#### Iir Filter

A
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from __future__ import annotations

class IIRFilter:
r"""
N-Order IIR filter
Assumes working with float samples normalized on [-1, 1]

---

Implementation details:
Based on the 2nd-order function from
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}}
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)
"""

def __init__(self, order: int) -> None:
self.order = order

# a_{0} ... a_{k}
self.a_coeffs = [1.0] + [0.0] * order
# b_{0} ... b_{k}
self.b_coeffs = [1.0] + [0.0] * order

# x[n-1] ... x[n-k]
self.input_history = [0.0] * self.order
# y[n-1] ... y[n-k]
self.output_history = [0.0] * self.order

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.

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)
"""
if len(a_coeffs) < self.order:
a_coeffs = [1.0, *a_coeffs]

if len(a_coeffs) != self.order + 1:
msg = (
f"Expected a_coeffs to have {self.order + 1} elements "
f"for {self.order}-order filter, got {len(a_coeffs)}"
)
raise ValueError(msg)

if len(b_coeffs) != self.order + 1:
msg = (
f"Expected b_coeffs to have {self.order + 1} elements "
f"for {self.order}-order filter, got {len(a_coeffs)}"
)
raise ValueError(msg)

self.a_coeffs = a_coeffs
self.b_coeffs = b_coeffs

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

>>> filt = IIRFilter(2)
>>> filt.process(0)
0.0
"""
result = 0.0

# Start at index 1 and do index 0 at the end.
for i in range(1, self.order + 1):
result += (
self.b_coeffs[i] * self.input_history[i - 1]
- self.a_coeffs[i] * self.output_history[i - 1]
)

result = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

self.input_history[1:] = self.input_history[:-1]
self.output_history[1:] = self.output_history[:-1]

self.input_history[0] = sample
self.output_history[0] = result

return result