#### Example 7.1 | #### Question 7.1 Question 7.2

## Nyquist sampling theorem – aliasing

If the Nyquist sampling criterion is not met, the effect is for the sum and difference components associated with each harmonic of the sampling signal to overlap with those of adjacent harmonics in the sampling spectrum. Clearly it is now not possible to filter out the wanted from the unwanted signals and thus perfect reconstruction of the original signal is not achieved. It is immediately apparent from this analysis that sampling at twice the maximum input signal frequency is thus the minimum sampling rate needed for A/D conversion. It is also evident that removal of the possible alias components when sampling at this minimum rate requires a 'brick wall' filter for signal recovery after D/A conversion. In practice, a sampling rate of at least three times the maximum sampling frequency is used in order to reduce the specification of these 'anti-aliasing' filters. Some modern A/D or D/A converters, called sigma-delta converters, use many-fold oversampling (x64 or x128 is typical) with in-built decimation or interpolation filters.

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