bilinear_transform

Bilinear transform: conversion from Laplace transform to z transform.

Namespace: dsp::filter

Prototype

FRat<cfloat> bilinear_transform(const FRat<cfloat> &ha, float fe)

Parameters

haLaplace transform of the system (rational fraction)
feSampling frequency

Returns

Z transform (rational fraction)

Description

The bilinear transform enables to approximate an analog transfert function (Laplace transform) with a digital tranfert function (z transform).

To do this, the \(s\) variable in Laplace transform is replaced by the following approximation: \[ s \mapsto 2 f_e \cdot \frac{1 - z^{-1}}{1 + z^{-1}} \]

See also

fd2fa(), fa2fd()