Copyright | (c) Matthew Donadio 2003 |
---|---|

License | GPL |

Maintainer | m.p.donadio@ieee.org |

Stability | experimental |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell98 |

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

- 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, Eq 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]

# Documentation

:: 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]

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`

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 #