kids don’t complain.

Fig 5: The headphone drivers - the "business end" of the headphones.
Fig 5: The headphone drivers – the “business end” of the headphones.

The final building block in the chain is the headphone driver itself. In most pairs of headphones, this is comprised of a circular-shaped magnet with a coil of wire inside it. The coil is glued to a diaphragm that can move like the skin of a drum. Sending electrical current back and forth through the coil causes it to move back and forth which pushes and pulls the diaphragm. That, in turn, pushes and pulls the air molecules next to it, generating high and low pressure waves that move outwards from the front of the diaphragm and towards your eardrum. If you’d like to know more about this basic concept – this posting will help.

One important thing to note about a headphone driver is its sensitivity. This is a measure of how loud the output sound is for a given input voltage. The persons who designed the headphone driver’s components determine this sensitivity by changing things like the strength of the magnet, the length of the coil of wire, the weight of the moving parts, resonant chambers around it, and other things. However, the basic point here is that different drivers will have different loudnesses at different frequencies for the same input voltage.

Now that we have all of those building blocks, let’s see how they’re put together so that you can listen to Foo Fighters on your phone.

Version 1: The good-old days

In the olden days, you had a pair of headphones with a wire hanging out of one or both sides and you plugged that wire into the headphone jack of a telephone or computer or something else. We’ll stick with the example of a telephone to keep things consistent.

Figure 6, below, shows an example of the path the audio signal takes from being a MP3 or .wav (or something else) file on your phone to the sound getting into your ears.

The file is read and then decoded into something called a “PCM” signal (Pulse Code Modulation – it doesn’t matter what this is for the purposes of this posting). So, we get to point “A” in the chain and we have audio. In some cases, the decoder doesn’t have to do anything (for example, if you use uncompressed PCM audio like a .wav file) – in other cases (like MP3) the decoder has to convert a stream of data into something that can be understood as an audio signal by the DSP. In essence, the decoder is just a kind of universal translator, because the DSP only speaks one language.

The signal then goes through the DSP, which, in a very simple case is just the volume control. For example, if you want the signal to have half the level, then the DSP just multiplies the incoming numbers (the audio signal) by 0.5 and spits them out again. (No, I’m not going to talk about dither today.) So, that gets us to point “B” in the chain. Note that, if your volume is set to maximum and you aren’t doing anything like changing the bass or treble or anything else – it could be that the DSP just spits out what it’s fed (by multiplying all incoming values by 1.0).

Now, the signal has to be converted to analogue using the DAC. Remember (from above) that the actual voltage at its output (at point “C”) is dependent on the brand and model of DAC we’re talking about. However, that will probably change anyway, since the signal is fed through the amplifiers which output to the minijack connector at point “D”.

Assuming that they’ve set the DSP so that output=input for now, then the voltage level at the output (at “D”) is determined by the telephone’s manufacturer by looking at the DAC’s output voltage and setting the gain of the amplifiers to produce a desired output.

Fig 6: An example of a basic signal flow that occurs when you plus a pair of passive headphones into your phone to listen to music.
Fig 6: An example of a basic signal flow that occurs when you plug a pair of passive headphones into your telephone’s headphone output to listen to music.

Then, you plug a pair of headphones into the minijack. The headphone drivers have a sensitivity (a measure of the amount of sound output for a given voltage/current input) that will have an influence on the output level at your eardrum. The more sensitive the drivers to the electrical input, the louder the output. However, since, in this case, we’re talking about an electromechanical system, it will not change its behaviour (much) for different sources. So, if you plug a pair of headphones into a minijack that is supplying 2.0 V RMS, you’ll get 4 times as much sound output as when you plug them into a minijack that is supplying 0.5 V RMS.

This is important, since different devices have VERY different output levels – and therefore the headphones will behave accordingly. I regularly measure the maximum output level of phones, computers, CD players, preamps and so on – just to get an idea of what’s on the market. I’ve seen maximum output levels on a headphone jack as low as 0.28 V RMS (on an Apple iPod Nano Gen4) and as high as 8.11 V RMS (on a Behringer Powerplay Pro-8 headphone distribution amp). This is a very big difference (29 dB, which also happens to be 29  times…).

