LR Rabiner and RW Schafer, June 3

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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
DRAFT: L. R. Rabiner and R. W. Schafer, June 3, 2009 BIBLIOGRAPHY 499 effects of the low quefrency lifter on the smoothed log magnitude spectrum. Use the file test 16k.wav with voiced frame starting sample of 13,000 and 40 msec frame duration to compute the real cepstrum of the voiced frame. Using a sequence of low quefrency lifters, compute the smoothed log magnitude spectrum and plot the results on top of the curve of the unsmoothed log magnitude spectrum. Repeat for low quefrency cutoffs of 20,40,60,80,100.
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LR Rabiner and RW Schafer, June 3

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