#56 in a series of articles about the technology behind Bang & Olufsen loudspeakers
This book was released some months ago as part of the 100 year anniversary of loudspeaker development in Denmark. There are a number of good articles in there, including a historical article on the importance of loudspeaker directivity at Bang & Olufsen.
Note that, unfortunately, the website that was associated with this book no longer exists… :-(
#55 in a series of articles about the technology behind Bang & Olufsen loudspeakers
In a previous posting, I talked about the relationship between its “Bl” or “force factor” curve and the stiffness characteristics of its suspension and the fact that this relationship has an effect on the distortion characteristics of the driver. What was missing in that article was the details in the punchline – the “so what?” That’s what this posting is about – the effect of a particular kind of distortion in a system, and its resulting output.
WARNING: There is an intentional, fundamental error in many of the plots in this article. If you want to know about this, please jump to the “appendix” at the end. If you aren’t interested in the pedantic details, but are only curious about an intuitive understanding of the topic, then don’t worry about this, and read on. As an exciting third option, you could just read the article, and then read the appendix to find out how I’ve been protecting you from the truth…
Let’s start by looking at something called a “transfer function” – this is a plot of the difference between what you want and what you get.
For example, if we look at the excursion of a loudspeaker driver: we have some intended excursion (for example, we want to push the woofer out by 5 mm) and we have some actual excursion (hopefully, it’s also 5 mm…)
If we have a system that behaves exactly as we want it to within some limit, and then at that limit it can’t move farther, we have a system that clips the signal. For example, let’s say that we have a loudspeaker driver that can move perfectly (in other words, it goes exactly where we want it to) until it hits 5 mm from the rest position (either inwards or outwards). In this case, its transfer function would look like Figure 1.
This means that if we try to move the driver with a sinusoidal wave that should peak at 10 mm and -10 mm, the tops and bottoms of the wave will be “chopped off” at ±5 mm. This is shown in Figure 2, below.
Let’s think carefully about the bottom plot in Figure 2. This is the difference between the actual excursion of the driver and the desired excursion (I calculated it by actually subtracting the top plot from the middle plot) – in other words, it’s the error in the signal. Another way to think of this is that the signal produced by the driver is what you want (the top plot) PLUS the error (the bottom plot). (Looking at the plots, if middle-top = bottom, then top+bottom = middle)
These plots show a rather simple case where the clipping of the signal is symmetrical. That is to say that the error on the positive part of the waveform is identical to that on the negative part of the waveform. As we saw in this posting, however, perfectly symmetrical distortion is not guaranteed… So, what happens if you have asymmetrical distortion? Let’s say, for example, that you have a system that behaves perfectly, except that it cannot move more than 5 mm outwards (moving inwards is not limited). The transfer function for this driver would look like Figure 3.
How would a sinusoidal waveform look if it were passed through that driver? This is shown in Figure 4, below.
As we also saw before, it is unlikely that the abrupt clipping of a signal is how a real driver will behave. This is because, usually, a driver has an increasing stiffness and a decreasing force to push against it, as the excursion increases. So, instead of the driver behaving perfectly to some limit, and then clipping, it is more likely that the error is gradually increasing with excursion. An example of this is shown below in Figure 5. Note that this plot is just a tanh (a hyperbolic tangent) function for illustrative purposes – it is not a measurement of a real loudspeaker driver’s behaviour.
If we were to pass a sinusoidal waveform through this system, the result would be as is shown in Figure 6.
The reason engineers love sinusoidal waveforms is that they only contain one frequency each. A 1000 Hz sine tone only has energy at 1000 Hz and no where else. This means that if you have a box that does something to audio, and you put a 1000 Hz sine tone into it, and a signal with frequencies other than 1000 Hz comes out, then the box is distorting your sine wave in some way.
This was a very general statement and should be taken with a grain of salt. A gain applied perfectly to a signal is also a distortion (since the output is different from the input), but will not necessarily add new frequency components (and therefore it is linear distortion, not non-linear distortion). A box that adds noise to the signal is, generally speaking, distorting the input – but the output’s extra components are unrelated to the input – which would classify the problem as noise instead of distortion.) To be more accurate, I would have said that “if you have a box that does something to audio, and you put a 1000 Hz sine tone into it, and a signal with frequencies other than 1000 Hz comes out, then the box is applying a non-linear distortion to your sine wave in some way.”
