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32 changes: 19 additions & 13 deletions audio_filters/iir_filter.py
Original file line number Diff line number Diff line change
Expand Up @@ -10,13 +10,17 @@ class IIRFilter:

Implementation details:
Based on the 2nd-order function from
https://en.wikipedia.org/wiki/Digital_biquad_filter,
https://en.wikipedia.org/wiki/Digital_biquad_filter,
this generalized N-order function was made.

Using the following transfer function
H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}{a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}
.. math:: H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}
{a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}

we can rewrite this to
y[n]={\frac{1}{a_{0}}}\left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-\left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
.. math:: y[n]={\frac{1}{a_{0}}}
\left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-
\left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
"""

def __init__(self, order: int) -> None:
Expand All @@ -34,17 +38,19 @@ def __init__(self, order: int) -> None:

def set_coefficients(self, a_coeffs: list[float], b_coeffs: list[float]) -> None:
"""
Set the coefficients for the IIR filter. These should both be of size order + 1.
a_0 may be left out, and it will use 1.0 as default value.
Set the coefficients for the IIR filter.
These should both be of size `order` + 1.
:math:`a_0` may be left out, and it will use 1.0 as default value.

This method works well with scipy's filter design functions
>>> # Make a 2nd-order 1000Hz butterworth lowpass filter
>>> import scipy.signal
>>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
... btype='lowpass',
... fs=48000)
>>> filt = IIRFilter(2)
>>> filt.set_coefficients(a_coeffs, b_coeffs)

>>> # Make a 2nd-order 1000Hz butterworth lowpass filter
>>> import scipy.signal
>>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
... btype='lowpass',
... fs=48000)
>>> filt = IIRFilter(2)
>>> filt.set_coefficients(a_coeffs, b_coeffs)
"""
if len(a_coeffs) < self.order:
a_coeffs = [1.0, *a_coeffs]
Expand All @@ -68,7 +74,7 @@ def set_coefficients(self, a_coeffs: list[float], b_coeffs: list[float]) -> None

def process(self, sample: float) -> float:
"""
Calculate y[n]
Calculate :math:`y[n]`

>>> filt = IIRFilter(2)
>>> filt.process(0)
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