Start with a signal x(t) = 8 cos(30t) and sample, window, and periodically repeat it using a sampling rate of _s = 60 and a window width of N = 32. For each signal in the process, graph the signal and its transform, either CTFT or DTFT.

Sample each signal x(t) N times at the rate fs creating the signal x[n]. Graph x(t) versus t and x[n] versus n Ts over the time range 0 _s. Find the DFT X[k] of the N samples. Then graph the magnitude and phase of X(f) versus f and X[k]/N versus kover the frequency range _s/2 _s/2, where = _s/N. Graph X[k]/N as an impulse function of kusing the MATLAB stem command to represent the impulses.

(a) x(t) = 4cos(200t), _s = 800, N = 32

(b) x(t) = 6 rect(2t) ₁(t), _s = 16, N = 128

(c) x(t) = 6sinc(4t) ₁(t), _s = 16, N = 128

(d) x(t) = 5cos(2t)cos(16t), _s = 64, N = 128