Homework 3 (Due: Dec. 4 th ) (1) Write a Matlab program for the scaled Gabor transform .

1. Homework 3 (Due: Dec. 4th) (1) Write a Matlab program for the scaled Gabor transform. y = Gabor(x, tau, t, f, sgm) (35 scores) x: input, tau: samples on t-axis for the input, t: samples on t-axis for the output f: samples on f-axis, sgm: bound of the integration y: output (i) The code should be mailed to me， (ii) Write as a function ，(iii) Choose an input x (Use *.wav)， plot theoutput y ， (iv) Usetic andtocto show therunning time，(v) Determinetau of the following example，(vi) The running time should be as short as possible (for the following example, within 2 seconds) [a1, fs] = wavread('Chord.wav'); x=a1(:,1).‘; % only extract the first channel tau = (? Please think how to determine tau); dt = 0.01; df= 1; t= 0:dt:max(tau); f= 80:df:1000; sgm= 200; tic y= Gabor (x, tau, t, f, sgm); toc

2. (2) Why the generalized spectrogram can have high clarity in both time axis and the frequency axis and avoid the cross term problem? (10 scores) (3) Suppose that the WDFs of x(t) and exp(j(at3+bt2+ct))x(dt +e) are the right and the left figures, respectively. Determine the values of a, b, c, d , e. (15 scores) (-3,2) (3,2) (1,4) (13,4) parabola (13,2) (1,2) (-3,-2) (3,-2) (7,0) (4) Among the Gabor transform and the WDF, which one is better for the applications of (a) filter design for deterministic signal , (b) signal sampling, (c) multiplexing, (d) optical system analysis, and (e) random process analysis? Also illustrate the reasons. (20 scores) (5) Why the Fresnel transform of a stationary random process is still a stationary one? (illustration by the WDF instead of mathematical analysis) (10 scores) (6) Write at least two concepts you learned from the presentation on 11/27. (10 scores)