Version 2: The more-recent past

So, you’ve recently gone out and bought yourself a newfangled pair of noise-cancelling headphones, but you’re a fan of wires, so you keep them plugged into the minijack output of your telephone. Ignoring the noise-cancelling portion, the signal flow that the audio follows, going from a file in the memory to some sound in your ears is probably something like that shown in Figure 7.

Fig 7: An example of a basic signal flow that occurs when you plug a pair of active headphones into your phone's headphone output to listen to music.
Fig 7: An example of a basic signal flow that occurs when you plug a pair of active headphones into your telephone’s headphone output to listen to music.

As you can see by comparing Figures 7 and 6, the two systems are probably identical until you hit the input of the headphones. So, everything that I said in the previous section up to the output of the telephone’s amplifiers is the same. However, things change when we hit the input of the headphones.

The input of the headphones is an analogue to digital converter. As we saw above, the designer of the ADC (and its analogue input stages) had to make a decision about its sensitivity – the relationship between the voltage of the analogue signal at its input and the level of the  digital signal at its output. In this case, the designer of the headphones had to make an assumption/decision about the maximum voltage output of the source device.

Now we’re at point “E” in the signal chain. Let’s say that there is no DSP in the headphones – no tuning, no volume – nothing. So, the signal that comes out of the ADC is sent, bit for bit, to its DAC. Just like the DAC in the source, the headphone’s DAC has some analogue output level for its digital input level. Note that there is no reason for the analogue signal level of the headphones’ input to be identical to the analogue output level of the DAC or the analogue output level of the amplifiers. The only reason a manufacturer might want to try to match the level between the analogue input and the amplifier output is if the headphones work when they’re turned off – thus connecting the source’s amplifier directly to the headphone drivers (just like in Figure 6). This was one of the goals with the BeoPlay H8 – to ensure that if your batteries die, the overall level of the headphones didn’t change considerably.

However, some headphones don’t bother with this alignment because when the batteries die, or you turn them off, they don’t work – there’s no bypass…

Version 3: Look ma! No wires!

These days, many people use Bluetooth to connect wirelessly from the source to the headphones. This means that some components in the chain are omitted (like the DAC’s in the source and the ADC in the headphones) and others are inserted (in Figures 8 and 9, the Bluetooth Transmitter and Receiver).

Note that, to keep things simple, I have not included the encoder and the decoder for the Bluetooth transmission in the chain. Depending mainly on your source’s capabilities, the audio signal will probably be encoded into one of the varieties of an SBC, an AAC, or an aptX codec before transmitting. It’s then decoded back to PCM after receiving. In theory, the output of the decoder has the same level as the input of the encoder, so I’ve left it out of this discussion. I won’t discuss either CODEC’s implications on audio quality in this posting.

Taking a look at Figure 8 or 9 and you’ll see that, in theory, the level of the digital audio signal inside the source is identical to that inside the headphones – or, at least, it can be.

Fig 6: An example of a basic signal flow that occurs when you plus a pair of passive headphones into your phone to listen to music.
Fig 8: One example of a basic signal flow that occurs when you connect a pair of active headphones to your telephone using Bluetooth to listen to music. Note that the volume control, in this example, is shown in the telephone.
Fig 9: One example of a basic signal flow that occurs when you connect a pair of active headphones to your telephone using Bluetooth to listen to music. Note that the volume control, in this example, is shown in the headphones.
Fig 9: One example of a basic signal flow that occurs when you connect a pair of active headphones to your telephone using Bluetooth to listen to music. Note that the volume control, in this example, is shown in the headphones.

This means that the potentially incorrect assumptions made by the headphone manufacturer about the analogue output levels of the source can be avoided. However, it also means that, if you have a pair of headphones like the BeoPlay H7 or H8 that can be used either via an analogue or a Bluetooth connection then there will, in many cases, be a difference in level when switching between the two signal paths.

For example…

Let’s take a simple case. We’ll build a pair of headphones that can be used in two ways. The first is using an analogue input that is processed through the headphone’s internal DSP (just as is shown in Figure 6). We’ll build the headphones so that they can be used with a 2.0 V RMS output – therefore we’ll set the input sensitivity so that a 2.0 V RMS signal will result in a 0 dB FS signal internally.

