
'''simple docstring'''

from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float = 1 / sqrt(2		)		)     ->    List[Any]:
  _lowerCAmelCase							:	Optional[Any] 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	Union[str, Any] 					=       sin(lowercase__		)
  _lowerCAmelCase							:	Any 					=       cos(lowercase__		)
  _lowerCAmelCase							:	Optional[int] 					=       _sin / (2 * q_factor)

  _lowerCAmelCase							:	Optional[Any] 					=       (1 - _cos) / 2
  _lowerCAmelCase							:	Dict 					=       1 - _cos

  _lowerCAmelCase							:	Any 					=       1 + alpha
  _lowerCAmelCase							:	Tuple 					=       -2 * _cos
  _lowerCAmelCase							:	Optional[int] 					=       1 - alpha

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


def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float = 1 / sqrt(2		)		)     ->    List[Any]:
  _lowerCAmelCase							:	List[str] 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	List[str] 					=       sin(lowercase__		)
  _lowerCAmelCase							:	Dict 					=       cos(lowercase__		)
  _lowerCAmelCase							:	str 					=       _sin / (2 * q_factor)

  _lowerCAmelCase							:	Any 					=       (1 + _cos) / 2
  _lowerCAmelCase							:	List[Any] 					=       -1 - _cos

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

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


def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float = 1 / sqrt(2		)		)     ->    List[Any]:
  _lowerCAmelCase							:	int 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	Tuple 					=       sin(lowercase__		)
  _lowerCAmelCase							:	List[str] 					=       cos(lowercase__		)
  _lowerCAmelCase							:	Dict 					=       _sin / (2 * q_factor)

  _lowerCAmelCase							:	str 					=       _sin / 2
  _lowerCAmelCase							:	Optional[int] 					=       0
  _lowerCAmelCase							:	Any 					=       -ba

  _lowerCAmelCase							:	Optional[Any] 					=       1 + alpha
  _lowerCAmelCase							:	Dict 					=       -2 * _cos
  _lowerCAmelCase							:	Optional[Any] 					=       1 - alpha

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


def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float = 1 / sqrt(2		)		)     ->    int:
  _lowerCAmelCase							:	List[str] 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	List[Any] 					=       sin(lowercase__		)
  _lowerCAmelCase							:	List[str] 					=       cos(lowercase__		)
  _lowerCAmelCase							:	Tuple 					=       _sin / (2 * q_factor)

  _lowerCAmelCase							:	Any 					=       1 - alpha
  _lowerCAmelCase							:	str 					=       -2 * _cos
  _lowerCAmelCase							:	Union[str, Any] 					=       1 + alpha

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


def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float	,   _lowerCamelCase    :							float = 1 / sqrt(2		)	,   )     ->    Optional[Any]:
  _lowerCAmelCase							:	List[str] 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	Optional[int] 					=       sin(lowercase__		)
  _lowerCAmelCase							:	Optional[int] 					=       cos(lowercase__		)
  _lowerCAmelCase							:	List[Any] 					=       _sin / (2 * q_factor)
  _lowerCAmelCase							:	List[str] 					=       10 ** (gain_db / 40)

  _lowerCAmelCase							:	List[str] 					=       1 + alpha * big_a
  _lowerCAmelCase							:	Union[str, Any] 					=       -2 * _cos
  _lowerCAmelCase							:	Dict 					=       1 - alpha * big_a
  _lowerCAmelCase							:	List[str] 					=       1 + alpha / big_a
  _lowerCAmelCase							:	Tuple 					=       -2 * _cos
  _lowerCAmelCase							:	int 					=       1 - alpha / big_a

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


def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float	,   _lowerCamelCase    :							float = 1 / sqrt(2		)	,   )     ->    Any:
  _lowerCAmelCase							:	int 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	List[str] 					=       sin(lowercase__		)
  _lowerCAmelCase							:	List[Any] 					=       cos(lowercase__		)
  _lowerCAmelCase							:	Any 					=       _sin / (2 * q_factor)
  _lowerCAmelCase							:	str 					=       10 ** (gain_db / 40)
  _lowerCAmelCase							:	List[Any] 					=       (big_a + 1) - (big_a - 1) * _cos
  _lowerCAmelCase							:	Optional[Any] 					=       (big_a + 1) + (big_a - 1) * _cos
  _lowerCAmelCase							:	Union[str, Any] 					=       (big_a - 1) - (big_a + 1) * _cos
  _lowerCAmelCase							:	Optional[Any] 					=       (big_a - 1) + (big_a + 1) * _cos
  _lowerCAmelCase							:	Tuple 					=       2 * sqrt(lowercase__		) * alpha

  _lowerCAmelCase							:	Optional[Any] 					=       big_a * (pmc + aaa)
  _lowerCAmelCase							:	Union[str, Any] 					=       2 * big_a * mpc
  _lowerCAmelCase							:	str 					=       big_a * (pmc - aaa)
  _lowerCAmelCase							:	Optional[int] 					=       ppmc + aaa
  _lowerCAmelCase							:	Optional[Any] 					=       -2 * pmpc
  _lowerCAmelCase							:	Tuple 					=       ppmc - aaa

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



def 						_UpperCAmelCase					(	_lowerCamelCase    :							int	,   _lowerCamelCase    :							int	,   _lowerCamelCase    :							float	,   _lowerCamelCase    :							float = 1 / sqrt(2		)	,   )     ->    Tuple:
  _lowerCAmelCase							:	List[Any] 					=       tau * frequency / samplerate
  _lowerCAmelCase							:	int 					=       sin(lowercase__		)
  _lowerCAmelCase							:	Union[str, Any] 					=       cos(lowercase__		)
  _lowerCAmelCase							:	Dict 					=       _sin / (2 * q_factor)
  _lowerCAmelCase							:	List[Any] 					=       10 ** (gain_db / 40)
  _lowerCAmelCase							:	Union[str, Any] 					=       (big_a + 1) - (big_a - 1) * _cos
  _lowerCAmelCase							:	Dict 					=       (big_a + 1) + (big_a - 1) * _cos
  _lowerCAmelCase							:	int 					=       (big_a - 1) - (big_a + 1) * _cos
  _lowerCAmelCase							:	Dict 					=       (big_a - 1) + (big_a + 1) * _cos
  _lowerCAmelCase							:	Any 					=       2 * sqrt(lowercase__		) * alpha

  _lowerCAmelCase							:	List[Any] 					=       big_a * (ppmc + aaa)
  _lowerCAmelCase							:	List[str] 					=       -2 * big_a * pmpc
  _lowerCAmelCase							:	int 					=       big_a * (ppmc - aaa)
  _lowerCAmelCase							:	List[str] 					=       pmc + aaa
  _lowerCAmelCase							:	Union[str, Any] 					=       2 * mpc
  _lowerCAmelCase							:	Tuple 					=       pmc - aaa

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





'''simple docstring'''

def 					__UpperCamelCase				(						lowercase__    :	list[int]			):






     '''simple docstring'''





     if not nums:  # Makes sure that the list is not empty
          raise ValueError('List is empty'			)

     __lowercase      		=sum(lowercase__			) / len(lowercase__			)  # Calculate the average
     return sum(abs(x - average			) for x in nums			) / len(lowercase__			)


if __name__ == "__main__":
       import doctest

       doctest.testmod()


