Impulse-train sampling If p(t) is an impulse-train then Fourier coefficients can be given by

so that the aliasing formula becomes

Alternative derivation It can be shown that

Note that some use the notation X(Ω) in place of X(jΩ), so that the above equation can be written as

About terminology The highest frequency in signal is known as Nyquist frequency. The minimum sampling rate which, in theory, allows perfect signal recovery is known as Nyquist rate. Therefore Nyquist rate is twice Nyquist frequency.

A signal, is generally sampled at more than twice the Nyquist frequency. One of the half the sampling rate is known as folding frequency. As an example, if the voice signal is band limited to 3.3 kHz and sampled at 8 kHz then Nyquist frequency = 3.3 kHz, the Nyquist rate = 6.6 kHz, and folding frequency = 4 kHz.

To add to ambiguity, some references use phrase Nyquist frequency to refer to one half of the sampling rate.

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