Fix sphinx/build_docs warnings for audio_filters (TheAlgorithms#12449)

* updating DIRECTORY.md * Fix sphinx/build_docs warnings for audio_filters * Improve * Fix * Fix * Fix --------- Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>

Author: MaximSmolskiy

audio_filters/iir_filter.py

@@ -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:
@@ -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]
@@ -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)