We then connect the headphones to an Apple MacBook Pro’s headphone output, we play a signal with a level of 0 dB FS, and we turn up the volume to maximum. This will result in an analogue violate level of 2.085 V RMS coming from the computer’s headphone output.

Now we’ll use the same headphones and connect them to an Apple iPhone 4s which has a maximum analogue output level of 0.92 V RMS. This is less than half the level of the MacBook Pro’s output. So, if we set the volume to maximum on the iPhone and play exactly the same file as on the MacBook Pro, the headphones will have half the output level.

A second way to connect the headphones is via Bluetooth using the signal flow shown in Figure 8. Now, if we use Bluetooth to connect the headphones to the MacBook Pro with its volume set to maximum, a 0 dB FS signal inside the computer results in a 0 dB FS signal inside the headphones.

If we connect the headphones to the iPhone 4s via Bluetooth and play the same file at maximum volume, we’ll get the same output as we did with the MacBook Pro. This is because the 0 dB FS signal inside the phone is also producing a 0 dB FS signal in the headphones.

So, if you’re on the computer, switching from a Bluetooth connection to an analogue wired connection using the same volume settings will result in the same output level from the headphones (because the headphones are designed for a max 2 V RMS analogue signal). However, if you’re using the telephone, switching from a Bluetooth connection to an analogue wired connection will results in a drop in the output level by more than 6 dB (because the telephone’s maximum output level is less than 1 V RMS).

Wrapping up

So, the answer to the initial question is that there’s a difference between the output of the H8 headphones when switching between Bluetooth and the cable because the output level of the source that you’re using is different from what was anticipated by the engineers who designed the input stage of the headphones. This is likely because the input stage of the headphones was designed to be compatible with a device with a higher maximum output level than the one you’re using.

B&O Tech: The Cube

#51 in a series of articles about the technology behind Bang & Olufsen loudspeakers

Figure X: A Beolab 8000 woofer undergoing near field measurements.
Figure 1: A Beolab 8000 woofer undergoing near field measurements in The Cube.

Sometimes, we have journalists visiting Bang & Olufsen in Struer to see our facilities. Of course, any visit to Struer means a visit to The Cube – our room where we do almost all of the measurements of the acoustical behaviour of our loudspeaker prototypes. Different people ask different questions about that room – but there are two that come up again and again:

  • Why is the room so big?
  • Why isn’t it an anechoic chamber?

Of course, the level of detail of the answer is different for different groups of people (technical journalists from audio magazines get a different level of answer than lifestyle journalists from interior design magazines). In this article, I’ll give an even more thorough answer than the one the geeks get. :-)

Introduction #1 – What do we want?

Our goal, when we measure a loudspeaker, is to find out something about its behaviour in the absence of a room. If we measured the loudspeaker in a “real” room, the measurement would be “infected” by the characteristics of the room itself. Since everyone’s room is different, we need to remove that part of the equation and try to measure how the loudspeaker would behave without any walls, ceiling or floor to disturb it.

So, this means (conceptually, at least) that we want to measure the loudspeaker when it’s floating in space.

Introduction #2 – What kind of measurements do we do?

Basically, the measurements that we perform on a loudspeaker can be boiled down into four types:

  1. on-axis frequency response
  2. off-axis frequency responses
  3. directivity
  4. power response

Luckily, if you’re just a wee bit clever (and we think that we are…), all four of these measurements can be done using the same basic underlying technique.

The very basic idea of doing any audio measurement is that you have some thing whose characteristics you’re trying to measure – the problem is that this thing is usually a link in a chain of things – but you’re only really interested in that one link. In our case, the things in the audio chain are electrical (like the DAC, microphone preamplifier, and ADC) and acoustical (like the measurement microphone and the room itself).

Figure 2: A block diagram of the measurement system in The Cube.
Figure 2: A block diagram of the measurement system in The Cube. The acoustical signals in the room are shown in red. Analogue electrical connections around shown in blue. (That thing on the bottom is supposed to look like a computer showing a magnitude response plot…)

The computer sends a special signal (we’ll come back to that…) out of its “sound card” to the input of the loudspeaker. The sound comes out of the loudspeaker and comes into the microphone (however, so do all the reflections from the walls, ceiling and floor of the Cube). The output of the microphone gets amplified by a preamplifier and sent back into the computer. The computer then “looks at” the difference between the signal that it sent out and the signal that came back in. Since we already know the characteristics of the sound card, the microphone and the mic preamp, then the only thing remaining that caused the output and input signals to be different is the loudspeaker.

