**Speech Processing
by Computer**

LECTURE 4

SPECTRAL ANALYSIS

**Objectives**

By the end of the
session you should:

• understand
that a discrete spectrum is just another way of describing a discrete signal

• be
able to outline the relationship between filterbank analysis and spectral
analysis

• be
able to describe the general operation of the discrete fourier transform (DFT)

• appreciate
the time and frequency resolution compromises associated with the DFT

• know
that the 'fast' fourier transform (FFT) is just an efficient implementation of
the DFT

• be
able to describe how a DFT can be used to create a spectrogram

• appreciate
that other mathematical analyses of the spectral content of a signal are
available

• appreciate
that linear prediction (LPC) gives us a smoothed spectral estimate of a speech
signal related to the vocal tract filter

**Outline**

4. Spectral Analysis

4.1. Basis of discrete
spectral analysis

4.1.1. Narrow bandpass
filtering

4.1.2. Convolution with
sinusoid

4.2. Discrete Fourier
Transform

4.2.1. General operation

4.2.2. Time and
frequency resolution

4.2.3. Fast
implementation

4.2.4. Spectrograms

4.3. Spectral
Modelling

4.3.1. Linear prediction

4.3.2. Inverse filtering

**Reading**

Rosen
and Howell, __Signals and Systems for Speech and Hearing__, Academic Press,
1991, Chapter 10.