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 therefore aliasing.

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… 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…

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.


Typical Errors in Digital Audio: Part 5 – What time is it there?

I’m originally from Newfoundland – one of the few places in the world with a 1/2-hour time zone. So, when it’s 10:00 a.m. in Montreal, it’s 11:30 a.m. in St. John’s – my home town. This meant that, when I was a kid 40 years ago, and we would call our relatives in Toronto or Germany to wish them a Merry Christmas, there were two questions that you could always rely on being asked: (1) what’s the weather like there? and (2) what time is it there?

These days, I have a similar problem that is well-described by “Segal’s Law“. My iPhone and my wristwatch (an old analogue one with hands that go around pointing at the floor and the fridge…) are never synchronised… This is because of two things: (1) I probably did a bad job of setting my watch and (more importantly) (2) my watch runs just a little bit slowly…

So, let’s say, for example, that I set my watch to be EXACTLY in sync with my phone on a Monday morning at 9:00 a.m. As the week goes by, my iPhone and my watch drift apart, and, just for the sake of argument let’s say that, one week later, when my iPhone turns over to 9:00 a.m. on Monday morning, my wristwatch turns over to 8:59 a.m. So, I lose 1 minute per week on my watch.

(It’s pretty safe to assume that my iPhone is also not perfect – but it’s different because, every once in a while, it compares its internal clock with another, more accurate clock somewhere else via a connection across the Internet (which, we will assume, for the purposes of this discussion, works).)

Let’s consider this from a strange point of view. Let’s assume that

  • I’m checking the time on my watch every minute, on the minute
  • someone else is “fixing” my watch every week so that it’s correct at 9:00 a.m. on Mondays. They do this by adjusting the watch to the correct time 30 seconds before the iPhone says it’s 9:00 a.m.
  • I don’t know that they’re doing this for me…

If we think about this from my perspective, I’ll live in a strange world where 8:59 on Mondays never exists. This is because at 8:58 and 30 seconds (on my watch), my friend re-sets the time to 8:59 and 30 seconds (while I’m not looking) to synchronise with the iPhone…


IF my watch was running fast – say, gaining one minute each week, then I would live in a different strange universe where 9:00 happens twice every Monday morning…


The basic problem here is that we have two clocks that do not run at the same rate – but they are expected to do so. So, we synchronise them regularly (in the above example, on Monday mornings at 9:00) – but between those synchronisation events, they drift apart in time.


So what?

The example above is very, very similar to the way a digital audio streaming system works – especially if you’re using a wireless connection between the transmitting device and a receiver.

Lets say that you’re playing a sound file that was recorded at 44.1 kHz and streaming it wirelessly to a receiver. I’m trying to be as generic as possible here, but I could be talking about a Bluetooth connection to a pair of headphones or a WiFi connection via DLNA to a device connected to a pair of loudspeakers, for example…

It is not unusual with such a connection for the transmitter to collect up a block of audio samples – say, 64 of them – and send them to the receiver’s input buffer. The receiver then pulls those samples out, one by one, and (eventually) sends them to a digital-to-analogue converter that produces a signal that (eventually) comes out as an audio signal. Then, 64/44100’ths of a second later (64 samples later) the transmitter sends another block, and so on and so on until the song ends.

This system works well if the clock inside the transmitter and the clock inside the receiver are perfectly synchronised. We can even be a little generous and say that they can drift apart a little – but not so much that we either run out of samples to play (because the receiver is playing them out faster than they’re coming in from the transmitter) or that we have samples left over to play when the next block comes in (because the receiver is playing them out slower than they’re coming in from the transmitter).


Dealing with this problem the right way

The right way to deal with this issue is for the receiver to always be checking what time it thinks it is when the block arrives from the transmitter. If the block arrives a little early, then the receiver should think “hmmmm, my clock is going too slowly – I’ll speed it up a bit”. If the block arrives a little late, then the receiver should adjust its clock to go a little slower.

So, in this case, the receiver has a basic, nominal speed for its internal clock – but it’s constantly adjusting it to be faster and slower to try and match the clock of the transmitter – but it can only do this adjustment at the block rate – the frequency at which the blocks of samples arrive, which is dependent on the block length (how many samples are in each block) and the sampling rate (how many samples per second). (Of course, this can result in “jitter and wander” problems if you’re not careful (I won’t talk about this here…) – so you have to pay a little attention to how quickly you’re adjusting your clock rate… but that’s “just” a matter of correct implementation.)


Dealing with this problem the wrong way

There is another way to deal with this problem, which, unfortunately, has measurable and possibly audible consequences. This implementation is basically the same as my original example, where I had a friend “fixing” my wristwatch once a week. You have a transmitter that sends blocks of samples to the receiver – and although these two devices should have exactly the same clock rate, they don’t.

