Subject: Speech Processing

Topic: Homomorphic Speech Processing

Difficulty: Medium

(i) The speech signals gives as input to system consists of periodic excitation convolved with the impulse response of the vocal tract which is slowly varying function.

(ii) The FFT block takes the DFT of a signal to obtained the spectrum of the signal. When we take the log magnitude we get amplitude calculation in dB.

(iii) It can be seen that the periodic excitation is rapidly varying and the vocal tract response, which is the envelop of the plot, is slowly varying function.

(iv) When we take IFFT of the signal, we find a slowly varying function of vocal tract cluster near the origin and a rapidly varying function appearing as regular pulses away from the origin.

(v) We can now use a cepstral window allowing the pitch information (the rapidly varying function) to pass through.

(vi) The FFT output of this windowed cepstrum will be spectrum with only a rapidly varying function.

(vii) We tract the peak of this spectrum, we find the pitch frequency.

(viii) The slowly varying function of vocal tract is now isolated and hence the possibility of the first formats overlapping with the pitch frequency removed.