Practical Digital Signal Processing

4

Frequency-domain representation of discrete-time signals

So far we have been looking at signals as a function of time or an index in time. Just like continuous-time signals, we can view a time signal as one that consists of a range of frequencies. A signal can be observed as a trace on an oscilloscope or we can observe it through a spectrum analyzer, which displays the strength of the frequency components that make up that signal. Analytically, Fourier analysis provides us with the connection between the time-domain and frequency-domain view of the signal. It tells us that provided some conditions are satisfied; the two views are equivalent. Thus sometimes it is more convenient to describe a signal in the time-domain whereas the frequency-domain ...