Let’s say, for example, that the receiver is playing the samples faster than they’re being sent by the transmitter. This means that the two will slowly drift farther and farther apart until, eventually, the receiver will have to play a sample, but nothing has come in from the transmitter yet, so there’s no sample there to play. In this case, the receiver says “no problem, I’ll just play the last sample again, and the next block will come in while I’m doing that” – so it inserts an extra sample that is just a duplicate of the previous one.

If the receiver’s clock is going slower than the transmitter’s, then, as the two drift farther apart, we will get to a moment where the receiver will receive a new block of samples but it’s not done playing all of the samples in the previous block yet. In this event, it says “no problem, I’ll just leave that last sample out and move on to the next block to catch up” – so it skips a sample.

This is called a “Skip / Insert”  strategy for dealing with clock synchronisation. It’s done by software and hardware engineers because it’s simple to implement, and, in many cases, a manufacturer can get away with this, since it is rarely audible for a couple of reasons.

Can this be measured?

The simple answer to this is “yes” – and it can be measured in a number of different ways. I’ll show one way below…

Can I hear it?

The honest answer to this question is “sometimes” – but it’s not as easy to detect as one might think. Of course, a skip/insert event (a duplicated sample or a dropped one) creates an artefact. However, the magnitude of this artefact relative to the “correct” signal is dependent on when it happens.

Let’s take a look at a couple of simple cases. We’ll “transmit” one period of a sine wave that should come out on the other side of the system looking like Figure 1.

Fig 1: The original signal that we want to transmit

But what happens if we don’t get a block in time to keep outputting a signal? We insert a duplicate sample and hope that the block comes in before I have to send out another one. Examples of this are shown in Figures 2 and 3, below.

Fig 2: Insert example 1
Fig 3: Insert example 2

You’ll probably notice that it’s much easier to see which sample I duplicated in Figure 3 than in Figure 2. In Figure 3 it was sample number 26 that was duplicated. In Figure 2 it’s sample number 13.

The reason it’s easier to see the error in Figure 3 is that duplicating the sample causes an obvious change in the slope of the signal, whereas in Figure 2 it does not – the slope of the signal is 0, and by duplicating a sample, I am also making it 0 – but for a slightly longer time.

This does not mean that we did not generate an error. It just means that we’ll probably “get away with it” in the case of Figure 2, and we probably won’t in the case of Figure 3.

However, since the drifting of the two clocks (in the receiver and transmitter) are not dependent on the signal, there’s no way to know when this is going to happen.

And, of course, if this happens in the middle of a snare drum hit or a ssssinger sssstarting a word in a ssssong with the letter “s” – then we also won’t hear it because there’s so much going on (frequency-wise) that the artefact will be buried in the mess.

Also, since this clock drifting is usually not completely regular, the errors do not usually come in at a regular rate (although I’ve seen exceptions…). So, it’s not like you can listen for “a click every second” or “one per minute”. They happen when they happen – hopefully when you’re not listening and/or when the tune is busy enough to hide it.


A skip event is similar to an insert, as you can see in the two examples in Figures 4 and 5.

Fig 4: Skip example 1
Fig 5: Skip example 2

Again, I’ve intentionally put in these two skips in places where they are least obvious (Figure 4) and most obvious (Figure 5).


The real world

One of the tests that can be done on an audio system is to send a sinusoidal signal with a swept frequency through a system, capture the output, and then do a spectrogram of the result. In theory, if you see anything other than a single frequency at any one time at the output, then you know that something has happened to the signal. You would probably then need to go back and look at the output signal itself to start evaluating exactly what happened… This is a test that is used to evaluate one aspect of the performance of different sampling rate converters, for example, at this site.

Let’s take a sine sweep and run it through a system. The sweep goes up logarithmically in frequency from 20 Hz to about 90% of Nyquist (which would correspond to 20,000 Hz in a system running at 44.1 kHz) over 60 seconds and has a level of -1 dB FS. We’ll then capture the output in a system that is behaving perfectly and do a spectrogram of this, looking for artefacts down to some level below the signal level. (If you’re really geeky, you’ll know that this signal-to-error ratio is dependent on the window length of the FFT I’m using to create the spectrogram – but this is beyond our discussion today…).

An example of the output of a system that is behaving well is shown in Figure 6.


Fig 6. A spectrogram of a sinusoidal signal, swept in frequency over 60 seconds. Notice that there are no additional signals within 50 dB (the scale on the right) of the signal.

You may notice that the plot looks a little “wide” in the beginning. This is because the window length of the FFT I’m using to analyse the signal isn’t long enough to get a precise analysis of a low-frequency signal. So, this is an artefact of the analysis – not an error in the playback system.

