A causal, stable discrete system has the rather strange transfer function H(z)=cos(z−1).
a. Write MATLAB code that will compute and plot the magnitude response of this system over an appropriate range of digital frequencies Ω. Comment on the system.
b. Determine the impulse response h[n]. Plot h[n] over (0 ≤ n ≤ 10).
c. Determine a difference equation description for an FIR filter that closely approximates the system H(z)=cos(z-1). To verify proper behavior, plot the FIR filter's magnitude response and compare it with the magnitude response computed.