Typical Errors in Digital Audio: Wrapping up

This “series” of postings was intended to describe some of the errors that I commonly see when I measure and evaluate digital audio systems. All of the examples I’ve shown are taken from measurements of commercially-available hardware and software – they’re not “beta” versions that are in development.

There are some reasons why I wrote this series that I’d like to make reasonably explicit.

  1. Many of the errors that I’ve described here are significant – but will, in some cases, not be detected by “typical” audio measurements such as frequency response or SNR measurements.
    1. For example, the small clicks caused by skip/insert artefacts will not show up in a SNR or a THD+N measurement due to the fact that the artefacts are so small with respect to the signal. This does not mean that they are not audible. Play a midrange sine tone (say, in the 2 -3 kHz region… nothing too annoying) and listen for clicks.
    2. As another example, the drifting time clock problems described here are not evident as jitter or sampling rate errors at the digital output of the device. These are caused by a clocking problems inside the signal path. So, a simple measurement of the digital output carrier will not, in any way, reveal the significance of the problem inside the system.
    3. Aliasing artefacts (described here) may not show up in a THD measurement (since aliasing artefacts are not Harmonic). They will show up as part of the Noise in a THD+N measurement, but they certainly do not sound like noise, since they are weirdly correlated with the signal. Therefore you cannot sweep them under the rug as “noise”…
  2. Some of the problems with some systems only exist with some combinations of file format / sampling rate / bit depth, as I showed here. So, for example, if you read a test of a streaming system that says “I checked the device/system using a 44.1 kHz, 16-bit WAV file, and found that its output is bit-perfect” Then this is probably true. However, there is no guarantee whatsoever that this “bit-perfect-ness” will hold for all other sampling rates, bit depths, and file formats.
  3. Sometimes, if you test a system, it will behave for a while, and then not behave. As we saw in Figure 10 of this posting, the first skip-insert error happened exactly 10 seconds after the file started playing. So, if you do a quick sweep that only lasts for 9.5 seconds you’ll think that this system is “bit-perfect” – which is true most of the time – but not all of the time…
  4. Sometimes, you just don’t get what you’ve paid for – although that’s not necessarily the fault of the company you’re paying…

Unfortunately, the only thing that I have concluded after having done lots of measurements of lots of systems is that, unless you do a full set of measurements on a given system, you don’t really know how it behaves. And, it might not behave the same tomorrow because something in the chain might have had a software update overnight.

However, there are two more thing that I’d like to point out (which I’ve already mentioned in one of the postings).

Firstly, just because a system has a digital input (or source, say, a file) and a digital output does not guarantee that it’s perfect. These days the weakest links in a digital audio signal path are typically in the signal processing software or the clocking of the devices in the audio chain.

Secondly, if you do have a digital audio system or device, and something sounds weird, there’s probably no need to look for the most complicated solution to the problem. Typically, the problem is in a poor implementation of an algorithm somewhere in the system. In other words, there’s no point in arguing over whether your DAC has a 120 dB or a 123 dB SNR if you have a sampling rate converter upstream that is generating aliasing at -60 dB… Don’t spend money “upgrading” your mains cables if your real problem is that audio samples are being left out every half second because your source and your receiver can’t agree on how fast their clocks should run.

 

So, the bad news is that trying to keep track of all of this is complicated at best. More likely impossible.

 

On the other hand, if you do have a system that you’re happy with, it’s best to not read anything I wrote and just keep listening to your music…

Typical Errors in Digital Audio: Part 8 – The Weakest Link

As a setup for this posting, I have to start with some background information…

Back when I was doing my bachelor’s of music degree, I used to make some pocket money playing background music for things like wedding receptions. One of the good things about playing such a gig was that, for the most part, no one is listening to you… You’re just filling in as part of the background noise. So, as the evening went on, and I grew more and more tired, I would change to simpler and simpler arrangements of the tunes. Leaving some notes out meant I didn’t have to think as quickly, and, since no one was really listening, I could get away with it.

If you watch the short video above, you’ll hear the same composition played 3 times (the 4th is just a copy of the first, for comparison). The first arrangement contains a total of 71 notes, as shown below.

Fig 1. Arrangement #1 – a total of 71 notes.

The second arrangement uses only 38 notes, as you can see in Figure 2, below.

Fig 2. Arrangement #2 – a total of 38 notes. A reduction in “data” of 46%.

The third arrangement uses even fewer notes – a total of only 27 notes, shown in Figure 3, below.

Fig 3. Arrangement #3 – a total of 27 notes. A reduction in “data” of 62% compared to the original.

