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The purpose of this document is to illustrate the use of the Scilab software package in a signal processing context. We have gathered a collection of signal processing algorithms which have been implemented as Scilab functions. This manual is in part a pedagogical tool concerning the study of signal processing and in part a practical guide to using the signal processing tools available in Scilab. For those who are already well versed in the study of signal processing the tutorial parts of the manual will be of less interest. For each signal processing tool available in the signal processing toolbox there is a tutorial section in the manual explaining the methodology behind the technique. This section is followed by a section which describes the use of a function designed to accomplish the signal processing described in the preceding sections. At this point the reader is encouraged to launch a Scilab session and to consult the on-line help related to the function in order to get the precise and complete description (syntax, description of its functionality, examples and related functions). This section is in turn followed by an examples section demonstrating the use of the function. In general, the example section illustrates more clearly than the syntax section how to use the different modes of the function.
This document is an updated version of a primary work by Carey Bunks, Franc¸ois Delebecque, Georges Le Vey and Serge Steer.
Description of the Basic Tools.
Introduction.
Signals.
Polynomials and System Transfer Functions.
State Space Representation.
Changing System Representation.
Interconnecting systems.
Discretising Continuous Systems.
Filtering of Signals.
Plotting Signals.
Development of Signal Processing Tools.
Representation of Signals.
Frequency Response.
Sampling.
Decimation and Interpolation.
The DFT and the FFT.
Convolution.
The Chirp Z-Transform.
FIR Filters.
Windowing Techniques.
Frequency Sampling Technique.
Optimal filters.
IIR Filters.
Analog filters.
Design of IIR Filters From Analog Filters.
Approximation of Analog Filters.
Design of Low Pass Filters.
Transforming Low Pass Filters.
How to Use the Function iir.
Examples.
Another Implementation of Digital IIR Filters.
Spectral Estimation.
Estimation of Power Spectra.
The Modified Periodogram Method.
The Correlation Method.
The Maximum Entropy Method.
Optimal Filtering and Smoothing.
The Kalman Filter.
The Square Root Kalman Filter.
The Wiener Filter.
Optimization in filter design.
Optimized IIR filters.
Optimized FIR filters.
Stochastic realization.
The sfact primitive.
Spectral Factorization via state-space models.
Computing the solution.
Levinson filtering.
Time-Frequency representations of signals.
The Wigner distribution.
Time-frequency spectral estimation.
Bibliography