What happens if we have random skip/insert events in the system? This is shown in Figure 7.

Fig 7. Intentionally-created skip/insert events seen as artefacts in the frequency domain.

The signal in Figure 7 was one that I created – I intentionally made skip/insert events at random times and applied them to my test signal.

There are two things to notice here. The first is that each event is visible as a vertical “spike” in the plot. This is because a skip/insert event will cause a short, wide-band “burst” that sounds like a click. However, the bandwidth of the click is dependent on when it happens relative to the signal. For example, the skip/insert events in Figure 2 and 4 would not create as much high-frequency energy as the ones in Figure 3 and 5. So, the bigger the effect on the slope of the signal, the more high frequency energy we’ll get in our “click” sound. Since the slope of a signal increases with frequency, then this also means that low-frequency signals will likely produce lower-bandwidth artefacts.

Now let’s look at the results from some real-world devices and systems that are commercially available.

Fig 8. The same test run on a commercially-available system/device. If you’re curious about some of the information listed in the plot, you can decode it as follows: The title “44k1_16_-1dBFS_chan1_100dB_snr” means that the original file I was playing was a 44.1k kHz / 16 bit file. The level of the sinusoidal sweep was -1 dB FS, and TPFD dithered. The analysis we’re looking at here is for channel 1 (the left channel), and we’re looking for artefacts down to 100 dB below the signal level. The “96000” you see on the top left of the plot indicates that the output of the system was captured at a sampling rate of 96 kHz (the internal sampling rate of the sound card that I used to do this measurement).


As you can see in Figure 8, there was one skip/insert event that happened during the 60 seconds I was running this test. Remember that the time that that event happened had nothing to do with the frequency it was playing. It just happens when it happens due to the relationship between the transmitter’s and the receiver’s clock speeds.


Fig 9. Another commercially-available system/device.


Figure 9 shows the results from a different system/device that obviously uses a skip/insert strategy to deal with clock synchronisation problems. It also obviously has some serious clock issues, since it has to correct on the order of approximately once a second…


Fig 10. Another commercially-available system/device.

Figure 10 shows the results from a different system/device that uses a skip/insert strategy – but appears to do so at scheduled intervals. In this case, there is a high probability of getting a skip/insert event every 10 seconds with the counter starting at the instant I starting hearing the music.


Addendum 1

Inquisitive readers may be asking why it is that, although I’m doing an analysis down to -101 dB FS (100 dB below the signal level of -1 dB FS), you can’t see the effects of the dither noise floor in my original 16-bit file (which is normally assumed to be at -93 dB FS). This is because the -93 dB FS estimate of a dither signal assumes that you are looking at the total energy from the entire frequency band. The spectrograms above are based on FFT’s that split up the total frequency band into “slices” (called frequency bins) – and the total energy in each of these bins is less than the total energy in all of them (one person clapping is not as loud as 1000 people clapping at the same time…). If we wanted to see the dither noise, I would have had to set my analysis to go down approximately 30 dB lower – but the actual value for this is dependent on the relationship between the sampling rate, the window length of the FFT’s, and the windowing function that I’m using.


Addendum 2

Do not bother contacting me to ask which “commercially-available system/device” I measured and in which I found these errors. I’m not doing this to get anyone in trouble. I’m just doing this to try to illustrate common errors that I see often when I evaluate and test audio devices.

An besides, it would not be fair for me to rat on specific companies, systems, or devices, since, in some cases, these errors may have already been fixed with a firmware update, meaning that “naming names” would be irrelevant and unnecessarily detrimental.

But, I will say that I see this problem often. A rough estimate is that I would see errors like this on roughly half of the commercially-available devices and systems I test. It can also be sneaky, as we saw in Figures 8 and 10. Sometimes you get one of these clicks only once in a minute. So, if you do a 10-second measurement to test if your wireless audio receiver is “bit accurate” – the answer can be “yes” – but if you keep measuring for 1 or 2 minutes, you find out the answer is “no”…


Addendum 3

If it helps, I could have used the example of a leap year instead of two clocks at the beginning. The reason we have a February 29 every 4 years is that our calendar “runs” a little faster than the time it takes us to get around the sun (because a “year” is actually 365.25 days long…). So, every 4 years we have to “insert” a day to put the two clocks back in sync.

