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Sampling Rates
When converting an analogue audio wave to digital, we take samples, as shown on the previous page, and record their level. The frequency of the samples is referred to as the sampling rate.
In the picture below, you can see that 5 samples are shown of the wave at exact intervals. Later, when the wave is re-created from the data the converter will use the measurements taken, but will have to guess the bit in between to make a complete wave. As a result, the number of samples we take has a direct influence on the accuracy of the restored wave later on, and so affects the sound quality.
How do we decide the sampling rate? Well firstly there is an obvious correlation between the number of samples and the amount of data we have. The higher the sample rate, the more data must be stored. So where we store it affects what we can record. The other important consideration is the frequency of the audio wave to be recorded. This is important because if we don't sample often enough, the high frequency sounds might happen between two of our samples and therefore not be recorded. As a general rule of thumb, the sampling rate needs to be a minimum of twice the highest audio frequency to be recorded.
Using the Compact Disc as an example, the sampling rate is 44.1 kHz. This was chosen because the human ear can hear up to approximately 20kHz, so the sound to be recorded needed to reach at least this level. For some headroom 22kHz was chosen as the maximum audio frequency to be sampled.
Higher Rates
As mentioned there is a minimum sampling rate that is needed of twice the maximum frequency to be recorded. However in the world of audio, 'minimum' is not usually the done thing! As the sampling rate is increased there can be a marked improvement in sound quality for a couple of reasons. Firstly higher frequencies present in the signal are recorded too. Whilst these are not audible to the human ear, they can affect lower frequencies that are so they do affect the sound. The other reason for quality improvement is due to the sampling at the top audio frequencies.
In a low frequency audio wave the sampling frequency is a large multiple of the wave period, so there are many samples with which to re-create the wave later. However, if you consider a 22kHz audio signal sampled by a 44kHz clock as on standard CDs, then there are only two samples taken for a complete wave period. When this data is later converted back to analogue, then the digital to analogue converter will of course produce a 22kHz audio signal but this is little more than a square wave and a very crude approximation of the original sine wave. It can be smoothed by filters of course but it is much better to have more data to get a better D to A conversion. In this same example a 1kHz tone will have 44 samples per period with which to approximate an analogue wave - much better.
So by increasing the sampling frequency way above 44kHz, the higher audible frequencies will have much better definition. It is now quite common for audio to be sampled above the original standards of 44.1kHz for CD and 48kHz for DAT, which were the accepted norms for many years. The next step used was 88.2 kHz and 96 kHz, a doubling of the original sampling rates, and the ultimate studio recording equipment now samples at 176.4 kHz or more commonly 192 kHz.
In the example above, when sampled at 192kHz, the 22kHz audio wave will have nearly 9 samples per period which is much better for the basic resolution of the DAC output, before final discrete filtering.