Back to the engineers… If you take a sinusoidal waveform and plot its frequency content, you’ll see something like Figure 7. This shows the frequency content of a signal consisting of a 1024 Hz sine wave.
If we clip this signal symmetrically, using the transfer function shown in Figure 1, resulting in the signal shown in the middle plot in Figure 2, and them measure the frequency content of the result, it will look like Figure 8.
There are at least two interesting things to note about the frequency content shown in Figure 8.
The first is that the level of the signal at the fundamental frequency “f” (1024 Hz, in this case) is lower than the input. This might be obvious, since the output cannot “go as loud” as the input of the system – so some level is lost. (Since we’re clipping at -6 dB, the fundamental has dropped by 6 dB.)
The second thing to notice is that the new frequencies that have appeared are at odd multiples of the frequency of the original signal. So, we have content at 3072 Hz (3*1024), 5120 Hz (5*1024), 7168 Hz (7*1024) and so on. This is a characteristic of a symmetrically distorted signal (meaning not only that we have distorted the top and the bottom of the signal in the same way, but also that the signal itself was symmetrical to begin with). In other words, whenever you see a distortion product that only produces odd-order harmonics of the fundamental, you have a system that is distorting a symmetrical signal symmetrically.
If we were to look at the frequency content of the asymmetrically-distorted signal (shown in Figures 3 and 4), the result would be as is shown in Figure 9.
In Figure 9, you can see at least two interesting things:
The first is that the level of the fundamental frequency of “f” (1024 Hz) is higher than it was in Figure 8. This is because we’re letting more of the energy of the original waveform through the distortion (because the negative portion is untouched).
The second thing that you can see in Figure 9 is that both the odd-order and the even-order harmonics are showing up. So, we get energy at 2048 Hz (2*1024), 3072 Hz (3*1024), 4096 Hz (4*1024), 5120 Hz (5*1024), and so on. The presence of the even-order harmonics tells us that either the input signal was asymmetrical (which it wasn’t) or that the distortion applied to it was asymmetrical (which is was) or both.
If the distortion we apply to the signal was less abrupt – using the “soft-clipping” function shown in Figure 5 and 6, the result would be different, as is shown in Figure 10.
Again, in Figure 10, you can see that only the odd-order harmonics appear as the distortion products, since the distortion we’re applying to the symmetrical signal is symmetrical.
So far, we’ve only been looking at the simple case of an input signal with a single frequency. Typically, however, research has shown that most persons listen to more than one frequency simultaneously (acoustical engineers and Stockhausen enthusiasts excepted…). So, let’s look at what happens when we have more than one frequency – say, two frequencies – in our input signal.
For example, let’s say that we have an input signal, the frequency content of which is shown in Figure 11, consisting of sinusoidal tones at 64 Hz and 1024 Hz. Both sine tones, individually, have a peak level of one-half of the maximum peak of the system. Therefore, they are shown in Figure 11 as having a level of approximately -6 dB each.
The sum of these two sinusoids will look like the top plot in Figure 12. As you can see there, the signal with the higher frequency is “riding on top of” the signal with the lower frequency. Each frequency, on its own, is pushing and pulling the excursion by ±5 mm. The total result therefore can move from -10 mm to +10 mm, but its instantaneous value is dependent on the overlap of the two signals at any one moment.
If we apply the symmetrical clipping shown in Figure 1 to this signal, the result is as is shown in the middle plot of Figure 12 (with the error shown in the bottom plot). This results in an interesting effect since, although the distortion we’re applying should be symmetrical, the result at any given moment is asymmetrical. This is because the signal itself is asymmetrical with respect to the clipping – the high frequency component alternates between getting clipped on the top and the bottom, depending on where the low frequency component has put it…
We can look at the frequency content of the resulting clipped signal. This is shown in Figure 13.
