DSP.Filter.IIR.Bilinear

Description

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

Synopsis

# Documentation

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

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

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

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

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

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

Arguments

 :: Double T_s -> ([Double], [Double]) (b,a) -> ([Double], [Double]) (b',a')

Performs the bilinear transform

Arguments

 :: Double w_c -> Double T_s -> Double W_c

Function for frequency prewarping