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, Eq 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 #

f4 :: [Double] -> [Double] Source #

f5 :: [Double] -> [Double] Source #