





from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase = 1 / sqrt(2					)					)						->			IIRFilter:
 UpperCamelCase     : str	     =       tau * frequency / samplerate
 UpperCamelCase     : Optional[Any]	     =       sin(_lowerCAmelCase					)
 UpperCamelCase     : List[str]	     =       cos(_lowerCAmelCase					)
 UpperCamelCase     : List[str]	     =       _sin / (2 * q_factor)

 UpperCamelCase     : Tuple	     =       (1 - _cos) / 2
 UpperCamelCase     : Tuple	     =       1 - _cos

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

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



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase = 1 / sqrt(2					)					)						->			IIRFilter:
 UpperCamelCase     : Any	     =       tau * frequency / samplerate
 UpperCamelCase     : int	     =       sin(_lowerCAmelCase					)
 UpperCamelCase     : str	     =       cos(_lowerCAmelCase					)
 UpperCamelCase     : Any	     =       _sin / (2 * q_factor)

 UpperCamelCase     : Optional[int]	     =       (1 + _cos) / 2
 UpperCamelCase     : int	     =       -1 - _cos

 UpperCamelCase     : Tuple	     =       1 + alpha
 UpperCamelCase     : str	     =       -2 * _cos
 UpperCamelCase     : Any	     =       1 - alpha

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



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase = 1 / sqrt(2					)					)						->			IIRFilter:
 UpperCamelCase     : Optional[Any]	     =       tau * frequency / samplerate
 UpperCamelCase     : Tuple	     =       sin(_lowerCAmelCase					)
 UpperCamelCase     : Dict	     =       cos(_lowerCAmelCase					)
 UpperCamelCase     : List[str]	     =       _sin / (2 * q_factor)

 UpperCamelCase     : Dict	     =       _sin / 2
 UpperCamelCase     : List[str]	     =       0
 UpperCamelCase     : Dict	     =       -ba

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

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



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase = 1 / sqrt(2					)					)						->			IIRFilter:
 UpperCamelCase     : List[Any]	     =       tau * frequency / samplerate
 UpperCamelCase     : List[Any]	     =       sin(_lowerCAmelCase					)
 UpperCamelCase     : List[Any]	     =       cos(_lowerCAmelCase					)
 UpperCamelCase     : Union[str, Any]	     =       _sin / (2 * q_factor)

 UpperCamelCase     : Dict	     =       1 - alpha
 UpperCamelCase     : Optional[int]	     =       -2 * _cos
 UpperCamelCase     : Union[str, Any]	     =       1 + alpha

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



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase = 1 / sqrt(2					)							,       )						->			IIRFilter:
 UpperCamelCase     : str	     =       tau * frequency / samplerate
 UpperCamelCase     : Dict	     =       sin(_lowerCAmelCase					)
 UpperCamelCase     : Dict	     =       cos(_lowerCAmelCase					)
 UpperCamelCase     : List[str]	     =       _sin / (2 * q_factor)
 UpperCamelCase     : List[str]	     =       10 ** (gain_db / 40)

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

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



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

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

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



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase = 1 / sqrt(2					)							,       )						->			IIRFilter:
 UpperCamelCase     : Dict	     =       tau * frequency / samplerate
 UpperCamelCase     : int	     =       sin(_lowerCAmelCase					)
 UpperCamelCase     : List[Any]	     =       cos(_lowerCAmelCase					)
 UpperCamelCase     : Tuple	     =       _sin / (2 * q_factor)
 UpperCamelCase     : Optional[Any]	     =       10 ** (gain_db / 40)
 UpperCamelCase     : Tuple	     =       (big_a + 1) - (big_a - 1) * _cos
 UpperCamelCase     : Tuple	     =       (big_a + 1) + (big_a - 1) * _cos
 UpperCamelCase     : List[Any]	     =       (big_a - 1) - (big_a + 1) * _cos
 UpperCamelCase     : List[Any]	     =       (big_a - 1) + (big_a + 1) * _cos
 UpperCamelCase     : Optional[Any]	     =       2 * sqrt(_lowerCAmelCase					) * alpha

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

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







from __future__ import annotations



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase					)						->			list[str]:
 if partitions <= 0:
  raise ValueError("partitions must be a positive number!"					)
 if partitions > number_of_bytes:
  raise ValueError("partitions can not > number_of_bytes!"					)
 UpperCamelCase     : str	     =       number_of_bytes // partitions
 UpperCamelCase     : List[Any]	     =       []
 for i in range(_lowerCAmelCase					):
  UpperCamelCase     : Optional[Any]	     =       i * bytes_per_partition + 1
  UpperCamelCase     : Any	     =       (
      number_of_bytes if i == partitions - 1 else (i + 1) * bytes_per_partition
  )
  allocation_list.append(F"""{start_bytes}-{end_bytes}"""					)
 return allocation_list


if __name__ == "__main__":
    import doctest

    doctest.testmod()
