
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_:							List[Any]		=  sin(lowerCamelCase  )
				UpperCamelCase_:							Optional[int]		=  cos(lowerCamelCase  )
				UpperCamelCase_:							str		=  _sin / (2 * q_factor)

				UpperCamelCase_:							Tuple		=  (1 - _cos) / 2
				UpperCamelCase_:							Union[str, Any]		=  1 - _cos

				UpperCamelCase_:							Optional[Any]		=  1 + alpha
				UpperCamelCase_:							str		=  -2 * _cos
				UpperCamelCase_:							Optional[int]		=  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_:							Tuple		=  tau * frequency / samplerate
				UpperCamelCase_:							Dict		=  sin(lowerCamelCase  )
				UpperCamelCase_:							List[Any]		=  cos(lowerCamelCase  )
				UpperCamelCase_:							List[Any]		=  _sin / (2 * q_factor)

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

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

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







def     A__   (  lowerCamelCase       ,      lowerCamelCase       ,      lowerCamelCase = 1 / sqrt(2  )  )					->		IIRFilter:
				UpperCamelCase_:							Dict		=  tau * frequency / samplerate
				UpperCamelCase_:							Tuple		=  sin(lowerCamelCase  )
				UpperCamelCase_:							str		=  cos(lowerCamelCase  )
				UpperCamelCase_:							str		=  _sin / (2 * q_factor)

				UpperCamelCase_:							Tuple		=  _sin / 2
				UpperCamelCase_:							Optional[Any]		=  0
				UpperCamelCase_:							str		=  -ba

				UpperCamelCase_:							Optional[Any]		=  1 + alpha
				UpperCamelCase_:							List[Any]		=  -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_:							Union[str, Any]		=  tau * frequency / samplerate
				UpperCamelCase_:							List[Any]		=  sin(lowerCamelCase  )
				UpperCamelCase_:							str		=  cos(lowerCamelCase  )
				UpperCamelCase_:							str		=  _sin / (2 * q_factor)

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

				UpperCamelCase_:							List[str]		=  IIRFilter(2  )
				filt.set_coefficients([ba, ba, ba]       ,      [ba, ba, ba]  )
				return filt







def     A__   (  lowerCamelCase       ,      lowerCamelCase       ,      lowerCamelCase       ,      lowerCamelCase = 1 / sqrt(2  )       ,      )					->		IIRFilter:
				UpperCamelCase_:							List[str]		=  tau * frequency / samplerate
				UpperCamelCase_:							Any		=  sin(lowerCamelCase  )
				UpperCamelCase_:							List[Any]		=  cos(lowerCamelCase  )
				UpperCamelCase_:							Any		=  _sin / (2 * q_factor)
				UpperCamelCase_:							Any		=  10 ** (gain_db / 40)

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

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







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

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

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

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

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








def     A__   (  lowerCamelCase       ,      lowerCamelCase  )					->		float:
				if mass < 0:
								raise ValueError("""The mass of a body cannot be negative"""  )
				return 0.5 * mass * abs(lowerCamelCase  ) * abs(lowerCamelCase  )


if __name__ == "__main__":
							import doctest

							doctest.testmod(verbose=True)






