**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.

**Task3:**Repeat the above tasks-1 and 2 for noisy speech signals.

**Task4:**Repeat the above tasks-1 and 2 for noisy musical signals.

**Task5:**Repeat the above tasks-1 and 2 for noisy musical speech signals.

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