It’s obvious from the plot in Figure 13 that we have a mess. However, although the mess is rather systematic, it’s difficult to see in that plot. If we plot the same information on a different scale, things get easier to understand. Take a look at Figure 14.
Figure 14 and Figure 13 show exactly the same information with only two differences. The first is that Figure 14 only shows frequencies up to 5 kHz instead of 20 kHz. The second is that the scale of the x-axis of Figure 13 is logarithmic whereas the scale of Figure 14 is linear. This is only a chance in spacing, but it makes things easier to understand.
As you can see in Figure 14, the extra frequencies added to the original signal by the clipping are regularly spaced. This is because the distortion that we have generated (called an intermodulation distortion, since it results from two two signals modulating each other), in the frequency domain, follows a pretty simple mathematical pattern.
Our original two frequencies of 64 Hz (called “f1” on the plot) and 1024 Hz (“f2”) are still present.
In addition, the sum and difference of these two frequencies are also present (f2+f1 = 1088 Hz and f2-f1 = 1018 Hz).
The sum and difference of the harmonic distortion products of the frequencies are also present. For example, 2*f2+f1 = 2*1024+64=2112 Hz, 3*fs-2*f1 = 3*1024-2*64 = 2944 Hz… There are many, many more of these. Take one frequency, multiply it by an integer and then add (or subtract) that from the other frequency multiplied by an integer – whatever the result, that frequency will be there. Don’t worry if your result is negative – that’s also in there (although we’re not going to talk about negative frequencies today – but trust me, they exist…)
If we apply the asymmetrical clipping to the same signal, we (of course) get a different result, but it exhibits the same characteristics, just with different values, as can be seen in Figures 15 and 16.
It’s important to state once more that none of the plots I’ve shown here are based on any real loudspeaker driver. I’m using simple examples of non-linear distortion just to illustrate the effects on an audio signal. The actual behaviour of an actual loudspeaker driver will be much more complicated than this, but also much more subtle (hopefully – if not, something it probably broken…).
As I mentioned at the very beginning of this posting, many of the plots in this article have an intentional error. The reason I wrote this article is to try to give you an intuitive understanding of the results of a problem with the stiffness and Bl curves of a loudspeaker driver with respect to its excursion. This means that my plots of the time domain (such as those in Figure 2) show the excursion of the driver in millimetres with respect to time. I then skip over to a magnitude response plot, pretending that the signal that comes from a driver (a measurement of the air pressure) is identical to the pattern of the driver’s excursion. This is not true. The modulation in air pressure caused by a moving loudspeaker driver are actually in phase with the acceleration of the loudspeaker driver – not its excursion. So, I skipped a step or two. However, since I wasn’t actually showing real responses from real drivers, I didn’t feel too guilty about this. Just be warned that, if you’re really digging into this, you should not directly jump from loudspeaker driver excursion to a plot of the sound pressure.
I’m on my way home from the Munich High End audio show where we were running continuous demos of the Beolab 90’s (an 8’45” mix of tracks on repeat from 10:00 a.m. to 6:00 p.m. for 4 days… It will be a while before I get the Chris Jones, Lyle Lovett and the Foo Fighters out of my head…)
We used an intentionally bare room – one Oppo Blu-ray player playing the .wav file off a USB stick, connected via S/P-DIF to the Beolab 90’s. Nothing else was in the room except three chairs, a lamp, and the people. The floor was carpeted, the ceiling was absorptive, and the walls were EXTREMELY reflective. (This helped people to hear the difference between Narrow and Wide mode – an intentional decision on my part… The room looks like a cell for someone in a straight jacket, but the listeners didn’t mind… In fact, many came back for a second listening session after hearing some of the other loudspeakers at the show…)
We spent a while the day before the show doing the Active Room Compensation measurements, and that was it – we were good to go!
