29 th Dec 1 Illustrate why a the multiplication of chirp and b analytic signal conversion are helpful for improving the efficiency of signal sampling 10 scores ID: 606139
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Homework 4 (Due: 26th Dec.) (1) Illustrate the following terms. (a) color noise; (b) scaling function (about the wavelet transform); (c) scalogram. (15 scores)(2) What are the vanish moments of (a) (b) x(t) = 2 for -1 < t < 1, x(t) = -1 for 1 < |t| < 3, x(t) = 0 otherwise. (10 scores)
(3) (a) What is the most important advantage of the Haar transform nowadays? (b) How many entries of the 2k-point Haar transform are equal to 0, 1, and -1? Express the solutions in term of k. (15 scores)
(4) Among the
STFT
, the
WDF
, and the
Hilbert-Huang transform
, which one is
better for the applications of (a) tone analysis, (b) random process analysis,
(c)
multiplexing, and (d) analyzing the variation of temperature?
Also illustrate the reasons
. (15 scores)Slide2
(7) 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 the t-axis, thr : the threshold used in Step 7. In Step 8, the number of non-boundary extremes can be no more than 3. The Matlab code should be handed out by Ceiba. (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);
(5) Which of the following signal is not an IMF?
Why?
(a) sin(
t
) +
t, (b) cos(t3). (5 scores)
(6)
Write two concepts you learned from the oral presentation on 12/5.
(10 scores)