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A quick primer on basic digital audio theory and pulse code modulation. Everyone needs to know this...

PCM stands for 'pulse code modulation' and is the basis of digital recording of all kinds from CD to digital tape to hard disk.

Don't bother trying to understand what the pulses are yet, or how the code is modulated - that will only make sense when you know the system backwards anyway.

Let's start with an electrical signal varying in voltage between around minus 1 volt and plus 1 volt - a typical audio signal. We want to describe this changing voltage in terms of numbers rather than leave it as volts. How many different numbers do we need?

65,536 would be good. That corresponds to 2 to the power of 16, which is exactly what you would find in the CD system. We call it '16-bit resolution'.

So now, at any moment we need to measure the level of the voltage (which is known as 'sampling'), and assign it to one of those 65,536 steps, then give it a binary number to say which step it was on.

So the full voltage range between around minus 1 volt and plus 1 volt is divided into 65,536 steps. Any voltage falling in between two steps is allocated to the nearest one. This is known as 'quantization'.

Now we need to know how often this needs to be done to represent the changing level of the signal adequately. Without too much theory, it turns out that we need to consider the upper frequency limit of human hearing, which we take to be 20,000 Hz, which is the same as 20 kHz. To adequately store changes in the signal level occuring this rapidly, we need to take samples at least at twice this rate, or 40,000 samples per second. In practice, we need a safety margin, so the 'sampling rate', as we call it, is commonly 44,100 Hz, or 44.1 kHz. Once again, this is what you would find in the CD system.

In summary therefore, we take samples of the voltage signal 44,100 times per second, and allocate each sample to the nearest of 65,536 steps, recording this as a sequence of binary numbers. On playback, these numbers can be converted back into a voltage.

In a nutshell, this is PCM. Nowhere near everything, but a good start.

By David Mellor Monday October 16, 2006