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Homework 3 (Due: Nov. 29 th ) (1) Write a Matlab program for the scaled Gabor transform .

Homework 3 (Due: Nov. 29 th ) (1) Write a Matlab program for the scaled Gabor transform . y = Gabor(x, tau, t, f, sgm) (35 scores)

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Homework 3 (Due: Nov. 29 th ) (1) Write a Matlab program for the scaled Gabor transform .

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  1. Homework 3 (Due: Nov. 29th) (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) 程式碼要寄給我， (ii) 用 function的指令寫成函式，(iii) 自己選一個 input x (用聲音檔)， 用你們的程式將 output y 算出來並畫出來， (iv) 用 tic和 toc的指令來計算程式的 running time，(v) 模擬的例子當中，請將 tau 正確的算出來，(vi) 程式執行的時間，越短越好 (以下的例子 2 秒以內) [a1, fs] = wavread('Chord.wav'); x=a1(:,1).‘; % 只取第一聲道 tau = (自己思考 tau 該怎麼算); 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) What are the advantage of (a) the S transform (b) the modified form II WDF on page 163 ? (15 scores) (3) Suppose that the WDF of x(t) is as the left figure and the WDF of exp(jat2+dt)x(bt +c). Please determine the values of a, b, c, d. (10 scores) (0,2) (-3,0) (1,0) (0, -1) (4) (a) What are the advantages of using the time-frequency analysis for filter design? (b) How do we remove the component in the right of the line f + 3t = 10 in the time-frequency plane? (20 scores) (5) 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) modulation and multiplexing, and (d) optical system analysis? Also illustrate the reasons. (20 scores) (7,4) (1,1) (7,2) (1,-1)

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