CD Audio Sampling and Reconstruction – by Dave Kimber

CD audio in a nutshell

The original audio signal is sampled at a rate of 44.1kHz. Each sample is digitised, using an analogue to digital converter (ADC) with 16-bit resolution. By clever means this binary data is stored on a plastic disc. In the CD player a laser diode reads off the data, and via various decoding and error correction methods, the original 16-bit data is accurately recovered. This data is fed to a digital to analogue converter (DAC) which recovers the original audio signal. This is then amplified in the usual way before going to loudspeakers or headphones.

The big complication comes from a fundamental restriction on sampling. The Nyquist criterion says that the original signal can only be recovered if the sampling rate is at least twice as high as the highest frequency component in the audio. Putting it the other way round, for a given sampling rate the audio must not exceed the Nyquist limit of half the sampling rate. So at a sampling rate of 44.1kHz, as used by CD, the audio must not exceed 22.05kHz. A low-pass filter is needed to ensure this. Ideally it should pass everything up to about 20kHz, attenuate anything from 20 to 22.05kHz, and completely block anything above 22.05kHz. This is called the anti-aliasing filter. Any signals above 22.05kHz getting through will produce a digital output which is indistinguishable from that produced by a lower frequency, reflected around the Nyquist limit. So a signal at 23kHz would look exactly like one at 21.1kHz. This is aliasing. No filter is perfect, and the constraints of causality mean that a sharp amplitude response causes problems with phase response. Nevertheless, we can assume that a CD contains little signal above 20kHz and it cannot carry any signal above 22.05kHz.

An issue similar to aliasing arises in the CD player. The bare output from the DAC includes both the wanted audio signal and unwanted image signals at higher frequencies. This can be seen in the 5kHz figure. The dark blue trace shows the original input sine wave. The red trace is the output from the DAC. The magenta trace shows the difference between this and the desired output (green); it is clear that the residual contains high frequency components. The CD player thus needs a low-pass filter, known as the reconstruction filter.

CD player technology

Early CD players used essentially the technique outlined above, but quickly acquired a reputation for poor sound quality. It was thought that the problem came from the reconstruction filter. A sharp cutoff at 20kHz caused phase problems at lower frequencies.

Philips developed a new technique, called oversampling. This replaces the sharp analogue filter with an even sharper digital filter. Digital filters can achieve results which would be difficult or realistically impossible with analogue filters. Phase correction can .....

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