4. Filter Design. Recall that an ideal low pass filter (here with cutoff w pi/12 ) has the following impulse and frequency response We want to modify this filter to

be an ideal band pass filter with passband centered at w = pi/4 and bandwidth 2pi/12 a) Make a sketch of the ideal band pass filter frequency response magnitude (Har (e)) with properties as described above b) Write an expression for H (e) in terms of H (e)(Hint: use the frequency shift property of the DTFT c) Write an expression for bandpass filter impulse response h {n} use MATLAB to evaluate your expressions for h [N] for n = 1 to 100 use freqz to plot the frequency response of this 100 point bandpass filter ( do not use firl to create your own bandpass filter)