## Nyquist sampling

One of the key goals in waveform sampling is to digitize only the minimum number of samples necessary to represent the waveform accurately and hence allow accurate reconstruction on reception.

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#### The minimum rate at which an arbitrary waveform can be sampled without loss of information is in fact twice the bandwidth of the input waveform.

#### This is known as the Nyquist sampling criterion. Sampling at less than twice the bandwidth of the input signal (equivalent to twice the maximum modulation frequency for baseband signals) results in what is termed aliasing.

The Nyquist sampling requirement can be derived intuitively from our knowledge of Fourier Series summarized in Chapter 1. We can view the sampling process as the mixing of the input signal with a train of very narrow data sampling pulses which will result in sum and difference components appearing at the mixer output for each harmonic of the pulse waveform mixing with the signal waveform as shown. This is the spectrum that would effectively appear at the output of a D/A converter. In order to reconstruct the input waveform correctly, the D/A output needs to be filtered so that only the spectral components present within the source signal remain.