Applications of digital signal processing - Continuous and Discrete Time Signals and Systems - page 790

of 0 ≤ k ≤ 19; (b) a 32-point DFT and a sample size of 0 ≤ k ≤ 31; (c)
a 64-point DFT and a sample size of 0 ≤ k ≤ 31; (d) a 128-point DFT
and a sample size of 0 ≤ k ≤ 31; and (e) a 128-point DFT and a sample
size of 0 ≤ k ≤ 63. Comment on the leakage effect in each case.
17.2 Calculate and plot the amplitude spectra of the following DT signals:
(i) x 1 [ k ] = cos(0 . 25 π k ) , 0 ≤ k ≤ 2000;
(ii) x 2 [ k ] = cos(2 . 5 10 − 4 π k 2 , 0 ≤ k ≤ 2000;
(iii) x 3 [ k ] = cos(2 . 5 10 − 7 π k 3 ) , 0 ≤ k ≤ 11000 .
Comment on the spectral content of the signals.
17.3 Calculate and plot the spectrograms of the three signals considered in
Problem 17.2. Compare the results with those obtained in Problem 17.2.
17.4 Using M ATLAB , estimate the power spectral density of the following
signal:
x [ k ] = 2 cos(0 . 4 π k + θ 1 ) + 4 cos(0 . 8 π k + θ 2 ) ,
where θ 1 and θ 2 are independent random variables with uniform distri-
bution between [0, π ]. Use a sample realization of x [ k ] with 10 000
samples, the Bartlett window with length 1024, an overlap of 600 sam-
ples, and the average Welch approach.
17.5 Determine the frequency content of the audio signal “ chord.wav ”,
provided in the accompanying CD using (i) a spectrogram and (ii) an
average periodogram.
17.6 Consider the “ testaudio4.wav ” file provided in the accompanying
CD. Load the audio signal using the wavread function available in
M ATLAB .
(a) What is the sampling rate used to discretize the signal? What is the
total number of samples stored in the file?
(b) How many bits are used to represent each sample?
(c) Is the audio signal stored in the mono or stereo format?
(d) Estimate the power spectrum of the signal
17.7 Repeat Problem 17.6 for “ testaudio3.wav ” provided in the accom-
panying CD.
17.8 Repeat Problem 17.6 for “ bell.wav ” provided in the accompanying
CD.
17.9 Repeat Problem 17.6 for “ test44k.wav ” provided in the accompa-
nying CD.
17.10 Repeat Example 17.7 for the following audio samples:
x 1 [ k ] = [66 , 67 , 68 , 69] and x 2 [ k ] = [66 , 72 , 61 , 56] .