Frequently, the function h(t) is not measured or specified continuously, but rather is measured at fixed intervals of time, or sampled. If h(t) is measured at the discrete times given by
n= ...-3,-2,-1,0,1,2,3...
where is known as the sampling
interval, we may write
and hn is a discrete representation of h(t).
The function h(t) is said to be band limited if its Fourier transform H(f) = 0 for |f| > fc, where fc is a finite `critical' frequency. A function may be band limited because it has been passed through a filter (e.g, an FM radio signal must be restricted by the station operators to the allowed band), or perhaps because it is generated by a process that has an upper limit to its frequency content (e.g. human speech).
The sampling theorem is very important, and states that a band-limited function f(t) is completely specified by the sampled values f(tn), provided that the sampling interval is no longer than
The frequency fc is then known as the Nyquist frequency, for the
given sampling interval .