The outside of the booth was simple – but the tree of Scan Speak drivers certainly attracted attention – audiophiles like drivers, apparently. :-)
Although it was nice to get out of the listening room in Struer for a while and meet some normal people – after four days on a 8’45” loop, it’s time to head home and listen to nothing for a day or two. :-)
#52 in a series of articles about the technology behind Bang & Olufsen loudspeakers
I often have to do demos of loudspeakers for people. Also, I frequently have to make recommendations on how to do (either for Bang & Olufsen dealers, or for things like press events). One of the problems that I face every time I have to do this is how to arrange the chairs so that everyone gets a reasonable impression of how a loudspeaker sounds. The problem is that this is basically impossible, due to the significant influence things like the loudspeakers’ locations, the listener location, and the room, have on the overall sound.
One aspect of how-a-loudspeaker-sounds is its magnitude response (often called a “frequency response”). A (perhaps too-simple) definition of a magnitude response is “a measure of how loud the output signal is at different frequencies if you put in a signal that is the same level at all frequencies”.
If we wanted to make a measurement of a loudspeaker’s magnitude response in a room at a particular position, we just have to put in a signal that contains all frequencies at the same magnitude (or level), capture that output with a microphone somewhere in the room, and compare how loud the signal is at different frequencies. Of course, in order to do this, we have to take care of some details. We have to make sure that the microphone (and everything else in the measurement part of the signal path) has a flat magnitude response. If it doesn’t, then at least we should know what its response is, so we can subtract it from the measurement to remove its influence on the result.
However, for the purposes of this posting, I’m not really interested in the absolute response of a loudspeaker. I’m more interested in how that response changes as you move in a room. Specifically, I want to show how much the magnitude response can change with very small changes in listening position.
Let’s start by measuring the magnitude response of a loudspeaker in a room at a location. For the purposes of this example, I’ve used a full-range, multi-way loudspeaker without a port. It’s placed roughly 1 m from the side wall and 1 m from the front wall, aimed at a listening position. The listening position is in the centre of the room’s width, and closer to the rear wall than the front wall by about a metre. The details of the location for the microphone (a 1/4″ omnidirectional measurement mic) for this measurement are shown in Figure 1, below.
I did an impulse response measurement (using an MLS signal with 4 averages (to improve SNR) and 4 sequences (to reduce the effect of distortion)) of the loudspeaker, the result of which is shown below in Figure 2. As you can see there, there are many obvious reflections after the initial impulse, and there is some kind of ringing in the room’s response.
The extremely long time before the onset of the impulse is arbitrary. The microphone was not actually 40 m away from the loudspeaker…
As I said above, I’m not interested in the resulting magnitude response of this measurement. I can tell you that it’s messy. There are bumps and dips in the low end caused (primarily) by room modes. The top end is messy due to the reflections. The overall curve is not flat due to the loudspeaker’s response, the microphone’s orientation, and various components in the signal path. However, I don’t care, since I’m not here to measure how the speaker behaves at one location in the room. I’m here to find out how its behaviour changes when you change location. So, let’s move the microphone.
As you can see in Figure 3, below, I started by moving the microphone only 100 mm, directly forwards in the room.
Again, I measured the impulse response, converted that to a magnitude response (reflections and all!), smoothed it with a running 1/3 octave smoothing and subtracted the magnitude response measured at the Reference position (also smoothed to 1/3 octave). The resulting difference is shown in Figure 4, below.
As you can see in Figure 3, moving the listening position only 100 mm results in a magnitude response deviation of about -2 to +4 dB. This is easily within the threshold of audibility for most people…
Now, let’s move the microphone sideways instead, as shown in Figure 5.
Again, a roughly 100 mm movement results in a large change in the magnitude response – although now the most significant changes have happened in the low end, as can be seen in Figure 6.
If we have more than one listener attending the demo, then I prefer to seat them “bus” style – one directly in front of the other – to ensure that everyone is getting a reasonably good phantom centre image. Sitting off-centre results in the time of arrival of signals from the two loudspeakers being mis-matched which will result in phantom images pulling towards the closer (and therefore earlier) loudspeaker.
Let’s say the we have a person roughly a half-metre behind the “good” chair, as shown in Figure 7. How different is the sound in that location?
Now we can see in Figure 8 that, by moving backwards in the room, we get more than ± 10 dB of variation in the magnitude response, with significant deviations happening as high as 1 kHz (depending on how you define “significant”).
