With radio, the bandwidth of the audio and thus the size of the side-bands determines the minimum spacing of adjacent radio carriers: the more tightly constrained the audio, the smaller the side-bands and the more radio channels you can fit into a given area of radio spectrum. In digital audio the side-bands are an unwanted side-effect of the sampling process, but they still determine the audio bandwidth we can use: if we sample an audio signal at We aren't going to use them, but they're there nonetheless, and we have to remove them when we output the wanted audio otherwise they could fry the tweeters in your speakers, or cause distortions in equipment that can't handle such high-frequency content cleanly.
Unfortunately, unlike the side-bands created in radio, these ones are pretty close in spectrum terms to the wanted audio, simply because the sampling rate is relatively low. If we sample a 20kHz signal at The wanted audio 20kHz and the unwanted lower side-band To remove the unwanted side-bands without affecting the wanted audio, we need a very steep low-pass filter the 'reconstruction filter'. In the example above, if the 20kHz signal is near peak level, and we want the side-bands to be attenuated below the noise floor, we need a filter that reduces them by more than dB in less than a quarter of an octave.
The steepest filter on most audio mixers has a slope of 18dB per octave, so you can appreciate the scale of the challenge!
Typical Errors in Digital Audio: Part 1
One solution is to sample at a much higher rate, so that the side-bands are further away from the wanted audio. However, the higher the sampling rate, the more data you have to store or process — and even The low-pass filters used in the earliest digital products weren't really up to the job of filtering out side-bands at the low sample rates of the time. Not only did they often fail to remove the lower side-band adequately, but they also affected the wanted audio in a way that had unpleasantly audible side effects — harsh, clinical, scratchy I'm sure you've heard these descriptions!
A very steep low-pass filter is needed to remove the unwanted side-bands when reconstructing the analogue output. The filtering challenge isn't restricted to the output side of a sampled system, and we need a virtually identical filter on the input: the 'anti-alias' filter see 'Aliasing' section must be there to make sure that the system operates correctly. You can't remove the unwanted side-bands if they're allowed to overlap the wanted audio, so we have to keep the two separated.
To do that we need to choose a sample rate that is at least twice the highest frequency that we want to sample. In that way the lower side-band can't extend down in frequency so far that it overlaps the wanted audio — but we have to make absolutely sure that the audio going into the system never extends to more than half the sample rate. In other words, we have to ensure that we stick to the self-imposed rule of not having any input signal higher than half the sampling rate, so that the resulting lower side-band doesn't reach down as far as the input audio.
This second low-pass filter at the input will suffer the same audible and technical issues as the output reconstruction filter: a double whammy!
Digital Audio Workstations
Fortunately, technology has advanced and almost all modern digital equipment uses 'delta-sigma' converters. These operate internally at much higher sample rates than that at which the system is running, and the steep low-pass filtering which is still needed is performed entirely in the digital domain, where it's far more accurate and has minimal audible side-effects. As mentioned in the main text, we've placed a number of audio files on the Sound On Sound web site that demonstrate some of the theory and problems described within this article. So if you want to know what the different snaps, crackles and pops sound like, or to hear an exaggerated example of what dither actually does, go to www.
Another common misunderstanding is caused by a widely-used diagram showing a sampled waveform. Each sample is shown as a thin bar, with adjacent samples then appearing as 'steps', and people mistakenly associate this 'stepped' appearance with quantising errors — even though sampling and quantising are entirely separate and independent elements of the process, and no quantising has yet taken place! The 'steps' on the diagram aren't there because something is missing, but because something has been added — something we don't want or need, and which the reconstruction filter removes: the 'steps' are actually created by the addition of the side-bands, nothing more and nothing less.
The stepped nature of the reconstructed samples is due to the presence of high-frequency images. The higher the sample rate, the higher the frequency of the images, and the smaller the steps. Intuitively, it is probably clear that the higher the sample rate, the easier the reconstruction filter's job becomes. If you redraw the graph with a much higher sample rate, the 'steps' appear smaller, and people mistakenly believe this is proof that sampling at higher rates is more accurate. It isn't: it actually shows that the reconstruction filter has an easier job at higher sampling rates, because the unwanted side-bands are moved further away from the wanted audio.
