S$.$

Design a digital spectrum analyzer for processing and analyzing speech signals by dividing them into distinct frequency bands. Consider a three$-$band discrete spectrum analyzer for speech signal processing. The analyzer must classify the input signal into low, mid, and high$-$frequency bands for further analysis or feature extraction.

a$)$ Record your speech or download a signal approximately $10$ seconds duration and save it in your computer. Plot the input speech signal and its corresponding spectrum.

$(10$ Marks$)$

b$)$ Design the filter for the following specification:

Let the sampling frequency be Fs $=10KHz.$ Consider the three bands, in KHz $,$ to be $[0F\frac{s}{4},(F\frac{s}{43}F\frac{s}{8}],$ and $(3$Fs$/8$ Fs$/2].$ Let all the filters be of order, and choose the cut$-$off frequencies so that the sum of the three filters is approximately an all$-$pass filter of unit gain.

$(20$ Marks$)$

i$.$ Plot the magnitude and phase response of each filter.

ii$.$ Compute the sum of the magnitude responses of the three filters and verify if the combined response approximates an all$-$pass filter

c$)$ Apply the designed filters to the test signal and analyze the outputs. Plot the frequency spectrum of filtered signal after filtering using low$-$pass, high$-$pass and band$-$pass filter.

$(15$ Marks$)$

d$)$ Discuss the effectiveness of the filters in isolating the respective frequency components.

$(5$ Marks$)$

e$)$ Demonstration of the above results in Matlab.

$(10$ Marks$)$