CONTENTS

Content                                                                                   Page No
Abstract (Brief description of the project)                                                  5
Chapter 1: Introduction (Brief theory)                                                       7
Chapter 2: Tasks and their simulation results
(a)    Task1:   Simulation results, Plots/graphs, figures,
tables etc                                                                             11
(b)   Task2:   Simulation results, Plots/graphs, figures,
tables etc                                                                             12
(c)    Task3:   Simulation results, Plots/graphs, figures,
tables etc                                                                             13

Chapter 3: Conclusions and future scope                                                    15

ABSTRACT
Objectives:
(a) Load, display and manipulation of speech signals.
(b) Estimate the fundamental frequency of a section of speech signal from its waveform using autocorrelation.
(c) Estimate the fundamental frequency of a section of speech signal from its spectrum using cepstrum.
(d) Compute and plot the spectrum of speech signals.
This process is shown in the following block diagram.

Fig 1: Computation of Cepstrum of a Signal

Task1: Fundamental frequency estimation-time domain: Auto-correlation
The perception of pitch is more strongly related to periodicity in the waveform itself. A means to estimate fundamental frequency from the waveform directly is to use autocorrelation. The autocorrelation function for a section of signal shows how well the waveform shape correlates with itself at a range of different delays. We expect a periodic signal to correlate well with itself at very short delays and at delays corresponding to multiples of pitch periods. We can estimate the fundamental frequency by looking for a peak in the delay interval corresponding to the normal pitch range in speech.

Task2: Fundamental frequency estimation- frequency domain: Cepstrum
A reliable way of obtaining an estimate of the dominant fundamental frequency for long, clean, stationary speech signals is to use the cepstrum. The cepstrum is a Fourier analysis of the logarithmic amplitude spectrum of the signal as shown in Fig.1. If the log amplitude spectrum contains many regularly spaced harmonics, then the Fourier analysis of the spectrum will show a peak corresponding to the spacing between the harmonics: i.e. the fundamental frequency. Effectively we are treating the signal spectrum as another signal, then looking for periodicity in the spectrum itself.
The cepstrum is so-called because it turns the spectrum inside-out. The x-axis of the cepstrum has units of frequency, and peaks in the cepstrum (which relate to periodicities in the spectrum) are called harmonics. To obtain an estimate of the fundamental frequency from the cepstrum we look for a peak in the frequency region corresponding to typical speech fundamental frequencies.