# 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-planeh=[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);