In fact, it doesn't make any difference whether we sample a Hz tone at Hz, Hz, 25,Hz or Assuming your player is engineered properly, there should be no audible difference between the two, as both sample rates satisfy the Nyquist Shannon criterion of being at least twice as high as the source signal bandwidth.
However, it is obviously a lot easier to design a filter that rolls off above Hz to remove side-bands centred on So the size of the steps in that sampled signal diagram simply reflects the challenge facing the reconstruction filter: the higher the sample rate, the easier the filter's job becomes. Once those unwanted side-bands are removed, we're left filter designs permitting! I wasn't lying when I said earlier that the sampling process is theoretically a perfect one! Cast your mind back to the 'wheels going backwards' effect I mentioned earlier when comparing film with audio sampling — an effect caused by the sampling rate being too low less than twice the bandwidth of the wanted signal.
Now imagine a wheel with one spoke painted bright red. The wagon is moving and the wheel is rotating, and the camera takes a picture for the first frame of a film — let's say the painted spoke happens to be vertical, in the 12 o'clock position.
This time the painted spoke happens to be at 9 o'clock, the next frame at 6 o'clock, and so on. When we replay the film it appears as if the wheel is rotating slowly anticlockwise, when in reality it was going clockwise at a much faster rate. The effect is called 'aliasing' because what we are seeing is false information — an alias. If the sample rate is less than twice the audio bandwidth, the lower side-band will overlay the wanted audio, and high-frequency input signals will be heard as low frequencies.
Even after the reconstruction filter has removed the upper side-band, the part of the lower side that overlays the wanted audio remains, and is audible. In a properly designed digital audio system, aliasing shouldn't happen. The sample rate is at least twice the bandwidth of the wanted audio, and a steep, 'brickwall' anti-alias filter ensures nothing above half the sample rate gets in. In that way, the lower side-band produced is kept clear of the wanted audio.
But what happens if we allow signals higher than half the sample rate into the system, or choose a sample rate that isn't more than twice the signal bandwidth? The answer is that part of the lower side-band ends up overlaying the wanted audio, and becomes audible. Since the lower side-band is spectrally reversed, high-frequency source signals appear as lower frequency signals aliases , the audible equivalent of the wheels going backwards. What's more, there's no musical relationship between the input and alias frequencies; the relationship is between the input frequency and the sample rate, and therefore sounds very discordant and unnatural.
A file on the SOS web site aliased piano. After about 10 seconds you'll hear a glitch, which is when I started reducing the sampling rate from the standard The reduction is through a series of switched settings and you'll hear some being introduced through the rest of the piece. As the sample rate comes down, the high piano harmonics start to appear at lower discordant frequencies, and the effect becomes stronger as the sample rate is reduced further. In the end, with the sample rate down to about 6kHz, the beautiful piano sounds like a very nasty electronic harpsichord sample!
As I said earlier, this kind of problem shouldn't happen with well-engineered equipment at least not within the analogue-digital conversion stage , but it can happen by accident if digital signals are passed between equipment operating at different sample rates, or if sample-rate conversion isn't performed properly. If you've ever received a greetings card with a voice message you'll have heard the effect of aliasing caused by improper sample rate conversion. The original sound has been sampled at a very low sample rate to save data without implementing the appropriate anti-alias filter, so frequencies higher than half the sample rate have been allowed into the digitising process, resulting in aliases.
This problem also commonly occurs in cheap computer games and some Internet video and audio clips. When you connect a computer into your digital audio setup, a whole raft of problems can arise, mostly relating to audio clicks, pops and gaps terms that generally refer to the length of the interruption, from a single sample to a sizeable chunk of audio.
Problems tend to fall within three broad areas: mains supply, recording, and playback. A low buffer setting may be needed for low-latency applications such as playing VST instruments live , but as your mix gets busier you may find you need to increase the buffer size to prevent unwanted glitching.
The trade-off is that higher buffer settings increase latency. Although the causes of interference riding piggyback on the mains supply can sometimes be tricky to track down, they're likely to affect both audio recording and playback, and their timing will bear no relation to anything happening in the music. Notice whether clicks and pops coincide with your central heating, oven, microwave or freezer switching on.
If so, they may be nothing to do with your computer at all, instead requiring interference suppression at source, or more careful connection of your gear to the mains. Intermittent crackling problems are often caused by faulty audio or mains cables, so check them before blaming your computer. Continuous hums and buzzes may also relate to electric light dimmers, so keep these away from the studio as well. Computer-related recording and playback problems may relate to clocking issues discussed in the main text , but most are due to hardware or software inside your computer.