Introduction #3 – The signal

There are lots of different ways to measure an audio device. One particularly useful way is to analyse how it behaves when you send it a signal called an “impulse” – a click. The nice thing about a theoretically perfect click is that it contains all frequencies at the same amplitude and with a known phase relationship. If you send the impulse through a device that has an “imperfect” frequency response, then the click changes its shape. By doing some analysis using some 200-year old mathematical tricks (called “Fourier analysis“), we can convert the shape of the impulse into a plot of the magnitude and phase responses of the device.

So, we measure the way the device (in our case, a loudspeaker) responds to an impulse – in other words, its “impulse response”.

Figure X: Simplified example of a loudspeaker impulse response from the Cube.
Figure 3: Simplified example of a loudspeaker impulse response from the Cube.

There are three things to initially notice in this figure.

  • The first is the time before the first impulse comes in. This is the time it takes the sound to travel from the loudspeaker to the microphone. Since we normally make measurements at a distance of 3 m, this is about 8.7 ms.
  • The second is the fact that the impulse doesn’t look perfect. That’s because it isn’t – the loudspeaker has made it different.
  • The third is the presence of the wall reflection. (In real life, we see 6 of these – 4 walls, a ceiling and the floor – but this example is a simulation that I created, just to show the concept.)

In order to get a measurement of the loudspeaker in the absence of a room, we have to get rid of those reflections… In this case, all we have to do is to tell the computer to “stop listening” before that reflection arrives. The result is the impulse response of the loudspeaker in the absence of any reflections – which is exactly what we want.

  • We make this measurement “on-axis” (usually directly in front of the loudspeaker, at some specific height which may or may not be the same height as the tweeter) to get a basic idea to begin with.
  • We can then rotate the crane (the device hanging from the ceiling that the loudspeaker is resting on) with a precision of 1º. This allows us to make an off-axis measurement at any horizontal angle.
  • In order to find the loudspeaker’s directivity (like Figure 5, 6, and 7 in this posting), we start by making a series of measurements (typically, every 5º for all 360º around the loudspeaker). We then tell the computer to compare the difference between each off-axis measurement and the on-axis measurement (because we’re only interested in how the sound changes with rotation – not its actual response at a given off-axis angle – we already got that in the previous measurement.
  • Finally, we have to get the power response. This one is a little more tricky. The power response is the behaviour of the loudspeaker when measured in all directions simultaneously. Think of this as putting the loudspeaker in the centre of a sphere with a diameter of 3 m made of microphones. We send a signal out of the loudspeaker and measure the response at all points on the sphere, add them all together and see what the total is. This is an expensive way to do this measurement, since microphones cost a lot… An easier way is to use one microphone and rotate the loudspeaker (both horizontally and vertically) and do a LOT of off-axis measurements – not just rotating around the loudspeaker,  but also going above and below it. We do each of these measurements individually, and then add the results to get a 3D sum of all responses in all directions. That total is the power response of the loudspeaker – a measurement of the total energy the loudspeaker radiates into the room.
Figure X: A prototype loudspeaker made of MDF on the crane, on its way out to be measured.
Figure 4: A prototype loudspeaker made of MDF on the crane, on its way out to be measured.
Figure 5: A BeoVision 11 during off-axis response measurements.
Figure 5: A BeoVision 11 during off-axis response measurements.

The original questions…

Great. That’s a list of the basic measurements that come out of The Cube. However, I still have’t directly answered the original questions…

Let’s take the second question first: “Why isn’t The Cube an anechoic chamber?”

This raises the question: “What’s an anechoic chamber?” An anechoic chamber is a room whose walls are designed to be absorptive (typically to sound waves, although there are some chambers that are designed to absorb radio waves – these are for testing antennae instead of loudspeakers). If the walls are perfectly absorptive, then there are no reflections, and the loudspeaker behaves as if there are no walls.