 

The point of this story is that, in all three arrangements, the piece of music is easily recognisable. And, if it’s late in the night and you’ve had too much to drink at the wedding reception, I’d probably get away with not playing the full arrangement without you even noticing the difference…

A psychoacoustic CODEC (Compression DECompression) algorithm works in a very similar way. I’ll explain…

If you do an “audiometry test”, you’ll be put in a very, very quiet room and given a pair of headphones and a button. in an adjacent room is a person who sees a light when you press the button and controls a tone generator. You’ll be told that you’ll hear a tone in one ear from the headphones, and when you do, you should push the button. When you do this, the tone will get quieter, and you’ll push the button again. This will happen over and over until you can’t hear the tone. This is repeated in your two ears at different frequencies (and, of course, the whole thing is randomised so that you can’t predict a response…)

If you do this test, and if you have textbook-quality hearing, then you’ll find out that your threshold of hearing is different at different frequencies. In fact, a plot of the quietest tones you can hear at different frequencies it will look something like that shown in Figure 4.

 

Fig 4. A hand-drawn representation of a typical threshold of hearing curve.

 

This red curve shows a typical curve for a threshold of hearing. Any frequency that was played at a level that would be below this red curve would not be audible. Note that the threshold is very different at different frequencies.

Fig 5. A 1 kHz tone played at 70 dB SPL will obviously be audible, since it’s above the red line.

Interestingly, if you do play this tone shown in Figure 5, then your threshold of hearing will change, as is shown in Figure 6.

Fig 6. The threshold of hearing changes when an audible tone is played.

IF you were not playing that loud 1 kHz tone, and, instead, you played a quieter tone just below 2 kHz, it would also be audible, since it’s also above the threshold of hearing (shown in Figure 7.

Fig 7. A quieter tone at a higher frequency is also audible.

However, if you play those two tones simultaneously, what happens?

Fig 8. The higher frequency quieter tone is not audible in the presence of the louder, lower-frequency tone.

 

This effect is called “psychoacoustic masking” – the quieter tone is masked by the louder tone if the two area reasonably close together in frequency. This is essentially the same reason that you can’t hear someone whispering to you at an AC/DC concert… Normal people call it being “drowned out” by the guitar solo. Scientists will call it “psychoacoustic masking”.

 

Let’s pull these two stories together… The reason I started leaving notes out when I was playing background music was that my processing power was getting limited (because I was getting tired) and the people listening weren’t able to tell the difference. This is how I got away with it. Of course, if you were listening, you would have noticed – but that’s just a chance I had to take.

If you want to record, store, or transmit an audio signal and you don’t have enough processing power, storage area, or bandwidth, you need to leave stuff out. There are lots of strategies for doing this – but one of them is to get a computer to analyse the frequency content of the signal and try to predict what components of the signal will be psychoacoustically masked and leave those components out. So, essentially, just like I was trying to predict which notes you wouldn’t miss, a computer is trying to predict what you won’t be able to hear…

This process is a general description of what is done in all the psychoacoustic CODECs like MP3, Ogg Vorbis, AC-3, AAC, SBC, and so on and so on. These are all called “lossy” CODECs because some components of the audio signal are lost in the encoding process. Of course, these CODECs have different perceived qualities because they all have different prediction algorithms, and some are better at predicting what you can’t hear than others. Also, depending on what bitrate is available, the algorithms may be more or less aggressive in making their decisions about your abilities.

 

There’s just one small problem… If you remove some components of the audio signal, then you create an error, and the creation of that error generates noise. However, the algorithm has an trick up its sleeve. It knows the error it has created, it knows the frequency content of the signal that it’s keeping (and therefore it knows the resulting elevated masking threshold). So it uses that “knowledge” to  shape the frequency spectrum of the error to sit under the resulting threshold of hearing, as shown by the gray area in Figure 9.

Fig 9. The black vertical line is the content that is kept by the encoder. The red line is the resulting elevated threshold of hearing. The gray area is the noise-shaped error caused by the omission of some frequency components in the original signal.

 

Let’s assume that this system works. (In fact, some of the algorithms work very well, if you consider how much data is being eliminated… There’s no need to be snobbish…)

 

Now to the real part of the story…

Okay – everything above was just the “setup” for this posting.

For this test, I put two .wav files on a NAS drive. Both files had a sampling rate of 48 kHz, one file was a 16-bit file and the other was a 24-bit file.

On the NAS drive, I have two different applications that act as audio servers. These two applications come from two different companies, and each one has an associated “player” app that I’ve put on my phone. However, the app on the phone is really just acting as a remote control in this case.

The two audio server applications on the NAS drive are able to stream via my 2.4 GHz WiFi to an audio device acting as a receiver. I captured the output from that receiver playing the two files using the two server applications. (therefore there were 4 tests run)

Fig 10. A block diagram of the system under test.

The content of the signal in the two .wav files was a swept sine tone, going from 20 Hz to 90% of Nyquist, at 0 dB FS. I captured the output of the audio device in Figure 10 and ran a spectrogram of the result, analysing the signal down to 100 dB below the signal’s level. The results are shown below.

Fig 11. A spectrogram of the output signal from the audio device using “Audio Server SW 1” playing the 48 kHz, 16-bit WAV file. This is good, since it shows only the signal, and no extraneous artefacts within 100 dB.

