Basic tools for Signal Processing

This article is detailing the very rich paper on Signal Processing in Scilab.

Polynomials and System Transfer Functions

Polynomials, matrix polynomials and transfer matrices are also defined and Scilab permits the definition and manipulation of these objects in a natural, symbolic fashion. Polynomials are easily created and manipulated. The poly primitive in Scilab can be used to specify the coefficients of a polynomial or the roots of a polynomial.

//demonstrate evaluation of discrete filter

//on the unit circle in the z-plane

h=[1:5,4:-1:1];

hz=poly(h,'z','c')

f=(0:.1:1);

hf=freq(hz,1,exp(%pi*%i*f));

hf'

State Space Representation

The classical state-space description of a continuous time linear system is :

where A, B, C, and D are matrices and x0 is a vector and for a discrete time system takes the form

State-space descriptions of systems in Scilab use the syslin function.

Changing System Representation

Sometimes linear systems are described by their transfer function and sometimes by their state equations. In the event where it is desirable to change the representation of a linear system there exists two Scilab functions which are available for this task. The first function tf2ss converts systems described by a transfer function to a system described by state space representation. The second function ss2tf works in the opposite sense.

//Illustrate use of ss2tf and tf2ss

sl=tf2ss(h)

h=ss2tf(sl)

h1=iir(3,'lp','butt',[.3 0],[0 0])

h1=syslin('d',h1);

s1=tf2ss(h1)

Here the transfer function of a discrete IIR filter is created using the function iir (see Section 4.2). The fourth element of h1 is set using the function syslin and then using tf2ss the state-space representation is obtained in list form.

Filtering of Signals

Filtering of signals by linear systems (or computing the time response of a system) is done by the function flts which has two formats . The first format calculates the filter output by recursion and the second format calculates the filter output by transform.

//make signal and filter

[h,hm,fr]=wfir('lp',33,[.2 0],'hm',[0 0]);

t=1:200;

x1=sin(2*%pi*t/20);

x2=sin(2*%pi*t/3);

x=x1+x2;

z=poly(0,'z');

hz=syslin('d',poly(h,'z','c')./z**33);

yhz=flts(x,hz);

subplot(1,2,1)

plot(x);

subplot(1,2,2)

plot(yhz);