EE 679 Speech Processing Computing Assignment 1: Signal synthesis and DTFT based analysis

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1. Given the following specification for a single-formant resonator, obtain the transfer function of the filter
H(z). Plot its magnitude response (dB magnitude versus frequency) and impulse response.
F1 (formant) = 1 kHz
B1(bandwidth) = 200 Hz
Fs (sampling freq) = 16 kHz
2. Excite the above resonator (filter) with a source given by an impulse train of F0 = 150 Hz. Compute the
output of the source-filter system over the duration of 0.5 second. Plot the time domain waveform. Also
play it out and comment on the sound quality.
3. Vary the parameters as indicated below and comment on the differences in waveform and sound quality
for the different parameter combinations.
(a) F1 = 300 Hz, B1 = 100 Hz; F1=1200 Hz, B1 = 200 Hz
(b) F0 = 120 Hz; F0 = 180 Hz
4. In place of the simple single-resonance signal, synthesize the following more realistic vowel sounds at
two distinct pitches (F0 = 120 Hz, F0 = 220 Hz). Keep the bandwidths constant at 100 Hz for all
formants. Duration of sound: 0.5 sec
Vowel F1, F2, F3
/a/ 730, 1090, 2440
/i/ 270, 2290, 3010
/u/ 300, 870, 2240
5. Signal Analysis:
Compute the DTFT magnitude (dB) spectrum of any 2 of the vowel sounds you have synthesized. Use
rectangular and Hamming windows of lengths: 10 ms, 40 ms, 100 ms. (i) Comment on the similarities
and differences between the different spectra. (ii) Estimate the signal parameters from each of the spectra
and compare with the ground-truth.