Subject: Speech Processing

Topic: Homomorphic Speech Processing

Difficulty: Medium

Pitch period measurement using cepstral domain.

(i) The speech signal 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 formants overlapping with the pitch frequency removed.

Evaluation of Formants using Cepstrum

Each formant is described by the three parameters:

a) Amplitude of the formants.

b) Position of the formants.

c) BW of the formants.

Evaluation of formants for voiced speech segment

(i) Speech signal given as input to the system consists of periodic excitation convolved with the impulse response of the vocal tract, which is slowly varying function.

(ii) The FFT block take DFT of the signal and gives out the spectrum of the signal. When we take the log of magnitude of FFT output, that the periodic excitation is seen as a rapidly varying function and the vocal tract response, which appears as the envelop of the spectrum, is slowly varying function.

(iii) IFFT, we got cepstral domain.

(iv) Allowing the formants information to pass through.

(v) Finally get formants.