 

Fig 12. A spectrogram of the output signal from the audio device using “Audio Server SW 1” playing the 48 kHz, 24-bit WAV file. This is also good, since it shows only the signal, and no extraneous artefacts within 100 dB.

 

Fig 13. A spectrogram of the output signal from the audio device using “Audio Server SW 2” playing the 48 kHz, 16-bit WAV file. This is also good, since it shows only the signal, and no extraneous artefacts within 100 dB.
Fig 14. A spectrogram of the output signal from the audio device using “Audio Server SW 2” playing the 48 kHz, 24-bit WAV file. This is obviously not good…

So, Figures 11 and 13 show the same file (the 16-bit version) played to the same output device over the same network, using two different audio server applications on my NAS drive.

Figures 12 and 14 also show the same file (the 24-bit version). As is immediately obvious, the “Audio Server SW 2” is not nearly as happy about playing the 24-bit file. There is harmonic distortion (the diagonal lines parallel with the signal), probably caused by clipping. This also generates aliasing, as we saw in a previous posting.

However, there is also a lot of visible noise around the signal – the “fuzzy blobs” that surround the signal. This has the same appearance as what you would see from the output of a psychoacoustic CODEC – it’s the noise that the encoder tries to “fit under” the signal, as shown in Figure 9… One give-away that this is probably the case is that the vertical width (the frequency spread) of that noise appears to be much wider when the signal is a low-frequency. This is because this plot has a logarithmic frequency scale, but a CODEC encoder “thinks” on a linear frequency scale. So, frequency bands of equal widths on a linear scale will appear to be wider in the low end on a log scale. (Another way to think of this is that there are as many “Hertz’s” from 0 Hz to 10 kHz as there are from 10 kHz to 20 kHz. The width of both of these bands is 10000 Hz. However, those of us who are still young enough to hear up there will only hear the second of these as the top octave – and there are lots of octaves in the first one. (I know, if we go all the way to 0 Hz, then there are an infinite number of octaves, but I don’t want to discuss Zeno today…))

 

Conclusion

So, it appears that “Audio Server SW 2” on my NAS drive doesn’t like sending 24 bits directly to my audio device. Instead, it probably decodes the wav file, and transcodes the lossless LPCM format into a lossy CODEC (clipping the signal in the process) and sends that instead. So, by playing a “high resolution” audio file using that application, I get poorer quality at the output.

As always, I’m not going to discuss whether this effect is audible or not. That’s irrelevant, since it’s dependent on too many other factors.

And, as always, I’m not going to put brand or model names on any of the software or hardware tested here. If, for no other reason, this is because this problem may have already been corrected in a firmware update that has come out since I tested it.

The take-home messages here are:

  • an entire audio signal path can be brought down by one piece of software in the audio chain
  • you can’t test a system with one audio file and assume that it will work for all other sampling rates, bit depths and formats
    • Normally, when I run this test, I do it for all combinations of 6 sampling rates, 2 bit depths, and 2 formats (WAV and FLAC), at at least 2 different signal levels – meaning 48 tests per DUT
    • What I often see is that a system that is “bit perfect” in one format / sampling rate / bit depth is not necessarily behaving in another, as I showed above..

So, if you read a test involving a particular NAS drive, or a particular Audio Server application, or a particular audio device using a file format with a sampling rate and a bit depth and the reviewer says “This system worked perfectly.” You cannot assume that your system will also work perfectly unless all aspects of your system are identical to the tested system. Changing one link in the chain (even upgrading the software version) can wreck everything…

This makes life confusing, unfortunately. However, it does mean that, if someone sounds wrong to you with your own system, there’s no need to chase down excruciating minutiae like how many nanoseconds of jitter you have at your DAC’s input, or whether the cat sleeping on your amplifier is absorbing enough cosmic rays. It could be because your high-res file is getting clipped, aliased, and converted to MP3 before sending to your speakers…

Addendum

Just in case you’re wondering, I tested these two systems above with all 6 standard sampling rates (44.1, 48, 88.2, 96, 176.4, and 192 kHz), 2 bit depths (16 & 24). I also did two formats (WAV and FLAC) and three signal levels (0, -1, and -60 dB FS) – although that doesn’t matter for this last comment.

“Audio Server SW 2” had the same behaviour in the case of all sampling rates – 16 bit files played without artefacts within 100 dB of the 0 dB FS signal, whereas 24-bit files in all sampling rates exhibited the same errors as are shown in Figure 14.

 

Typical Errors in Digital Audio: Part 7 – Just a sec…

We’ve seen in a previous posting that timing errors can occur in wireless audio systems. As we saw there, the wrong way to deal with this is to simply drop or repeat samples when the receiver realises it’s out of synchronisation with the transmitter. A better way to do it is to smoothly drift the sampling rate to either catch up or slow down – although this causes the modern-day equivalent of “wow and flutter”, since variations in the sampling rate will cause pitch shifts at the output. The trick here is to make changes slowly so as to get away with it…

However, what I didn’t address in that posting was how bad the problem can be – I only talked about how not to correct the problem when you know you have one.

