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Homework 2 (Due: 4/25)

Homework 2 (Due: 4/25).

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Homework 2 (Due: 4/25)

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  1. Homework 2 (Due: 4/25) (1) Suppose that the ideal filter is Hd(F) = jF when 0 ≦ F < 0.5, Hd(0.5) = 0, Hd(F) = j(F–1) when 0.5 < F < 1 where F is the normalized frequency . Write a Matlab program that uses the frequency sampling method to design a (2k+1)-point discrete filter(kis an input parameter and can be any integer). The impulse response of the filter should be shown and the Matlab program should be mailed to me. (25 scores) (2) What are the advantages and the disadvantages of the IIR filter when compared with the FIR filter? (15 scores) (3) Suppose that an IIR filter is as follows: (a) Find its cepstrum. (b) Convert the IIR filter into the minimum phase filter. (20 scores)

  2. (4) (a) Why the cepstrum is more suitable for dealing with the multipath problem than the equalizer? (b) Why the Mel-frequency cepstrum is more suitable for dealing with the acoustic signal than the original cepstrum? (15 scores) (5) Which of the following voice sounds louder? Why? (i) cos(250πt), (ii) cos(500πt), (iii) cos(1000πt), (iv) cos(2000πt). (10 scores) (6) Suppose that a smooth filter is h[n] = 0.8|n| for |n| ≦ 10, h[n] = 0 otherwise. Also suppose that x[n] = 0 for n < 0 and n > 1000. Try to implement y[n] =x[n] * h[n] (* means the convolution) with the least number of multiplications. (The number of multiplications should be shown). (15 scores)

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