Similarly, moving forwards by a half metre from the Reference position (shown in Figure 9) results in a similar amount of change in the magnitude response, shown in Figure 10.
Just for comparison, I’ve re-plotted the 4 magnitude response differences shown above in one plot. This is to show that the changes are not necessarily easily predicable with a simple knowledge of room layout. In other words, it would be almost impossible, without some serious simulation software, to predict these changes just by looking at a floorplan of the room and the chairs.
What’s the moral of the story here? There are many – but I’ll just mention three.
The first is the message that, even a very small change in location (like leaning to one side in your chair – or leaning forwards to rest your elbows on your knees and your chin on your hands) can dramatically change the simple magnitude response of a loudspeaker (we won’t get into the effects on the spatial behaviour of the system).
The second is that, when you’re sitting with a friend, auditioning a pair of loudspeakers, switch chairs now and again. It is extremely unlikely that you’re both hearing the same thing at the same time.
Thirdly, the fact that there are significant differences between magnitude responses at different listening positions (even within a half-metre radius) means that, if you’re doing measurements for a room compensation system using a microphone around the listening position, it’s always smarter to make more than one measurement. In fact, there are some people who argue that, in this case, having only one measurement is worse than having no measurements, since you can easily get distracted by something in the magnitude or the time response that is a problem at only that location and nowhere else.
Finally, it’s worth considering that first point a different way. Let’s say you’re the type of person who likes to tweak a stereo system by upgrading components like wires. And, let’s say that you have incredible powers of “sonic memory” – in other words, you can listen to a system, take a break, listen to it again, and you are able to detect extremely small changes in system performance (like the magnitude response). So, you listen to your system – then you get out of your chair, change the component, sit down again, and start listening to the same tune at the same level. Remember that, unless you are in exactly the same location that you were before (not just “in the same chair”…), it could be that there is a larger difference in the magnitude response of the loudspeaker due your change in position than there is due to the component you just changed… So if you are a tweaker – get someone else to do the dirty work for you so you can sit there, in your chair, with your head in a clamp, waiting to evaluate the “upgrade”…
#51 in a series of articles about the technology behind Bang & Olufsen loudspeakers
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:
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. :-)
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.
Basically, the measurements that we perform on a loudspeaker can be boiled down into four types:
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).
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.
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”.
There are three things to initially notice in this figure.
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.
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.
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.
If we were to do an impulse response measurement of that system, it would look like the plot in Figure 8, below.
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.
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 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.
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…)
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.
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.
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.
A video of the robot that polishes the “crowns” – the aluminium frame around the fabric grilles.
A video from the assembly
Screwing in the loudspeaker drivers
#50 in a series of articles about the technology behind Bang & Olufsen loudspeakers
Before we begin, if you’re unfamiliar with the concept of a “room mode”, it might be useful to review three other postings:
But what if my room is Scandinavian?
and
Active Room Compensation – Some Details, Part 1
At the end of that last posting, I said:
“P.S. As I mentioned briefly in this posting, Active Room Compensation has one additional feature – multichannel processing. That will be explained later in Part 2.”
So, that’s the theme for this article – the multichannel aspect of Active Room Compensation.
Let’s start by looking at Figure 1, below.
This is a basic representation of the fundamental room mode in one dimension of a room. If a loudspeaker is placed at the location of the red circle and it produces energy at the same frequency of the room mode, then the room will resonate, just like a closed pipe, as can be seen in the animation.
One important thing to notice in the figure above is that when the pressure on one side of the room goes positive, the opposite side goes negative. In other words, the two sides of the room are in opposite polarity. This information will come in handy later.
Now let’s look at the second harmonic – this is a resonance that has a frequency that is two times that of the fundamental mode. Its behaviour in one dimension of the room is shown below. Again, the loudspeaker is in the position of the red circle.
Now, you’ll notice, the two sides of the room have the same polarity – when one goes positive, so does the other. It’s the centre of the room that is in opposite polarity to the sides.