So, let’s do a different (but related) test. I made a signal that consists of “digital black” – a long string of zeros – and therefore silence. Then, I made a single-sample spike every second (for example, every 44100 samples in a 44.1 kHz sampling rate system). In order to not make anything unhappy, I gave the clicks a value of 0.5 – so nothing is close to overloading…

Then, I transmitted that signal to an audio device wirelessly and recorded its output.

Figure 1, below, shows the original signal on top, and the recorded output of the device under test (the “DUT”) on the bottom.

 

Fig 1. The top plot shows the original signal set to the DUT using a wireless audio connection. The bottom plot shows the output of the DUT.

 

You may notice that there is a little noise in the bottom plot. This is because this particular DUT has an acoustical output, and the noise you see there (partly) is acoustical noise in the room and measurement system.

Note that this plot shows only the first 5 seconds of a test that actually ran for 10 minutes.

Then, I wrote a little Matlab script that finds the spikes in each signal, and counts the number of samples between spikes. So, in a system running at 44.1 kHz I would expect that there is 1 spike every 44100 samples – both at the input to the system (the original signal) and its output. In other words, I’m finding out how far apart those spikes are with a resolution of 1 sample.

So, I find the duration between clicks at the output of the DUT, convert from samples to milliseconds, and plot the error over the full 600 seconds (10 minutes) of the test. In theory, there is no error – and each duration is exactly 1 second ±0 ms. In practice, however, this is not true.

For this posting, I tested two commercially-available devices, transmitting from the same device.

Figure 2 shows the results for that first device. As you can see there, one second at the device’s input does not correspond to 1 second at its output. It drifts from a little under 999.7 ms to a little over 1000.2 ms. Note that, for this test, I don’t know from the measurement how that change takes place – whether it’s shifting slowly or using a skip/insert strategy. I just know one version of how bad the problems is over time on a second-by-second basis.

Fig 2. The deviation (in milliseconds) from the expected 1-second interval between spikes in the audio signal at the output of the DUT.

 

Figure 3, below, shows the same analysis for another device. Notice that there are three colours in this plot, corresponding to three separate tests of the same device…

Fig 3. Three tests of a second device, showing the deviation from a 1-second interval between clicks at the output.

As you can see there, this device seems to be behaving most of the time, but occasionally gets a little lost and jumps by to about ±70 ms in a worst case. This means that, for this test, we can see that “1 second” can last anything between about 930 ms and 1070 ms. Note that this analysis doesn’t show what happens at the moment (or during the time) that jump occurs – we only know that it has happened sometime between clicks at the output.

You may be wondering why the plot in Figure 2 is more “jagged” than the one in Figure 3. This is mostly because the scale of the two plots is so different. If we were to zoom in to the plot in Figure 3, we would see that it is roughly as busy, as is shown below in Figure 4.

Fig 4. The same information shown in Figure 3, zoomed in on the vertical scale.

 

One significant difference between these two devices is that the first has an acoustical output and the second has an electrical output. This may cause you to wonder whether the acoustical noise in the first measurement contributes to the error. This may be possible. However, a 0.2 ms (or 200 µs) error is roughly equivalent to 9 samples at 44.1 kHz (or a 6.9 cm shift in distance between the DUT and the microphone). This is well outside the range of the error generated by acoustical noise – so that cannot be held responsible as being the only contributor to the error measurement.

I should say that the wireless audio protocol that was used for these two tests were the same… So, this is not a comparison of two different transmission systems. Also, as I mentioned above, the transmitter was the same for both DUT’s. So, the difference in results here are attributable to the skill and attention to the execution of the manufacturers of the two receiving devices.

As always, don’t bother asking which devices these DUT’s are. I’m not telling – primarily because it doesn’t matter. I’m just using these two devices as examples of errors I often see when I measure audio equipment…

 

One additional thing that might be of interest to geeks like me. That second DUT has a digital audio output, which is what I used to capture its signal. Interestingly, when I measure the sampling rate of that output with a digital audio signal analyser, the sampling rate is typically within 2 ppm of the correct frequency. So, ignoring the big spikes in Figure 3 (which are probably the result of buffer over- or under-runs) if the timing errors we see in Figure 4 were solely caused by a clock error that was visible on the digital audio output, then we should not see deviations of no more than approximately 2 microseconds per second. Instead, we see changes on the order of 1 to 2 milliseconds per second, which indicates a sample rate drift of 1000 to 2000 ppm… So, this means that, although the sampling rate of my transmitter and the output sampling rate of my receiver (the DUT) are nominally the same, AND there is very low jitter / error on the DUT’s output sampling rate, something else in the audio signal path is causing this error. In other words, a simple measurement of the digital output’s sampling rate is not adequate to verify that the DUT’s clock is behaving.

