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# bilt

bilinear or biquadratic transform SISO system given by a zero/poles representation

### Syntax

`[npl,nzr,ngn] = bilt(pl,zr,gn,num,den)`

### Arguments

pl

a vector, the poles of the given system.

zr

a vector, the zeros of the given system.

num

a polynomial with degree equal to the degree of `den`, the numerator of the transform.

den

a polynomial with degree 1 or 2, the denominator of the transform.

npl

a vector, the poles of the transformed system.

nzr

a vector, the zeros of the transformed system.

ngn

a scalar, the gain of the transformed system.

### Description

function for calculating the gain poles and zeros which result from a bilinear transform or from a biquadratic transform. Used by the functions iir and trans.

### Examples

```Hlp=iir(3,'lp','ellip',[0.1 0],[.08 .03]);
pl=roots(Hlp.den);
zr=roots(Hlp.num);
gn=coeff(Hlp.num,degree(Hlp.num))/coeff(Hlp.den,degree(Hlp.den));
z=poly(0,'z');
a=0.3;
num=z-a;
den=1-a*z;
[npl,nzr,ngn] = bilt(pl,zr,gn,num,den)

Hlpt=ngn*poly(nzr,'z','r')/poly(npl,'z','r')

//comparison with horner
horner(Hlp,num/den)```

### See also

• iir — iir digital filter
• trans — low-pass to other filter transform
• horner — avaliação polinomial/racional
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