So, this question has already been answered – albeit indirectly. We do an impulse response measurement of the loudspeaker, which is converted to magnitude and phase response measurements. As we saw in Figure 5, the reflections off the walls are easily visible in the impulse response. Since, after the impulse response measurement is done, we can “delete” the reflection (using a process called “windowing”) we end up with an impulse response that has no reflections. This is why we typically say that The Cube is “pseudo-anechoic” – the room is not anechoic, but we can modify the measurements after they’re done to be the same as if it were.

Now to the harder question to answer: “Why is the room so big?”

Let’s say that you have a device (for example, a loudspeaker), and it’s your job to measure its magnitude response. One typical way to do this is to measure its impulse response and to do a DFT (or FFT) on that to arrive at a magnitude response.

Let’s also say that you didn’t do your impulse response measurement in a REAL free field (a space where there are no reflections – the wave is free to keep going forever without hitting anything) – but, instead, that you did your measurement in a real space where there are some reflections. “No problem,” you say “I’ll just window out the reflections” (translation: “I’ll just cut the length of the impulse response so that I slice off the end before the first reflection shows up.”)

This is a common method of making a “pseudo-anechoic” measurement of a loudspeaker. You do the measurement in a space, and then slice off the end of the impulse response before you do an FFT to get a magnitude response.

Generally speaking, this procedure works fairly well… One thing that you have to worry about is a well-known relationship between the length of the impulse response (after you’ve sliced it) and the reliability of your measurement. The shorter the impulse response, the less you can trust the low-frequency result from your FFT. One reason for this is that, when you do an FFT, it uses a “slice” of time to convert the signal into a frequency response. In order to be able to measure a given frequency accurately, the FFT math needs at least one full cycle within the slice of time. Take a look at Figure 6, below.

Figure 4: A 100 Hz and a 20 Hz sine tone, plotted for the first 20 ms.
Figure 6: A 100 Hz (blue) and a 20 Hz (red) sine tone, plotted for the first 20 ms.

As you can see in that plot, if the slice of time that we’re looking at is 20 ms long, there is enough time to “see” two complete cycles of a 100 Hz sine tone (in blue). However, 20 ms is not long enough to see even one half of a cycle of a 20 Hz sine tone (in red).

However, there is something else to worry about – a less-well-known relationship between the level and extension of the low-frequency content of the device under test and the impulse response length. (Actually, these two issues are basically the same thing – we’re just playing with how low is “low”…)

Let’s start be inventing a loudspeaker that has a perfectly flat on-axis magnitude response but a low-frequency limitation with a roll-off at 10 Hz. I’ve simulated this very unrealistic loudspeaker by building a signal processing flow as shown in Figure 7.

Figure X:
Figure 7: Signal Processing created to simulate a loudspeaker described above.

If we were to do an impulse response measurement of that system, it would look like the plot in Figure 8, below.

Figure X:
Figure 8: As you can see, this is almost a perfect impulse. It goes to a value of 1 at time 0 (therefore there’s no delay) and then it’s a value of 0 for the rest of all time… Or is it? Look very carefully at the line just after the impulse. Notice how it dips just below the 0 line? Let’s zoom in on that…
Figure X:
Figure 9: Zooming in on Figure 8.

Figure 9, above shows a closeup of what happens just after the impulse. Notice that the signal drops below 0, then swings back up, then negative again. In fact, this keeps happening – the signal goes positive, negative, positive, negative – theoretically for an infinite amount of time – it never stops. (This is why the filters that I used to make this high pass are called “IIR” filters or “Infinite Impulse Response” filters.)

The problem is that this “ringing” in time (to infinity) is very small. However, it’s more easily visible if we plot it on a logarithmic scale, as shown below in Figure 10.

Figure X:
Figure 10: The same plot as shown in Figure 8, plotted on a logarithmic scale by converting to decibels.

As you can see there, after 1 second (1000 ms) the oscillation caused by the filtering has dropped by about 400 dB relative to the initial impulse (that means it has a level of about 0.000 000 000 000 000 000 01 if the initial impulse has a value of 1). This is very small – but it exists. This means that, if we “cut off” the impulse to measure its frequency response, we’ll be cutting off some of the signal (the oscillation) and therefore getting some error in the conversion to frequency. The question then is: how much error is generated when we shorten the impulse length?