Despite having reviewed over 84 audio interfaces, I've rarely run into this category of click and pop — largely because I choose the hardware components in my PC carefully for maximum compatibility with music hardware and software, and carefully set up my operating system with the same end in mind. Stick with recommended motherboard chip sets, avoid unusual expansion cards wherever possible, and if you have a Firewire audio interface make sure your computer features one of the Firewire controller chips recommended by the interface manufacturer.
Mac users generally have an easier time here, simply because there are fewer hardware variations for audio interface manufacturers to test. Software problems often stem from the audio interface RAM buffers being too small, and the data running out before the operating system can get back to top them up playback or empty them recording. So if you hear even a single click in your audio recording or playback, it's probably due to something preventing the operating system from filling and emptying those audio buffers in time for smooth delivery to your audio interface.
If those interruptions become more frequent, the isolated clicks and pops turn into occasional crackles, and eventually to almost continuous interruptions that sound like distortion as the audio starts to break up more regularly. The most obvious cure is to increase the audio interface buffer size, and make sure you have the latest drivers installed and the recommended operating system tweaks in place.
If you only get an occasional click, see if it coincides with a soft synth playing more notes and temporarily pushing the CPU 'over the edge', or a non-musical background task cutting in unexpectedly from time to time, that you can disable. Occasionally a rogue plug-in or soft synth can cause sudden processing 'spikes' as well, so to track down problems try temporarily disabling the plug-ins you're using, one at a time, to see if it cures the problem.
Once you have compatible hardware and no unexpected software interruptions you should hear no clicks or pops until the audio buffer size is at 2ms — or even lower. Martin Walker. A lot of fuss is still made about jitter, but while it is potentially a serious issue it's rarely a practical problem these days — simply because equipment designers and chip manufacturers have found very effective ways of both preventing it and dealing with it. Jitter is the word used to describe very short-term timing variations between one sampling moment and the next. In a 48kHz sampled system, the time between each clock pulse should be If the gap between some pulses is, say This can happen at either the A-D stage, or the D-A stage, but it is more serious if it happens at the former, because those distortions are then locked into the digital signal.
A jittery A-D clock means that the amplitude of audio samples is measured fractionally early or late, but stored as if taken at the precise required time. So these digitised sample amplitudes are really telling lies about the true amplitude at the required moment in time. This extreme example of jitter shows how the first blue sample is produced too early and the second too late, with the result that the intended waveform red is distorted purple. A similar problem afflicts the D-A converter because it is trying to reconstruct analogue samples from the digitised amplitude data.
If it produces those sample amplitudes slightly early or late, again it is distorting the true waveform. The saving grace is that if the jitter can be removed by using a better D-A converter, say , then the original data can be used to reconstruct the proper waveform. If the clock jitter is entirely random, the resulting distortion will also be random, and a random signal is noise.
Since a high-frequency signal changes faster than a low-frequency one, small timing errors will produce larger amplitude errors in a high-frequency signal. So random jitter tends to produce a predominately high frequency hiss. I've yet to hear that on any current digital system, though — clocking circuits these days are just too good for this to be a practical problem. On the other hand, if the jitter variations are cyclical or related to the audio, the distortions will be tonal similar to aliasing or harmonic, and they'd tend to be far more obvious and audible.
But I've not heard that on any current digital audio system either: other than in very low cost equipment with extremely inferior clocking structures, A-D and D-A jitter just isn't a practical problem anymore. Another source of jitter the strongest source these days is cable-induced. If you pass digital signals down a long cable or fibre , the nice square-wave signals that enter degrade into something that looks more like shark fins at the other end, with slowed rise and fall times.
This is caused by the cable's capacitance or the fibre's internal light dispersion , so the longer the cable, the worse the degradation becomes. That's why digital cables need to be wide-bandwidth, low-capacitance types. This matters because most digital signals incorporate embedded clocks along with the audio data, and that clocking information is determined from the rise and fall between the data pulses.