 

Typical Errors in Digital Audio: Part 6 – Aliasing

In a previous posting, I tried to explain the concept of aliasing. The easiest way to illustrate this is to try to sample an audio signal that has a frequency that is higher than the Nyquist frequency – one half of the sampling rate. If you do this, then the signal that will come out of your digital audio system will have a different frequency than the original signal. In fact, it will be the Nyquist frequency minus the difference between the original signal and the Nyquist frequency.

For example, if we have an LPCM audio system that has a sampling rate of 48 kHz, then its Nyquist frequency is 24 kHz. If you allow any audio signal to be sampled by that system, and you record a sine wave with a frequency of 30 kHz, then the signal that will be played back by the system will be

Nyquist – (signal freq – Nyquist)
24 kHz – (30 kHz – 24 kHz)
24 kHz – 6 kHz
18 kHz

Digging a little deeper

The example I gave above is only part of the story. It’s the part of the story that’s told because it’s easy to tell, and relatively easy to grasp. However, let’s look into this a little more…

If I ask you “what is the square root of 4?” you’ll probably say that the answer is “2”. However, this is also only part of the story. The square root of 4 is also -2, since -2 * -2 = 4. So, there are two correct answers to the question – in other words, both answers exist and are equally valid.

Aliasing is somewhat similar. If we manage to get a 30 kHz sine wave into an LPCM recording system with a sampling rate of 48 kHz, we will appear to have recorded an 18 kHz sine wave. However, the samples that we have captured are also equally valid for the original 30 kHz sine wave. In fact, both the 18 kHz and the 30 kHz tones can be thought of as being equally valid answers to the set of samples we recorded.

This means that, if I record an 18 kHz sine tone in the 48 kHz system, we can consider the 30 kHz sine tone to also exist simultaneously, inside the digital domain.

Oddly, this is also true at other frequencies. So, you do not only get a mirror effect around the Nyquist, but you also get it at the 1.5 times the sampling rate (or the sampling rate + Nyquist).

I won’t go into this any deeper for now – but if you want to continue, the section on “Folding” at the Wikipedia page on Aliasing is a good place to start.

 

Normally, we try to prevent audio signals higher with frequency content higher than the Nyquist frequency from getting into an LPCM system. This is done by low-pass filtering the audio signal to eliminate any content that might cause aliasing. That’s why the low-pass filter at the input of an analogue-to-digital converter is called an anti-aliasing filter. (At least, that’s the theory. In reality, the anti-aliasing filter of many ADC’s allow a little signal to get through above Nyquist…)

However, what happens if you create signals with a frequency above the Nyquist within the digital domain? Is this possible? Can it happen accidentally?

The short answer to this question is “yes”.

For example, let’s take a sine wave with a frequency of 2212 Hz (this is an arbitrary number… it could have been something else…), record it with an LPCM system with a sampling rate of 48 kHz. Then, after the signal is in the digital domain, I clip it at 85% of the peak value, so it looks like the waveform shown in Figure 1.

Fig 1. A sine wave that has been symmetrically clipped at 85% of its peak value.

By clipping the sine wave symmetrically (meaning that we have made the same change in the wave’s shape on the top and the bottom), we create odd-order harmonics. This means that, when we look at the spectrum of the signal’s frequency content, we will see energy at the fundamental frequency (the original sine wave’s frequency) and also peaks at 3x, 5x, 7x, 9x, that frequency – and so on.

(If I had clipped only on the top or the bottom, and therefore made asymmetrical distortion, we would see energy in the even-order harmonics at 2x, 4x,  6x, 8x, the fundamental frequency – and so on.)

So, let’s look at the frequency content of the clipped signal shown in Figure 1. This is shown in Figure 2, below.

Fig 2. The frequency content of the signal shown in Figure 1. Notice that the harmonics are all at frequencies that are the fundamental frequency (2212 Hz) multiplied by an odd number, as is explained above.

As you can see in Figure 2, we are expecting to see harmonics that extend (at least in this plot) up to 37604 Hz (or 17 x 2212 Hz). Of course, there are harmonics that go higher than this – but they aren’t visible in this plot because I’m only plotting signals with a level down to -60 dB FS.

You may notice that the width of the plot at 2212 Hz increases at the bottom. This is just an artefact of the math being done to find the frequency components in the signal. That spread in the frequency domain isn’t actually in the signal itself, so it can be ignored.

As I said above, the signal was clipped in the digital domain, in an LPCM system running at 48 kHz. So, just for reference, I’ve put in blue lines in Figure 2 that show the sampling rate and the Nyquist frequency – one half the sampling rate.

