LR Rabiner and RW Schafer, June 3

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DRAFT: L. R. Rabiner and R. W. Schafer, June 3, 2009 496 BIBLIOGRAPHY 1. the analytical solution for the cepstrum of x1[n] 2. the recursion for ˆx1[n] based on x1[n] being a minimum phase signal 3. the computational solution for ˆx1[n] using an appropriate size FFT Your code should accept an appropriate value for a (typically in the range 0.5 to 0.99), and a size for the FFT to minimize aliasing effects. Plot the 3 resulting complex cepstrums on a common plot and plot the differences between the complex cepstrums for the recursion and the analytical solution (should be essentially zero) and for the differences between the analytical solution and the computational solution. 8.13 (MATLAB Exercise) Write a MATLAB program to compute the complex and real cesptrums of the signal: x2[n] = δ[0] + 0.85 δ[n − 100] Compute the complex and real cepstrums using computational methods discussed in this chapter, i.e., use an FFT of appropriate size with phase unwrapping to compute the complex cepstrum and use the log magnitude to compute the real cepstrum. (You might want to compare your results with those obtained using the MATLAB toolbox functions rcep and ccep). Plot the signal, the complex cepstrum and the real cepstrum on a series of 3 plots, all on a single page. 8.14 (MATLAB Exercise) Write a MATLAB program to compute the complex and real cesptrums of the signal: x3[n] = sin 2πn 100 Compute the complex and real cepstrums using computational methods discussed in this chapter, i.e., use an FFT of appropriate size with phase unwrapping to compute the complex cepstrum and use the log magnitude to compute the real cepstrum. (You might want to compare your results with those obtained using the MATLAB toolbox functions rcep and ccep). Plot the signal, the complex cepstrum and the real cepstrum on a series of 3 plots, all on a single page. 8.15 (MATLAB Exercise) Write a MATLAB program to compute the complex and real cepstrums of the following signals: 1. a section of voiced speech 2. a section of unvoiced speech
DRAFT: L. R. Rabiner and R. W. Schafer, June 3, 2009 BIBLIOGRAPHY 497 For each of the two speech signals plot the signal, the log magnitude spectrum, the real cepstrum, and the appropriately low quefrency liftered log magnitude spectrum. Use the file test 16k.wav to test your program. Specify the voiced section as starting at sample 13,000 in the file, and of duration 400 samples. Specify the unvoiced section as starting at sample 3400 in the file, and of duration 400 samples. Use a Hamming window before computing the cepstrums of the speech files. 8.16 (MATLAB Exercise) Write a MATLAB program to compute the real cepstrum of a speech file and lifter the cepstrum using both a low quefrency lifter and a high quefrency lifter to illustrate the differences in retrieving a representation of the vocal tract response (the low quefrency lifter) or the source excitation (the high quefrency lifter). Use the speech file test 16k.wav with a voiced frame beginning at sample 13,000 (of duration 40 msec) and an unvoiced frame beginning at sample 1000 (again of duration 40 msec). Use a Hamming window to isolate the frame of speech being processed. For both the voiced and unvoiced frames, plot the following quantities: 1. the Hamming window weighted speech section (make sure that your window length of 40 msec reflects the correct number of samples, based on the sampling rate of the speech signal) 2. the log magnitude spectrum of the signal with the cepstrally smoothed log magnitude spectrum (in the case of a low quefrency lifter) 3. the real cepstrum of the speech signal 4. the liftered log magnitude spectrum (for both low quefrency and high quefrency liftering operations) Make plots for both the voiced and unvoiced sections of speech, and for both the low and high quefrency lifters. Your program should accept the following inputs: the speech file being processed the starting sample for the speech frame being processed the duration of the speech frame (in msec) which must be converted to a frame duration in samples, based on the speech sampling rate the size of FFT used in cepstral computation the cutoff point of the cepstral lifter (either the high cutoff for a low quefrency lifter, or the low cutoff for a high quefrency lifter) the type of lifter (low quefrency or high quefrency)
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LR Rabiner and RW Schafer, June 3

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