@@ -10,13 +10,17 @@ class IIRFilter:
1010
1111 Implementation details:
1212 Based on the 2nd-order function from
13- https://en.wikipedia.org/wiki/Digital_biquad_filter,
13+ https://en.wikipedia.org/wiki/Digital_biquad_filter,
1414 this generalized N-order function was made.
1515
1616 Using the following transfer function
17- 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}}
17+ .. math:: H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}
18+ {a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}
19+
1820 we can rewrite this to
19- 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)
21+ .. math:: y[n]={\frac{1}{a_{0}}}
22+ \left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-
23+ \left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
2024 """
2125
2226 def __init__ (self , order : int ) -> None :
@@ -34,17 +38,19 @@ def __init__(self, order: int) -> None:
3438
3539 def set_coefficients (self , a_coeffs : list [float ], b_coeffs : list [float ]) -> None :
3640 """
37- Set the coefficients for the IIR filter. These should both be of size order + 1.
38- a_0 may be left out, and it will use 1.0 as default value.
41+ Set the coefficients for the IIR filter.
42+ These should both be of size `order` + 1.
43+ :math:`a_0` may be left out, and it will use 1.0 as default value.
3944
4045 This method works well with scipy's filter design functions
41- >>> # Make a 2nd-order 1000Hz butterworth lowpass filter
42- >>> import scipy.signal
43- >>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
44- ... btype='lowpass',
45- ... fs=48000)
46- >>> filt = IIRFilter(2)
47- >>> filt.set_coefficients(a_coeffs, b_coeffs)
46+
47+ >>> # Make a 2nd-order 1000Hz butterworth lowpass filter
48+ >>> import scipy.signal
49+ >>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
50+ ... btype='lowpass',
51+ ... fs=48000)
52+ >>> filt = IIRFilter(2)
53+ >>> filt.set_coefficients(a_coeffs, b_coeffs)
4854 """
4955 if len (a_coeffs ) < self .order :
5056 a_coeffs = [1.0 , * a_coeffs ]
@@ -68,7 +74,7 @@ def set_coefficients(self, a_coeffs: list[float], b_coeffs: list[float]) -> None
6874
6975 def process (self , sample : float ) -> float :
7076 """
71- Calculate y[n]
77+ Calculate :math:` y[n]`
7278
7379 >>> filt = IIRFilter(2)
7480 >>> filt.process(0)
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