To design a three-band discrete spectrum analyzer for audio signals, we need to design a low-pass, a band-pass, and a high-pass IIR filters. Let the sampling frequency be F_s =10 kHz. Consider the three bands, in kHz, to be [0 F_s/4], (F_s/4 3F_s/8], and (3F_s/8F_s/2].

(a) Let all the filters be of order N = 20, and choose the cutoff frequencies so that the sum of the tree filters is an all-pass filter of unit gain.

(b) Consider the MATLAB test signal handel, use the designed spectrum analyzer to obtain the spectrum in the three bands.