# Documentation

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# zpkftransf

Zero-pole-gain frequency transformation

## Syntax

[Z2,P2,K2] = zpkftransf(Z,P,K,AllpassNum,AllpassDen)

## Description

[Z2,P2,K2] = zpkftransf(Z,P,K,AllpassNum,AllpassDen) returns zeros, Z2, poles, P2, and gain factor, K2, of the transformed lowpass digital filter. The prototype lowpass filter is given with zeros, Z, poles, P, and gain factor, K. If AllpassDen is not specified it will default to 1. If neither AllpassNum nor AllpassDen is specified, then the function returns the input filter.

## Examples

Design a prototype real IIR halfband filter using a standard elliptic approach:

[b, a] = ellip(3,0.1,30,0.409);
[AlpNum, AlpDen] = allpasslp2lp(0.5, 0.25);
[z2, p2, k2] = zpkftransf(roots(b),roots(a),b(1),AlpNum,AlpDen);

Verify the result by comparing the prototype filter with the target filter:

fvtool(b, a, k2*poly(z2), poly(p2));

After transforming the filter, you get the response shown in the figure, where the passband has been shifted towards zero.

## Arguments

VariableDescription
Z

Zeros of the prototype lowpass filter

P

Poles of the prototype lowpass filter

K

Gain factor of the prototype lowpass filter

FTFNum

Numerator of the mapping filter

FTFDen

Denominator of the mapping filter

Z2

Zeros of the target filter

P2

Poles of the target filter

K2

Gain factor of the target filter