If the clocking edges are vertical, the clocking moments are obvious. However, if the clocking edges slope, the timing point becomes ambiguous — and we now have embedded jittery clocks! When passing digital audio between one system and the next, the precise clock timing actually doesn't matter that much, as long as the average sample rate is the same for both. All that's needed is to be able to determine at each clock moment what the binary value of each bit is in the binary word.
However, when sampling or reconstructing an analogue signal, the clocking moments are critically important, as explained. So if a D-A relies on using the jittery embedded clocking information from its input signal to reconstruct the analogue output, there could be a problem with jitter noise or distortions. Fortunately, most modern D-As incorporate sophisticated jitter-removal systems to provide isolation between the inherently jittery incoming clocks embedded in the digital signal, and the converter stage's own reconstruction clock.
In most cases, A-D converters operate from an internal, low-jitter clock, and it is only necessary to use external embedded clocks when slaving multiple A-D converters. To minimise the potential for clock jitter, it is generally best to use the A-D converter's internal clock as the system master whenever possible.
If you have to use external clocks, use the shortest and best-quality clocking cables between devices that you can, fed from the most stable clock master available. A linear system has a linear transfer curve in which the relationship between input level and output level is proportional.
The other big stumbling block in the digitisation process is the concept of 'resolution. These measurement errors reduce with increasing word length because there are more quantising levels, spaced more closely together , so while eight bits can only count levels, 16 bits can count to 65, levels and 24 bits can count to 16,, levels — so it seems obvious that 24 bits gives higher 'resolution' and is more accurate than 16 or 8 bits.
This may be true, but it is also very misleading, because audio quantising isn't implemented in that simplistic way. If you draw a graph to show the relationship between input signal level and output signal level often called a transfer curve , and show what happens with an analogue system operating with unity gain, you get a straight line at 45 degrees. As the input level increases, the output level increases in direct proportion — which means we have a straight-line graph, and the system is described as being 'linear', or free from amplitude distortions.
With the simple quantising system, we get a staircase. As the input level rises, the output remains at a fixed level until the next quantising threshold is reached, at which point the level suddenly jumps to a new fixed output level. Clearly, this is very non-linear and the audible result is a distorted output. There are audio files on the web site to demonstrate this with simple piano music. A crudely quantised system has a stepped transfer curve in which the output level increases in quantised steps as the input level rises linearly. As you can hear, the fewer the bits, the bigger the quantising steps, the more non-linear the quantised digitisation becomes, and the worse the distortion.
At just three bits the piano is almost unrecognisable. You'll also notice at least in the 8-bit version that when the signal level is quite high the quantising errors are essentially random, and sound like noise, but as the level of the piano falls the errors become more identifiable as distortion. When the level falls below that of the lowest quantising threshold the output is completely silent— there's no background hiss unless introduced by your monitoring system!
In these examples, I've maintained the original source audio amplitude and just reduced the word length, in order to make the effects very obvious.
Analog Waves vs. Digital Waves
But exactly the same effects will happen in a crudely quantised bit system as the signal is decreased in amplitude to the point where it only crosses the bottom eight, or just the bottom three, bits. The distortion effects would then be less audible, simply because the signal level would be very low — but they would still be there, and that non-linearity is unacceptable. This analog signal is then converted to a digital signal by an analog-to-digital converter and passed to the DSP. During the playback phase, the file is taken from memory, decoded by the DSP and then converted back to an analog signal through the digital-to-analog converter so it can be output through the speaker system.
In a more complex example, the DSP would perform other functions such as volume control, equalization and user interface. A DSP's information can be used by a computer to control such things as security, telephone, home theater systems, and video compression.
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- A Digital Audio Primer - Joel Strait?
- Saving Private Ryan - Piano Solo.
- Jar Jars Mistake.
- Real-world applications of 3D audio.
- Untangling Confusing Terms;
Signals may be compressed so that they can be transmitted quickly and more efficiently from one place to another e. Signals may also be enhanced or manipulated to improve their quality or provide information that is not sensed by humans e.
Although real-world signals can be processed in their analog form, processing signals digitally provides the advantages of high speed and accuracy. Because it's programmable, a DSP can be used in a wide variety of applications. You can create your own software or use software provided by ADI and its third parties to design a DSP solution for an application.
Digital Signal Processing is a complex subject that can overwhelm even the most experienced DSP professionals. Although we have provided a general overview, Analog Devices offers the following resources that contain more extensive information about Digital Signal Processing:.
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