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.