So: we can see that some of the artefacts created by clipping the signal are sitting at frequencies above the Nyquist frequency in this system. This means that this content will be “mirrored” or “folded down” or – more correctly – aliased to other frequencies below the Nyquist frequency. For example, the harmonic at 24332 Hz will be mirrored to 23668 Hz, according to the following math:

Nyquist – (signal freq – Nyquist)
24000 – (24332 – 24000)
24000 – 332
23668 Hz

So, looking at the top 60 dB of the signal content (shown in Figure 3): the resulting actual output of the LPCM signal will contain:

  1. the original fundamental frequency at 2212 Hz
  2. four harmonics of that frequency (shown as the other red numbers in Figure 3), and
  3. four more frequencies that are not harmonically related to the fundamental (the blue numbers)

 

Fig 3. The frequency content of the actual output of the signal from an LPCM system with a 48 kHz sampling rate. The frequencies indicated in blue are the aliased artefacts.

As you may already know, an LPCM system has a low-pass filter at its output stage – part of the system that is used to convert the signal back to an analogue output. However, that low pass filter typically has a cutoff frequency around the Nyquist frequency of the system. However, the artefacts that we have created here have aliased down to frequencies below the Nyquist within the digital domain – so, by the time the signal reaches the low pass filter at the output (known as a “reconstruction filter”) they’re already in the audio band, and therefore they’re not filtered out.

So, as we can see in this rather simple example: it is easily possible that a digital audio system that has some processing (specifically “non-linear” processing) can create harmonics that are higher than the Nyquist frequency and will have “aliases” below the Nyquist frequency, and therefore will not be removed by an anti-aliasing filter.

Since the aliased artefacts are not harmonically related to the fundamental frequency, they are more easily audible than “normal” distortion artefacts that generate harmonically-related artefacts. There are a couple of reasons for this, but the most obvious one can be demonstrated by sweeping the frequency of the fundamental. If the artefacts are harmonically related, then as the fundamental frequency of the signal goes up, so do the artefacts. However, if the artefacts are the result of aliasing, then as the fundamental frequency of the signal goes up, some of the artefacts go down in frequency, which sounds quite strange…

The example I gave above (of clipping) is just one way to create distortion that generates harmonically-related artefacts that alias in the system. Lots of different processes can create those artefacts. One of the usual suspects is a poorly-made sampling rate converter.

Many systems use sampling rate converters for different reasons. For example, if you have a loudspeaker or processor that has a lot of filtering in its processing chain, the best architecture is to run the digital signal processing (the  DSP) at a constant (or “fixed”) sampling rate, regardless of the sampling rate of the incoming signal. This is because, if you were to change sampling rates in the DSP to match the incoming signal, you would have to load an entirely new set of coefficients (a fancy word that basically means “multiplications values inside the digital filters”) into the processor. This takes some time, and you don’t want to miss the first part of the song every time the sampling rate changes while you’re waiting to load a bunch of new coefficients into your filters… So, instead, the smart thing to do is to keep the DSP running at a constant rate, and sample rate convert all incoming signals to the internal sampling rate. This way, there’s no dropout at the start of the song.

However, you have to be careful if you do this, since a poorly-made sampling rate converter will certainly create aliasing artefacts.

In part 5 of this series of postings, I described one kind of test that can be made on an audio system. This test consists of sending a sine wave with a swept frequency into the system and recording its output. You then do a spectrogram of the output, looking for signals at frequencies other than the one you sent in.

To get an idea of what aliasing will look like in this plot, I made a DSP algorithm that creates the same kinds of artefacts. The resulting plot is shown in Figure 4, below. (Remember that this is a measurement of a system that I made to intentionally generate similar artefacts to aliasing – this isn’t actually the output of a system that is aliasing).

 

Fig 4. An example of an analysis of a system that has the same kind of artefacts as a system that is aliasing. Notice that, as the original signal increases in frequency (the straight diagonal line), some of the aliasing artefacts decrease in frequency.

Now that you know what to look for in the plot, let’s look at the measurements of some commercially-available systems. Figure 5, below is a measurement of a system that has two problems. One can be seen as the vertical lines – these are “skip/insert” artefacts that I described in an earlier posting. The aliasing artefacts can also be seen in this plot. Note that, in this case, the input and output of the system are both digital connections to my measurement equipment.

 

Fig 5. An example of aliasing (and skip insert artefacts) in a commercially-available digital audio system. The original signal was a 48 kHz, 16-bit .wav file.

 

If I send a signal at a different sampling rate into the same system, I get a different behaviour. This is not unusual in systems with sampling rate converters. In this plot, you can see the skip/insert artefacts (the vertical stripes) the aliasing artefacts, and the obvious band-limiting of the system. Notice that nothing above about 24 kHz comes out of the system, which would mean that, internally, it is probably running at a sampling rate of 48 kHz. (The input signal in this measurement was at 192 kHz and my analysis system was running at 96 kHz.)

Fig 6. An example of aliasing (and skip insert artefacts) in the same commercially-available digital audio system as shown in Figure 5. The original signal was a 192 kHz, 16-bit .wav file.

Let’s look at another system. In this case, I put a 48 kHz, 16-bit .flac file on a hard drive, and played it through another digital audio system, again capturing its digital output. The result of this is shown in Figure 7.

Fig 6. An example of a lack of aliasing in another commercially-available digital audio system. The original signal was a 48 Hz, 16-bit .flac file.

