 | dsp-0.2: Digital Signal Processing | Contents | Index |
| DSP.Filter.IIR.IIR |
|
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
| integrator :: Num a => a -> [a] -> [a] |
| fos_df1 :: Num a => a -> a -> a -> [a] -> [a] |
| fos_df2 :: Num a => a -> a -> a -> [a] -> [a] |
| fos_df2t :: Num a => a -> a -> a -> [a] -> [a] |
| biquad_df1 :: Num a => a -> a -> a -> a -> a -> [a] -> [a] |
| biquad_df2 :: Num a => a -> a -> a -> a -> a -> [a] -> [a] |
| biquad_df2t :: Num a => a -> a -> a -> a -> a -> [a] -> [a] |
| iir_df1 :: Num a => (Array Int a, Array Int a) -> [a] -> [a] |
| iir_df2 :: Num a => (Array Int a, Array Int a) -> [a] -> [a] |
| xt :: [Double] |
| yt :: [Double] |
| f1 :: Fractional a => [a] -> [a] |
| f2 :: Fractional a => [a] -> [a] |
| f3 :: Fractional a => [a] -> [a] |
| f4 :: [Double] -> [Double] |
| f5 :: [Double] -> [Double] |
| :: 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] | |
| :: 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] | |
| :: 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] | |
| :: 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] | |
| :: 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] | |
| :: 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] | |
| :: 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] | |
| :: 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 | |
| :: 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] | |