Update butterworth_filter.py

[Aryan-Rajesh-Python]

Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

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• I have read CONTRIBUTING.md.
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[imSanko]

from math import cos, sin, sqrt, tau
from audio_filters.iir_filter import IIRFilter

"""
Create 2nd-order IIR filters with Butterworth design.
Code based on https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html
Alternatively, you can use scipy.signal.butter, which should yield the same results.
"""

def make_highshelf(frequency, samplerate, gain_db, q_factor=0.707):
    """
    Creates a high-shelf filter based on the specified parameters.

    Args:
        frequency (float): Center frequency of the filter.
        samplerate (float): Sampling rate.
        gain_db (float): Gain in decibels.
        q_factor (float): Quality factor.

    Returns:
        IIRFilter: Configured high-shelf filter.

    Examples:
        >>> filter = make_highshelf(1000, 48000, 6)
        >>> filter.a_coeffs  # doctest: +NORMALIZE_WHITESPACE
        [2.2229172136088806, -3.9587208137297303, 1.7841414181566304]
        >>> filter.b_coeffs  # doctest: +NORMALIZE_WHITESPACE
        [4.295432981120543, -7.922740859457287, 3.6756456963725253]
    """
    w0 = tau * frequency / samplerate
    _sin = sin(w0)
    _cos = cos(w0)
    alpha = _sin / (2 * q_factor)
    big_a = 10 ** (gain_db / 40)

    pmc = (big_a + 1) + (big_a - 1) * _cos
    ppmc = (big_a + 1) - (big_a - 1) * _cos
    mpc = (big_a - 1) + (big_a + 1) * _cos
    pmpc = (big_a - 1) - (big_a + 1) * _cos
    aa2 = 2 * sqrt(big_a) * alpha

    b0 = big_a * (ppmc + aa2)
    b1 = -2 * big_a * pmpc
    b2 = big_a * (ppmc - aa2)
    a0 = pmc + aa2
    a1 = -2 * mpc
    a2 = pmc - aa2

    filt = IIRFilter(2)
    filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
    return filt

if __name__ == "__main__":
    import doctest
    doctest.testmod()

[imSanko]

try to implement these change

[MaximSmolskiy]

I don't understand why high-shelf filter formulas should be changed.
Current formulas correspond to https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html