We won’t do an analysis of how to answer this question – I’ll just give some examples. Let’s take the total impulse response shown in Figure 6 and cut it to different lengths – 10, 15, 20, 25, 30 and 1000 ms. For each of those versions, I’ll take an FFT and look at the resulting magnitude response. These are shown below in Figure 11.

Figure X:

Figure 11: The magnitude responses resulting from taking an FFT of a shortened portion of a single impulse response plotted in Figure 8.

We’ll assume that the light blue curve in Figure 9 is the “reference” since, although it has some error due to the fact that the impulse response is “only” one second long, that error is very small. You can see in the dark blue curve that, by doing an FFT on only the first 10 ms of the total impulse response, we get a strange behaviour in the result. The first is that we’ve lost a lot in the low frequency region (notice that the dark blue curve is below the light blue curve at 10 Hz). We also see a strange bump at about 70 Hz – which is the beginning of a “ripple” in the magnitude response that goes all the way up into the high frequency region.

The amount of error that we get – and the specific details of how wrong it is – are dependent on the length of the portion of the impulse response that we use.

If we plot this as an error – how wrong is each of the curves relative to our reference, the result looks like Figure 12.

Figure X:
Figure 12: The magnitude of the error resulting from using too-short an impulse response to calculate the magnitude response. This is the “reference” curve in Figure 9 subtracted from each curve in the same plot.

So what?

As you can see there, using a shorted impulse response produces an error in our measurement when the signal has a significant low frequency output. However, as we said above, we shorten the impulse response to delete the early reflections from the walls of The Cube in our measurement to make it “pseudo-anechoic”. This means, therefore, that we must have some error in our measurement. In fact, this is true – we do have some error in our measurement – but the error is smaller than it would have been if the room had been smaller. A bigger room means that we can have a longer impulse response which, in turn, means that we have a more accurate magnitude response measurement.

“So why not use an anechoic chamber and not mess around with this ‘pseudo-anechoic’ stuff?” I hear you cry… This is a good idea, in theory – however, in practice, the problem that we see above is caused by the fact that the loudspeaker has a low-frequency output. Making a room anechoic at a very low frequency (say, 10 Hz) would be very expensive AND it would have to be VERY big (because the absorptive wedges on the walls would have to be VERY deep – a good rule of thumb is that the wedges should be 1/4 of the wavelength of the lowest frequency you’re trying to absorb, and a 10 Hz wave has a wavelength of 34.4 m, so you’d need wedges about 8.6 m deep on all surfaces… This would therefore be a very big room…)

Appendix 1 – Tricks

Of course, there are some tricks that can be played to make the room seem bigger than it is. One trick that we use is to do our low-frequency measurements in the “near field” which is much closer than 3 m from the loudspeaker, as is shown in Figure 13 below. The advantage of doing this is that it makes the direct sound MUCH louder than the wall reflections (in addition to making the difference in their time of arrival at the microphone slightly longer) which reduces their impact on the measurement. The problem with doing near-field measurements is that you are very sensitive to distance – and you typically have to assume that the loudspeaker is radiating omnidirectional – but this is a fairly safe assumption in most cases.

Figure X: A closeup of a Beolab 8000 woofer undergoing near field measurements.
Figure 13: A closeup of a Beolab 8000 woofer undergoing near field measurements.

Appendix 2 – Windowing

Those of you with some experience with FFT’s may have heard of something called a windowing function which is just a fact way to slice up the impulse response. Instead of either letting signal through or not, we can choose to “fade out” the impulse response more gradually. This changes the error that we’ll get, but we’ll still get an error, as can be seen below.

Figure X:
Figure 14: Windowing functions showing the gain vs. time for a 1-second impulse response, assuming that the impulse is at time=0.
Figure X:
Figure 15: The magnitude responses for the impulse response in Figure 8, using a Hann window to cut the impulse response to various lengths.
Figure 16:
Figure 16: The magnitude responses for the impulse response in Figure 8, using a Hamming window to cut the impulse response to various lengths.
Figure X:
Figure 17: The magnitude responses for the impulse response in Figure 8, using a Blackman window to cut the impulse response to various lengths.
Figure X:
Figure 18: The magnitude responses for the impulse response in Figure 8, using a Blackman-Harris window to cut the impulse response to various lengths.
Figure X:
Figure 19: The magnitude responses for the impulse response in Figure 8, using a Bartlett window to cut the impulse response to various lengths.

