(4) What is the most important advantage of the Haar transform nowadays ? (10 scores)

1. Homework 4 (Due: 26th Dec.) (1) (a) Why the linear canonical transform of a white noise is still a white noise? (illustration by the WDF instead of mathematical analysis) (b) Find the constraints of the parameters {a, b, c, d} of the LCT such that the LCT of a stationary random process is still a stationary one. (20 scores) (2) Among the Gabor transform, the WDF, the HHT, and the wavelet transform , which one is better for the applications of (a) modulation and multiplexing,(b) climate data analysis, (c) image compression, (d) random processanalysis? Also illustrate the reasons. (15 scores) (3) What are the similarities and differences between the sinusoid function and the empirical mode function? (10 scores) (4) What is the most important advantage of the Haar transform nowadays ? (10 scores)

2. (5) What are the roles of (a) the vanish moment and (b) the scaling function for the wavelet continuous wavelet transform ? (15 scores) (6)Write a Matlab program of the Hilbert-Huang transform. y = hht(x, t, thr) x: input, y: output (each row of y is one of the IMFs of x), t: samples on thet-axis, thr : the threshold used in Step 7. The code should be mailed to me. (30 scores) Example: t = [0: 0.01: 10]; x = 0.2*t + cos(2*pi*t) + 0.4*cos(10*pi*t); thr = 0.2; y = hht(x, t, thr);