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) 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)
(7,4)
(0,2)
(-3,0)
(1,0)
(1,1)
(7,2)
(0, -1)
(1,-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)