As you can see in Figure 6, this system is behaving very well in this particular test. I see the nice, clean signal with only one frequency at only one time. No artefacts down to 100 dB below the signal level. This is good.

Now let’s test exactly the same system, at exactly the same sampling rate, again with a .flac file – but this time with a 24-bit word length in the file. The result of this is shown in Figure 7.

Fig 7. Artefacts in the same commercially-available digital audio system as shown in Figure 6. The original signal was a 48 kHz, 24-bit .wav file.

So, by going from a 16-bit file to a 24-bit file, this system obviously behaves very, very differently. It now has harmonic distortion (the straight diagonal lines running parallel to the fundamental frequency), aliasing of those harmonics when they go beyond 24 kHz, and strange noises as well (the large area of blue blobs in the lower left corner, and surrounding the fundamental frequency all the way up.

Those “strange noises” –  the blobs – are probably artefacts caused by a lossy codec similar to MP3. Typically, systems like this are built to reduce the data rate of the audio signal by trying to predict what you can’t hear in the signal – and leaving that out. In doing so, they create errors that produce noise, so the encoder tries to shape that noise so that it “hides” under the signal that it keeps. The end result looks something like the blobs shown in Figure 7… For a more thorough discussion of this, see this posting.

So, based only on the information from this test, we can guess that the system might be decoding the 24-bit file, “transcoding” it to a lossy format, and transmitting that through the system. However, this is just a guess based on one test… So it could easily be wrong.

One thing we can conclude, however, is that the 48 kHz / 16-bit file behaves MUCH better than a 48 kHz / 24-bit file in this system… So, in this particular case, a higher resolution is not necessarily better…

I should also point out that the digital output of that system was capable of outputting 24 bits. The reason I’m pointing this out is that many persons think that if a system or device has a digital output, then it is good. This is too simple a conclusion to make, because, as I’m trying to illustrate with this series of postings, the “weak link” in the chain is very likely NOT the physical output of the system. It’s more likely some part of the processing in the DSP chain (for example, a poorly-made sampling rate converter that aliases) or a poorly-implemented clocking system (for example, a skip/insert strategy).

For more aliasing fun…

If you’re intrigued by this, and you’d like to compare the aliasing caused by other sampling rate converters, I’d recommend checking out the page at http://src.infinitewave.ca. They plot the signals with a linear frequency scale instead of a logarithmic one. Consequently, the sweep of the fundamental looks like a curve (instead of the straight lines in my plots) but the harmonic distortion and aliasing artefacts are easier to see as being related to the fundamental.

 

Addendum – 2018/05/14

Last week, I ran a quick test on another commercially-available device – this time, a stand-alone audio file player with a digital output. I was running the test using a 44.1 kHz, 16-bit FLAC file, but the device had a 48 kHz output. The interesting thing about this one was that the artefacts that showed up were almost exclusively aliasing errors. So, I thought it would be interesting to show the plots here.

Figure 8. The results of a test on a different commercially-available audio file player with a digital output. The original file was a 44.1 kHz, 16 bit FLAC file with a signal level of 0 dB FS. The output of the device was running at 48 kHz. The aliasing artefacts are easily visible, even within 50 dB of the signal level!

 

Figure 9. The same output as was shown in Figure 8, but in this plot, with an analysis depth of 100 dB.

 

B&O Tech: Airtight excuses

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

“Love at first sight? Let me just put on my glasses.”
 Ljupka Cvetanova, The New Land

When I’m working on the sound design for a new pair of (over-ear, closed) headphones, I have to take off my glasses (which makes it difficult for me to see my computer screen…) I’ll explain.

Let’s over-simplify and consider a block diagram of a closed (and therefore “over-ear”) headphone, sitting on one side of your head. This is represented by Figure 1.

Fig 1. A simplified diagram of an over-ear headphone with a sealed cabinet, sitting correctly on the side of your head.

One of the important things to note there is that the air in the chamber between the headphone diaphragm and the ear canal is sealed from the outside world.

So, if I put such a headphone on an artificial ear (which is a microphone in a small hole in the middle of a plate – it is remarkably well-represented by the red lines in Figure 1….) I can  measure its magnitude response. I’ll call this the “reference”. It doesn’t matter to me what the measurement looks like, since this is just a magnitude response which is the combination of the headphone’s response and the artificial ear’s response – with some incorrect positioning thrown into the mix.

Fig 2. The headphones in question, placed on an Artificial Ear for the first measurement.

If I then remove the headphones from the plate, and put them back on, in what I think is the same position, and then do the measurement again, I’ll get another curve.

Then, I’ll subtract the “reference measurement” (the first one) from the second measurement to see what the difference is. An example of this is plotted in Figure 2.

 

Fig 3. The difference between a magnitude response measurement and the reference measurement of the same ear cup on the same headphones, 1/6th octave smoothed. As you can see, it’s slightly different – but not much. I was VERY careful about re-positioning the headphones on the plate.

