




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)				):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      int							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      Any							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      Any							=    _sin / (2 * q_factor)

  SCREAMING_SNAKE_CASE       :      str							=    (1 - _cos) / 2
  SCREAMING_SNAKE_CASE       :      Dict							=    1 - _cos

  SCREAMING_SNAKE_CASE       :      Dict							=    1 + alpha
  SCREAMING_SNAKE_CASE       :      str							=    -2 * _cos
  SCREAMING_SNAKE_CASE       :      str							=    1 - alpha

  SCREAMING_SNAKE_CASE       :      Tuple							=    IIRFilter(2				)
  filt.set_coefficients([aa, aa, aa]						,     [ba, ba, ba]				)
  return filt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)				):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      Any							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      Dict							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      int							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      Any							=    _sin / (2 * q_factor)

  SCREAMING_SNAKE_CASE       :      Optional[int]							=    (1 + _cos) / 2
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    -1 - _cos

  SCREAMING_SNAKE_CASE       :      List[str]							=    1 + alpha
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    -2 * _cos
  SCREAMING_SNAKE_CASE       :      int							=    1 - alpha

  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    IIRFilter(2				)
  filt.set_coefficients([aa, aa, aa]						,     [ba, ba, ba]				)
  return filt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)				):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      str							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      Any							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      int							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      List[str]							=    _sin / (2 * q_factor)

  SCREAMING_SNAKE_CASE       :      Dict							=    _sin / 2
  SCREAMING_SNAKE_CASE       :      str							=    0
  SCREAMING_SNAKE_CASE       :      int							=    -ba

  SCREAMING_SNAKE_CASE       :      List[Any]							=    1 + alpha
  SCREAMING_SNAKE_CASE       :      int							=    -2 * _cos
  SCREAMING_SNAKE_CASE       :      Dict							=    1 - alpha

  SCREAMING_SNAKE_CASE       :      Any							=    IIRFilter(2				)
  filt.set_coefficients([aa, aa, aa]						,     [ba, ba, ba]				)
  return filt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)				):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      Dict							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      str							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      Optional[Any]							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    _sin / (2 * q_factor)

  SCREAMING_SNAKE_CASE       :      str							=    1 - alpha
  SCREAMING_SNAKE_CASE       :      str							=    -2 * _cos
  SCREAMING_SNAKE_CASE       :      Tuple							=    1 + alpha

  SCREAMING_SNAKE_CASE       :      Optional[Any]							=    IIRFilter(2				)
  filt.set_coefficients([ba, ba, ba]						,     [ba, ba, ba]				)
  return filt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)						,     ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      Tuple							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    _sin / (2 * q_factor)
  SCREAMING_SNAKE_CASE       :      Optional[Any]							=    10 ** (gain_db / 40)

  SCREAMING_SNAKE_CASE       :      int							=    1 + alpha * big_a
  SCREAMING_SNAKE_CASE       :      str							=    -2 * _cos
  SCREAMING_SNAKE_CASE       :      List[str]							=    1 - alpha * big_a
  SCREAMING_SNAKE_CASE       :      Any							=    1 + alpha / big_a
  SCREAMING_SNAKE_CASE       :      Any							=    -2 * _cos
  SCREAMING_SNAKE_CASE       :      Optional[Any]							=    1 - alpha / big_a

  SCREAMING_SNAKE_CASE       :      Dict							=    IIRFilter(2				)
  filt.set_coefficients([aa, aa, aa]						,     [ba, ba, ba]				)
  return filt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)						,     ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      List[str]							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      Dict							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      str							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      int							=    _sin / (2 * q_factor)
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    10 ** (gain_db / 40)
  SCREAMING_SNAKE_CASE       :      Dict							=    (big_a + 1) - (big_a - 1) * _cos
  SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    (big_a + 1) + (big_a - 1) * _cos
  SCREAMING_SNAKE_CASE       :      int							=    (big_a - 1) - (big_a + 1) * _cos
  SCREAMING_SNAKE_CASE       :      Tuple							=    (big_a - 1) + (big_a + 1) * _cos
  SCREAMING_SNAKE_CASE       :      List[Any]							=    2 * sqrt(lowercase				) * alpha

  SCREAMING_SNAKE_CASE       :      List[Any]							=    big_a * (pmc + aaa)
  SCREAMING_SNAKE_CASE       :      Dict							=    2 * big_a * mpc
  SCREAMING_SNAKE_CASE       :      List[str]							=    big_a * (pmc - aaa)
  SCREAMING_SNAKE_CASE       :      int							=    ppmc + aaa
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    -2 * pmpc
  SCREAMING_SNAKE_CASE       :      Any							=    ppmc - aaa

  SCREAMING_SNAKE_CASE       :      int							=    IIRFilter(2				)
  filt.set_coefficients([aa, aa, aa]						,     [ba, ba, ba]				)
  return filt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase						,     lowercase = 1 / sqrt(2				)						,     ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      Any							=    tau * frequency / samplerate
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    sin(lowercase				)
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    cos(lowercase				)
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    _sin / (2 * q_factor)
  SCREAMING_SNAKE_CASE       :      str							=    10 ** (gain_db / 40)
  SCREAMING_SNAKE_CASE       :      str							=    (big_a + 1) - (big_a - 1) * _cos
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    (big_a + 1) + (big_a - 1) * _cos
  SCREAMING_SNAKE_CASE       :      int							=    (big_a - 1) - (big_a + 1) * _cos
  SCREAMING_SNAKE_CASE       :      List[str]							=    (big_a - 1) + (big_a + 1) * _cos
  SCREAMING_SNAKE_CASE       :      Tuple							=    2 * sqrt(lowercase				) * alpha

  SCREAMING_SNAKE_CASE       :      Optional[Any]							=    big_a * (ppmc + aaa)
  SCREAMING_SNAKE_CASE       :      Tuple							=    -2 * big_a * pmpc
  SCREAMING_SNAKE_CASE       :      Dict							=    big_a * (ppmc - aaa)
  SCREAMING_SNAKE_CASE       :      Tuple							=    pmc + aaa
  SCREAMING_SNAKE_CASE       :      Optional[int]							=    2 * mpc
  SCREAMING_SNAKE_CASE       :      Optional[Any]							=    pmc - aaa

  SCREAMING_SNAKE_CASE       :      Tuple							=    IIRFilter(2				)
  filt.set_coefficients([aa, aa, aa]						,     [ba, ba, ba]				)
  return filt














from __future__ import annotations

from cmath import sqrt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase				):

  """simple docstring"""






  if a == 0:
    raise ValueError("Coefficient 'a' must not be zero."				)
  SCREAMING_SNAKE_CASE       :      List[str]							=    b * b - 4 * a * c

  SCREAMING_SNAKE_CASE       :      str							=    (-b + sqrt(lowercase				)) / (2 * a)
  SCREAMING_SNAKE_CASE       :      Any							=    (-b - sqrt(lowercase				)) / (2 * a)

  return (
      root_a.real if not root_a.imag else root_a,
      root_a.real if not root_a.imag else root_a,
  )


def   lowerCamelCase__			(     ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE						,  SCREAMING_SNAKE_CASE       :      Dict							=    quadratic_roots(a=5						,     b=6						,     c=1				)
  print(F'''The solutions are: {solutiona} and {solutiona}'''				)


if __name__ == "__main__":
   main()






