Let us look at the signal xs(t) coming from the sampling of x(t) at the sampling frequency fs:
According to equation (3.24), the Fourier transform of the signal xs(t) verifies the following relation:
If we introduce fr, the frequency reduced or normalized in relation to the sampling frequency , we will have:
The Fourier transform of a discrete sequence is one of the most commonly used spectrum analysis tools. It consists in decomposing the discrete-time signal on an orthonormal base of complex exponential functions.
Xs (fr) is generally a complex function of the reduced frequency fr, as we see in the following expression:
Among the properties of the Fourier transform, we can first of all consider that:
Then, using equation (3.54), we have:
Secondly, we can verify that the Fourier ...