Summary: Correlates the unit response with the frequency and time domains.

Because we are interested in actual computations rather than
analytic calculations, we must consider the details of the
discrete Fourier transform. To compute the length-
*a unit-sample input results in the output's Fourier
transform equaling the system's transfer function*.

This statement is a very important result. Derive it yourself.

The DTFT of the unit sample equals a constant (equaling 1). In this case, the Fourier transform of the output equals the transfer function.

In the time-domain, the output for a unit-sample input is known
as the system's unit-sample response, and is
denoted by
*in terms of the discrete-time Fourier
transform*.