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4. Suppose that the frequency response of a filter is given by:
a) Write the difference equation that relates the input a[n] to the output y[n].
(b) What is the output if the input is x[n] = δ [n]?
(c) If the input is of the form z[n] = Acos(ŵn + pi), for what values of w will the output y[n] be zero?(more…)
2. Consider the system defined by the relation y[n] = x[n] +2x[n− 1] + x[n-2]
(a) Obtain an expression for the frequency response of the system
(b) Graph the system frequency response (magnitude and phase) using the freqz command in MATLAB (attach code listing and output)
(c) Determine the output when the input is the signal x[n] = 10+4 cos(0.5πn+π/4)
(d) Determine the output with the input is the unit impulse function x[n] = δ [n].
(e) Determine the output with the input is the unit step function z[n] = u[n].(more…)