DSP.Filter.IIR.Bilinear

The module contains a function for performing the bilinear transform.

The input is a rational polynomial representation of the s-domain function to be transformed.

In the bilinear transform, we substitute

       2    1 - z^-1

s <--  -- * --------

       ts   1 + z^-1

into the rational polynomial, where ts is the sampling period. To get a rational polynomial back, we use the following method:

1. Substitute s^n with (2/ts * (1-z^-1))^n == [ -2/ts, 2/ts ]^n
2. Multiply the results by (1+z^-1)^n == [ 1, 1 ]^n
3. Add up all of the common terms
4. Normalize all of the coeficients by a0

where n is the maximum order of the numerator and denominator

Documentation

zm :: (Integral b, Fractional a) => a -> b -> [a]

zp :: (Integral b, Num a) => b -> [a]

step1 :: Fractional a => a -> [a] -> [[a]]

step2 :: (Num a, Integral b) => b -> [[a]] -> [[a]]

step3 :: Num a => [[a]] -> [a]

step4 :: Fractional a => a -> [a] -> [a]

bilinear

Arguments

:: Double

T_s

-> ([Double], [Double])

(b,a)

-> ([Double], [Double])

(b',a')

Performs the bilinear transform

prewarp

Arguments

:: Double

w_c

-> Double

T_s

-> Double

W_c

Function for frequency prewarping