LR Rabiner and RW Schafer, June 3

DRAFT: L. R. Rabiner and R. W. Schafer, June 3, 2009
498 BIBLIOGRAPHY
8.17 (MATLAB Exercise) Write a MATLAB program to demonstrate
phase unwrapping for computation of the complex cepstrum of a
speech file. You must carefully compensate any linear phase component
before attempting to do phase unwrapping. Choose a section
of a voiced speech signal and compute its DFT and decompose it
into the log magnitude and phase components (this is the wrapped
phase). Use the MATLAB toolbox command for phase unwrapping
to unwrap the phase. Compute the complex cepstrum, lifter the
cepstrum using either a low or high quefrency lifter and transform
the liftered signal back to the frequency domain and ultimately to
the time domain. Plot the following quantities on a single page:
1. the original and cepstrally smoothed (in the case of a low quefrency
lifter) log magnitude spectra
2. the original (wrapped) phase, the unwrapped phase, and the
cepstrally smoothed phase
3. the complex cepstrum calculated with a large size FFT
4. the resulting estimate of the vocal tract response (obtained by
low quefrency liftering) or the excitation signal (obtained by
high quefrency liftering)
Use the speech file test 16k.wav with starting sample 13,000 and
frame size 40 msec to test your program. Use an FFT size of 4096
samples and a lifter cutoff of 50 samples. Plot the results for both a
low quefrency and a high quefrency lifter.
8.18 ( MATLAB Exercies) Write a MATLAB program to illustrate the
effects and magnitude of aliasing in computing the real cepstrum of a
speech signal. Your program should compute the real cepstrum of a
frame of speech using an FFT size of 8192 (the standard) and repeat
the computation of the exact same frame of speech with FFT sizes
of 4096, 2048, 1024 and 512. Compare the resulting cepstrums and
plot the differences between the real cepstrum computed using an
8192 point FFT with each of the cepstrums computed using smaller
size FFTs. This exercise illustrates the level of aliasing that is common
in speech processing using reasonable size frames of speech and
reasonable size FFTs. Use the speech file test 16k.wav to illustrate
the effects of aliasing. Choose a voiced speech frame starting
at sample 13,000, of duration 40 msec for this exercise. Plot the
8192 point FFT cepstrum (the standard) in the top panel and the
differences between the 8192 point FFT cepstrum and cepstrums
computed using smaller size FFTs in the lower panel.
8.19 (MATLAB Exercise) Write a MATLAB program to demonstrate
the effects of the cutoff quefrency of the low quefrency lifter on the
smoothing of the log magnitude spectrum. Using a voiced section of
a speech file, calculate the real cepstrum and apply a low quefrency
lifter with cutoff quefrencies of 20, 40, 60, 80 and 100, and show the