Consider the first-order system described by y[n] = 0.8y[n−1] +0.2x[n]. It is excited by the…

Consider the first-order system described by y[n] = 0.8y[n−1] +0.2x[n]. It is excited by the linear FM signal (see Example 5.2) given by

where B = 10 Hz, Fs = 100 Hz, and τ = N/Fs = 10 sec.

(c) Process the signal x[n] through the system using MATLAB to obtain y[n] = y(nT) and plot it over 0 ≤ t ≤ τ sec. Verify that the amplitude of x[n] is attenuated according to the frequency response H(ej2πF).

Example 5.2

The procedure illustrated in Figure 5.1 provides the magnitude and phase response at a single frequency ω. If we repeat this process for various values of ω, we can compute the frequency response at any frequency interval of interest with the desired resolution.