So, as you can see with all of those, the error is different for each windowing function and impulse response length – but there’s no “magic bullet” here that makes the problems go away. If you have a loudspeaker with low-frequency output, then you need a longer impulse response to see what it’s doing, even in the higher frequencies.

Max gen~ Delay analysis

I use Cycling 74’s Max/MSP every  day. It’s almost gotten to the point where I use it for emailing. But, until yesterday, I never used the gen~ option. So, in order to come up-to-speed, I decided to sit down and follow a couple of tutorials to figure out whether gen~ would help me make things either faster or better – or both.

One of the cool options in the gen~ environment is that you can choose the interpolation type of the audio delay. You have 4 options: linear, spline, cosine, or cubic interpolation. So, I decided to make a little experiment to test which I’d like to use as a default.

I made a little patcher which is shown below.

Figure 1: The Max patcher I used for the test.
Figure 1: The Max patcher I used for the test.

I only changed two variables – one was the interpolation type and the second was the delay time (either 20.25 samples or 20.5 samples – as can be seen in the message boxes in the main patcher).

As you can see there, the result is recorded as a wav. file (just 16-bit – but that’s good enough for this test) at 44.1 kHz (the sampling rate I used for the test).

I then imported 8 wav. files into Matlab for analysis. There were 4 interpolation types for each of the two delay values.

The big question in my head was “what is the influence of the interpolation type on the magnitude response of the delayed signal?” So, I did a 16k FFT of the delayed click (with rectangular windowing, which is fine, since I’m measuring an impulse response response and I’m starting and ending with 0’s). The results of the two delay times are shown in Figures 2 and 3, below.


Figure 2: Magnitude responses of the delayed signal with a delay time of x.5 samples.
Figure 2: Magnitude responses of the delayed signal with a delay time of x.5 samples. Note that the linear and the cosine magnitude responses are identical for a delay time of x.5 samples which is why only 3 curves are visible.


Figure 3: Magnitude responses of the delayed signal with a delay time of x.25 samples.
Figure 3: Magnitude responses of the delayed signal with a delay time of x.25 samples.

As can be seen there, things are behaving more or less like they should. The Linear and Cosine interpolations have identical magnitude responses when the delay time is exactly x.5 samples. In addition, it’s worth noting that the linearly interpolated has the biggest roll-off when the the delay time is not x.5 samples.

So far so good.


But, just to be thorough, I figured I’d plot the time responses as well. These are shown below in Figures 4 and 5.


Figure 4: Time responses of the delayed signal with a delay time of x.5 samples.
Figure 4: Time responses of the delayed signal with a delay time of 20.5 samples. Note again that the linear and cosine time responses are identical for a delay time of 20.5 samples.



Figure 5: Time responses of the delayed signal with a delay time of x.25 samples.
Figure 5: Time responses of the delayed signal with a delay time of 20.25 samples.


Interesting! It appears that we have a small bug. It looks like, in both cases, the linear and the cosine interpolations are 1 sample late… Time to send an email to Cycling74 and ask them to look into this.


In case you’re a geek, and you need the details:

  • I’m running Max/MSP Version 7.1.0 on a late 2011 17″ MacBook Pro running OS 10.11.2.
  • Max was using the internal I/O and had I/O Vector and Signal Vector sizes of 1024 samples.



2016/04/14 – Max 7.2.1 Update

As you can see in the “Replies” to this posting, a quick message came in from Andrew Pask (at Cycling74) on April 12 asking me to try this again in Max 7.2.1.

So, I made the patcher again, saved the .wav’s again, put them in Matlab again, and the results are plotted below.

Figure 6
Figure 6: Time responses of the delayed signal with a delay time of 20.5 samples.


Figure 7
Figure 7: Time responses of the delayed signal with a delay time of 20.25 samples.


So, it looks to me like things are fixed. Thanks Andrew!


Now, can you do something about the fact that the levelmeter~ object forgets/ignores its saved ballistics settings (attack and release time values) when you load a patcher? :-)