Now, let’s consider what happens when the seal is broken. I’ll stick a small piece of metal (actually an Allan key, or a hex wrench, depending on where you live) in between the headphones and the plate, causing a leak in the air between the internal cavity and the outside world, as shown in Figure 4.

Fig 4. A small piece of metal that lifts the leather of the ear cup and causes a small leak around it.

 

 

Fig 5. A simplified diagram of an over-ear headphone with a sealed cabinet, sitting incorrectly on the side of your head.

 

We then repeat the measurement, and subtract the original Reference measurement to see what happened. This is shown in Figure 6.

Fig 6. The magnitude response difference caused by a small leak in the chamber.

As you can see, the leak in the system causes us to lose bass, primarily. In the very low end, the loss is significant – more than 10 dB down at 20 Hz! Basically, what we’ve done here is to create an acoustical high-pass filter. (I’m not going to go into the physics of why this happens… That’s too much information for this posting.) You can also see that there’s a bump around 200 Hz which is also a result of the leak. The sharp peak up at 8 kHz is not caused by the leak – it’s just an artefact of the headphones having moved a little on the plate when I put in the Allen Key.

Now let’s make the leak bigger. I’ll stick the arm of my glasses in between the plate and the leather pad.

Fig 7. The arm of my glasses, stuck in the system to make the leak worse…

The result of this measurement (again with the Reference subtracted) is shown in Figure 8.

Fig 8. The magnitude response difference caused by a bigger leak in the chamber.

Now you can see that the high pass filter’s cutoff frequency has risen, and the resonance in the system has not only increased in frequency (to 400 Hz or so) but also in magnitude (to almost +10 dB! Again, the sharp wiggles at the top are mostly just artefacts caused by changes in position…

Just to check and see that I haven’t done something stupid, I’ll remove the glasses, and run the measurement again…

Fig 9. Back to the original – just as a sanity check

The result of this measurement is shown in Figure 10.

Fig 10. Back to a system without leaks… and a magnitude response that closely matches the original – at least in the low end…

 

So, there are a couple of things to be learned here…

Firstly, if you and a friend both listen to the same pair of closed, sealed headphones, and you disagree about the relative level of bass, check that you’re both not wearing glasses or large earrings…

The more general interpretation of that previous point is that small leaks in the system have a big effect on the response of the headphones in the low-frequency region. Those leaks can happen as a result of many things – not just the arm of your glasses. Hair can also cause the problem. Or, for example, if the headphones are slightly big, and/or your head is slightly small, then the area where your jaw meets your neck under your pinna (around your mastoid gland) is one possile place for leaks. This can also happen if you have a very sharp corner around your jaw (say you are Audrey Hepburn, for example), and the ear cup padding is stiff. Interestingly, as time passes, the foam and covering soften and may change shape slightly to seal these leaks. So, as the headphones match the shape of your head over time, you might get a better seal and a change in the bass level. This might be interpreted by some people as having “broken in” the headphones – but what you’ve actually done is to “break in” the padding so that it fits your head better.

Secondly, those big, sharp spikes up the high end aren’t insignificant… They’re the result of small movements in the headphones on the measuring system. A similar thing happens when you move headphones on your head – but it can be even more significant due to effects caused by your pinna. This is why, many people, when doing headphone measurements, will do many measurements (say, 5 to 10) and average the results. Those errors in placement are not just the result of shifts on the plate – they may also be caused by differences in “clamping pressure” – so, if I angled the headphones a little on that table, then they might be pressing harder on the artificial ear, possibly only on one side of the ear cup, and this will also change the measured response in the high frequency bands.

 

Fig 11. My glasses on a B&K HATS used for measurements instead of the artificial ear. Check out that leak… This is similar to the problem that I have when I wear glasses when listening to the same headphones.

Of course, it’s possible to reduce this problem by making the foam more compliant (a fancy word for “squishy”) – which may, in turn, mean that the response will be more different for different users due to different head widths. Or the problem could be reduced by increasing the clamping force, which will in turn make the headphones uncomfortable because they’re squeezing your head. Or, you could embrace the leak, and make a pair of open headphones – but those will not give you much passive noise isolation from the outside world. In fact, you won’t have any at all…

So as you can see, as a manufacturer, this issue has to be balanced with other issues when designing the headphones in the first place…

Or you can just take off your glasses, close your eyes, and listen…

 

Addendum

Please don’t jump too far in your conclusions as a result of seeing these measurements. You should NOT interpret them to mean that, if you wear glasses, you will get a 10 dB bump at 400 Hz. The actual response that you will get from your headphones depends on the size of the leak, the volume of the chamber in the ear cup (which is partly dependent on the size of your pinna, since that occupies a significant portion of the volume inside the chamber) and other factors.

The take-home message here is: when you’re evaluating a pair of closed, over-ear headphones: small leaks have an effect on the low frequency response, and small changes in position have an effect on the high-frequency response. The details of those effects are almost impossible to predict accurately.