Nyquist ISI Criterion - Nyquist Criterion

Nyquist Criterion

If we denote the channel impulse response as, then the condition for an ISI-free response can be expressed as:

for all integers, where is the symbol period. The Nyquist theorem says that this is equivalent to:

,

where is the Fourier transform of . This is the Nyquist ISI criterion.

This criterion can be intuitively understood in the following way: frequency-shifted replicas of H(f) must add up to a constant value.

In practice this criterion is applied to baseband filtering by regarding the symbol sequence as weighted impulses (Dirac delta function). When the baseband filters in the communication system satisfy the Nyquist criterion, symbols can be transmitted over a channel with flat response within a limited frequency band, without ISI. Examples of such baseband filters are the raised-cosine filter, or the sinc filter as the ideal case.