dsp-0.2.1: Haskell Digital Signal Processing

Portability portable experimental m.p.donadio@ieee.org

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