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The sampling theorem can be applied in several ways. One way is to simplify a signal by expanding it to a series of finite, equally-spaced samples, such that successive samples are separated by the sample interval, T. If the sampling rate is fs samples/sec and the signal has a period T, then the sampling theorem states that the samples can be reconstructed by applying the DTFT to the discrete-time signal s(n t), n = 0, 1, 2, â€¦, N, where N = fs/T.[5] This process is known as sampsonization.

In the digital domain, the sampling theorem states that for a band-limited signal {s(t)}, there is a discrete-time signal {s(n t), n = 0, 1, 2, â€¦}, such that s(t) can be reconstructed from s(n t) if the sampling rate is greater than or equal to twice the bandwidth of the signal, B (in cycles/second).[1][2] If the signal is also periodic with a period of T, then s(n t) can be computed using the discrete-time Fourier transform (DTFT).[3][4]

Another way to apply the sampling theorem is to quantize a continuous-time signal, which yields a discrete-time signal s(n t), n = 0, 1, 2, â€¦, N, where N = f 827ec27edc