Homework 1 (Due: 16 th Oct.)
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(1) Which of the following applications are the proper applications of time frequency analysis? Also illustrate the reasons. (a) Filter Design. (b) Music signal analysis. (c) Image analysis. (15 scores)
(2) Does the scaling operation x(σt) affect the number of sampling points? Why?
(3) What are the most important advantage and disadvantage of the wavelet transform when compared with time-frequency analysis? (10 scores)
(4) (a) How does the parameter B affect the resolution of the rec-STFT?
(b) If we want to analyze a vocal signal (the units in the t-axis and the f-axis are second and Hz), should we use a larger or a smaller value of B? Why?
(5) (a) What is the relation between the Gaussian function and the rectangular function? (b) Why better time-frequency analysis result can be obtained if one uses the Gaussian window instead of the rectangular window?
(6) Does satisfy the lower bound of
the uncertainty principle ( )? Why? (10 scores)
(7) Write a Matlab program gwave.m that can generate a *.wav file whose instantaneous frequency is ±(at2 + bt + c) Hz, the length of the file is T second, and the sampling frequency is Fs Hz.
gwave (a, b, c, T, Fs)
The Matlab code should be mailed to me. (25 scores)