A linear-phase FIR filter should be designed with the ideal magnitude response shown in the following figure. The lower cutoff frequency, fL , is 1,200 Hz, and higher cutoff frequency, fH , is 2,200 Hz. Sampling frequency fS = 8,000 Hz.
I. Using the Fourier method, design a 9-tap filter to obtain noncausal impulse response h[n] for the desired response.
II. Compute a 9-sample Hamming window (noncausal) then apply the window to the filter.
III. Write the filter frequency response equations (magnitude and phase).