dsp-0.2.1: Haskell Digital Signal Processing

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

DSP.Filter.IIR.IIR

Description

IIR functions

IMPORTANT NOTE:

Except in integrator, we use the convention that

`y[n] = sum(k=0..M) b_k*x[n-k] - sum(k=1..N) a_k*y[n-k]`
`         sum(k=0..M) b_k*z^-1`
`H(z) = ------------------------`
`       1 + sum(k=1..N) a_k*z^-1`

Synopsis

# Documentation

Arguments

 :: Num a => a a -> [a] x[n] -> [a] y[n]

This is an integrator when a==1, and a leaky integrator when `0 < a < 1`.

`y[n] = a * y[n-1] + x[n]`

Arguments

 :: Num a => a a_1 -> a b_0 -> a b_1 -> [a] x[n] -> [a] y[n]

First order section, DF1

`v[n] = b0 * x[n] + b1 * x[n-1]`
`y[n] = v[n] - a1 * y[n-1]`

Arguments

 :: Num a => a a_1 -> a b_0 -> a b_1 -> [a] x[n] -> [a] y[n]

First order section, DF2

`w[n] = -a1 * w[n-1] + x[n]`
`y[n] = b0 * w[n] + b1 * w[n-1]`

Arguments

 :: Num a => a a_1 -> a b_0 -> a b_1 -> [a] x[n] -> [a] y[n]

First order section, DF2T

`v0[n] = b0 * x[n] + v1[n-1]`
`y[n] = v0[n]`
`v1[n] = -a1 * y[n] + b1 * x[n]`

Arguments

 :: Num a => a a_1 -> a a_2 -> a b_0 -> a b_1 -> a b_2 -> [a] x[n] -> [a] y[n]

Direct Form I for a second order section

`v[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2]`
`y[n] = v[n] - a1 * y[n-1] - a2 * y[n-2]`

Arguments

 :: Num a => a a_1 -> a a_2 -> a b_0 -> a b_1 -> a b_2 -> [a] x[n] -> [a] y[n]

Direct Form II for a second order section (biquad)

`w[n] = -a1 * w[n-1] - a2 * w[n-2] + x[n]`
`y[n] = b0 * w[n] + b1 * w[n-1] + b2 * w[n-2]`

Arguments

 :: Num a => a a_1 -> a a_2 -> a b_0 -> a b_1 -> a b_2 -> [a] x[n] -> [a] y[n]

Transposed Direct Form II for a second order section

`v0[n] = b0 * x[n] + v1[n-1]`
`y[n] = v0[n]`
`v1[n] = -a1 * y[n] + b1 * x[n] + v2[n-1]`
`v2[n] = -a2 * y[n] + b2 * x[n]`

Arguments

 :: Num a => (Array Int a, Array Int a) (b,a) -> [a] x[n] -> [a] y[n]

Direct Form I IIR

`v[n] = sum(k=0..M) b_k*x[n-k]`
`y[n] = v[n] - sum(k=1..N) a_k*y[n-k]`

`v[n]` is calculated with `fir`

Arguments

 :: Num a => (Array Int a, Array Int a) (b,a) -> [a] x[n] -> [a] y[n]

Direct Form II IIR

`w[n] = x[n] - sum(k=1..N) a_k*w[n-k]`
`y[n] = sum(k=0..M) b_k*w[n-k]`

f1 :: Fractional a => [a] -> [a]Source

f2 :: Fractional a => [a] -> [a]Source

f3 :: Fractional a => [a] -> [a]Source