Also, since a “year” is not exactly 365.25 days long, we also have the occasional “leap second” as well. But most people don’t notice this, since it’s rarely useful as an excuse when you’ve missed a meeting…

Typical Errors in Digital Audio: Part 4 – Ode to Billy Joe

It was the third of June, another sleepy, dusty Delta day
I was out choppin’ cotton, and my brother was balin’ hay

I’ve always liked the song “Ode to Billy Joe”. It starts on a 7-chord, so you know it’s going to go somewhere… I love how Papa, when he hears that Billy Joe jumped off the Tallahatchie Bridge just says that he “never had a lick of sense”, and asks for more biscuits. And who, exactly, did Brother Taylor see with Billy Joe? What did they throw off the bridge?

I like the fact that there are many questions and few answers – and life just goes on anyway…

But we’re not here to talk about songwriting, we’re here to talk about typical errors in digital audio – specifically today – streaming services.

This error is an easy one to discuss – but an important one nonetheless…

When I’m sitting at work, typing on my computer, I listen to music a lot. Usually, I use the “Audirvana” software on my Mac, with an external Teac UD-501 USB-Audio headphone DAC (which does the digital-to-analogue conversion and the amplification for the headphones, all in one box). The reasons I choose to use Audirvana are (1) that it can play all of my files (I have some DSD stuff on my hard drive), it can stream directly to my external DAC without routing the audio through Mac’s OS, and it can also see my Tidal account.

Now, just to be clear, this posting is not an advertisement for Apple, Audirvana, Teac, or Tidal. I mention all of that just as background information… I also drive an 11-year old base-model Honda Civic (that will come up later in this posting) and I wear Ecco shoes (which is completely irrelevant…).

If you use Audirvana to search Tidal for tracks called “Ode to Billy Joe” You will get 300 hits. I don’t know if this is because there are 300 covers of that song on Tidal (I doubt it) or if 300 is a limit on the number of tracks either Tidal or Audirvana will report in a Search function (I suspect that this is the case…)

As you can see in the screenshot in Figure 1, all of them are 16 bit, 44.1 kHz files. So far so good…


Fig 1: There are many “Ode to Billy Joe” covers in Tidal

I have two favourite versions of this song. One of them is by Paula Cole (the other is by Patty Smyth). If I press “play” on the Paul Cole version, and I look at the top of the screen, I see something like the screenshot in Figure 2.


Fig 2: Ode to Billy Joe

One of the nice things about Audirvana is that it tells you a little technical information about the track to which you’re listening. Notice there on the right-hand side of the screenshot above, that we’re listening to a 16-bit, 44.1 kHz FLAC file.

This makes sense. In fact, it’s what I expect, since my Tidal subscription promises “lossless high fidelity sound quality” – that’s why I pay extra for a Tidal HiFi subscription…

So far so good.

One of my less-favourite renditions of “Ode to Billy Joe” is performed by The Stadium Saxophone Players on their album “Timeless Sax Instrumentals – Volume 2”. IF I press play on this version, and look at the top of my Audirvana window, I see the information in Figure 3.

Fig 3: Ode to Billy Joe

Interesting…. Notice that I am now listening to a 96 kbps AAC file with a 16-bit word length, and a sampling rate of “22.1 kHz” (actually 22.05 kHz – half of 44.1). So much for “lossless high fidelity sound quality”.

This calls for more investigation.

So, I pressed “Play” on the top hits in my search, one by one, and checked the file format displayed on the screen. The results of this “test” was that, in the first 66 “Ode to Billy Joe’s” listed, 6 of them were 96 kbps AAC files, 60 of them were FLAC.

So, for this sampling, roughly 9% of the available tracks were not in a lossless format, and were not even full bandwidth. Admittedly, the tracks that were in the lower-quality format were versions that I would not listen to anyway – so, to be honest, I don’t really care too much.

Now, before you mis-interpret me, I want to be very explicit and state that this is NOT Tidal’s fault. Of course they did not ask for an AAC version of the file they put on their hard drives. This was the file format supplied to them by the record label (to use an increasingly old-fashioned term…). So, we can’t blame Tidal for this – and I’m quite certain that they’re not the only streaming service that “suffers” from this issue.

However, what my little test shows is that what Tidal is actually selling me is the capability of streaming “lossless high fidelity sound quality” – and not a guarantee that what is in the “pipe” really is lossless.

Of course, this is not just true for streaming services. Other people have shown that some higher-priced “high resolution” audio files that you can purchase online are actually just a bit-for-bit copy of the “normal resolution” version of the same track. I have at least one CD that contains at least one track that has MP3 artefacts obvious enough that I can hear them on my unbranded audio system in my 11-year old Honda Civic while I’m driving… (It’s a compilation disc, so I guess the label was supplied with an MP3 version that they decoded to PCM and put on the CD.)

So, just like Ode to Billy Joe – there are some questions here… and you don’t need to know much about digital audio to answer them… But the basic moral of this part of the story is that the format that is used to deliver your music is not a guarantee of higher quality…