If you measure the natural response of a loudspeaker that is otherwise flat (let’s not split hairs over whether we’re talking about on-axis magnitude response or the power response – for the purposes of this discussion, it’s irrelevant) in a one-dimensional room like the one shown above, you’ll see that there is a natural peak in the response at each frequency where you have a room mode. The result will look something like Figure 3, below
As you can see there, every mode is excited by the loudspeaker (we’re assuming that the loudspeaker is not sitting on a “node” and therefore not coupling to the room mode at all).
So, if you build a room compensation system that only takes one loudspeaker into account, then it will measure a response similar to the one in Figure 3, and it will create a compensation filter that looks something like the one shown in Figure 4.
Assuming that you’re careful about your measurements, and you consider things like phase response in your creation of the filter, this system will work very well with just one small problem: most people don’t use only one loudspeaker – they use at least two.
So, how does this change things?
Let’s go back and consider our room modes again, this time with two loudspeakers.
Figure 5, above, shows the same room as in Figure 1, but now I’ve plotted the locations of two loudspeakers, one on the left (atypically, in red) and one on the right (in black). Notice that these two points in the room, when the room mode is ringing, are opposite in polarity (or “out of phase” as many people say…). However, consider that, in most recordings, the bass (which is, in most cases, a good estimation of the frequency band of the fundamental room mode) is panned to the centre, and therefore is “in phase” in the two channels.
In other words, in almost all cases, the two loudspeakers are producing the same signal at the same level, in phase (and therefore with the same polarity). However, the room is ringing in opposite polarity at the two loudspeakers.
What’s the result of this conflict? It’s simple – the room mode is naturally cancelled by the signals in the loudspeakers. In other words, there is no need to apply room correction for a recording like this, with the loudspeakers in the locations that they’re shown in, for this room mode.
So, if you measure each loudspeaker individually, you’ll put a dip in their responses that should not be there to compensate for a room mode that is not ringing. You must consider both loudspeakers playing a correlated signal, and how that will interact with the room mode.
Now let’s look at the next harmonic, shown below in Figure 6.
Now you can see that the mode is ringing in the same phase at the two loudspeaker positions. So, if the bass (still a good guess…) is in phase in the two channels (also a good guess…) then this resonance will be twice as bad as it would be with only one loudspeaker. Again, we need to consider the behaviour of the room mode with a correlated signal in the two loudspeakers – but this time things are worse instead of non-existent.
So, this means that we have to re-consider our room compensation filter. Instead of measuring each loudspeaker independently and building a filter for each one and ignoring that people rarely listen in mono, we have to measure the two (or more) loudspeakers and analyse the way that different signals will interact with the room modes.
For example, in the simple case shown above, we might wind up with the two filters shown in Figure 7 and 8.
Now, you might be saying “I understand Figure 7 – lots of signals have the same polarity in the two loudspeakers (like the vocals, the bass, the kick drum – anything panned to the centre). But what signals are out-of-phase if I’ve connected by loudspeakers correctly?”
The answer to this comes mainly from classical recordings where it is normal to use microphones (usually omnidirectional) that are spaced apart. In this case, signals enter the two microphones are different times (depending on the angle to the sound source) – and a time difference results in a phase difference.
This processing is done in Beolab 90‘s Active Room Compensation to ensure that the loudspeakers are best optimised, not only to the room they’re in, but their locations within it, and its interaction with the recordings you’re playing. The end result is that each loudspeaker “knows” that the other one is in the room – each not only considers the other’s effect on the room’s response, but they “help each other” to control the room modes.
Of course, I’ve left out a lot of details in this description – for example, the actual responses of the correlated and negatively correlated signals will not really look like the ones I’ve shown here; most rooms contain more than one dimension; and I haven’t talked about boundary effects. In addition, everything I’ve said here is just an example using a very simplified view of the universe. The measurements of the loudspeakers at the microphone positions will result in very different responses than the ones shown here, which will, in turn, result in very different compensation filters.
*Most people don’t seem to know it, but “stereophonic sound” (or “stereo” if you’re into the whole brevity thing) means that you have two or more audio channels. Just thought I’d be explicit here – in case anyone was wondering.