
def       A       (					lowercase    ,       lowercase = False )   ->  Optional[Any]:
		'''simple docstring'''

		if not isinstance(__lowerCamelCase    ,       __lowerCamelCase ):
				UpperCamelCase		=     f'''Expected string as input, found {type(__lowerCamelCase )}'''
				raise ValueError(__lowerCamelCase )
		if not isinstance(__lowerCamelCase    ,       __lowerCamelCase ):
				UpperCamelCase		=     f'''Expected boolean as use_pascal parameter, found {type(__lowerCamelCase )}'''
				raise ValueError(__lowerCamelCase )

		UpperCamelCase		=     input_str.split('_' )

		UpperCamelCase		=     0 if use_pascal else 1

		UpperCamelCase		=     words[start_index:]

		UpperCamelCase		=     [word[0].upper() + word[1:] for word in words_to_capitalize]

		UpperCamelCase		=     "" if use_pascal else words[0]

		return "".join([initial_word, *capitalized_words] )


if __name__ == "__main__":
					from doctest import testmod

					testmod()


"""simple docstring"""





from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter







def 	__a     (		__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase = 1 / sqrt(2  )  ):
   UpperCAmelCase_					:					int			     =    tau * frequency / samplerate
   UpperCAmelCase_					:					List[str]			     =    sin(__lowerCamelCase  )
   UpperCAmelCase_					:					int			     =    cos(__lowerCamelCase  )
   UpperCAmelCase_					:					Optional[Any]			     =    _sin / (2 * q_factor)

   UpperCAmelCase_					:					int			     =    (1 - _cos) / 2
   UpperCAmelCase_					:					Optional[Any]			     =    1 - _cos

   UpperCAmelCase_					:					int			     =    1 + alpha
   UpperCAmelCase_					:					Dict			     =    -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  )  ):
   UpperCAmelCase_					:					Dict			     =    tau * frequency / samplerate
   UpperCAmelCase_					:					Tuple			     =    sin(__lowerCamelCase  )
   UpperCAmelCase_					:					Any			     =    cos(__lowerCamelCase  )
   UpperCAmelCase_					:					List[str]			     =    _sin / (2 * q_factor)

   UpperCAmelCase_					:					List[Any]			     =    (1 + _cos) / 2
   UpperCAmelCase_					:					Optional[int]			     =    -1 - _cos

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

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







def 	__a     (		__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase = 1 / sqrt(2  )  ):
   UpperCAmelCase_					:					Union[str, Any]			     =    tau * frequency / samplerate
   UpperCAmelCase_					:					str			     =    sin(__lowerCamelCase  )
   UpperCAmelCase_					:					Tuple			     =    cos(__lowerCamelCase  )
   UpperCAmelCase_					:					List[Any]			     =    _sin / (2 * q_factor)

   UpperCAmelCase_					:					Any			     =    _sin / 2
   UpperCAmelCase_					:					Union[str, Any]			     =    0
   UpperCAmelCase_					:					Tuple			     =    -ba

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

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







def 	__a     (		__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase = 1 / sqrt(2  )  ):
   UpperCAmelCase_					:					Any			     =    tau * frequency / samplerate
   UpperCAmelCase_					:					Any			     =    sin(__lowerCamelCase  )
   UpperCAmelCase_					:					Optional[int]			     =    cos(__lowerCamelCase  )
   UpperCAmelCase_					:					str			     =    _sin / (2 * q_factor)

   UpperCAmelCase_					:					List[str]			     =    1 - alpha
   UpperCAmelCase_					:					str			     =    -2 * _cos
   UpperCAmelCase_					:					Any			     =    1 + alpha

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







def 	__a     (		__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase = 1 / sqrt(2  ),		):
   UpperCAmelCase_					:					Dict			     =    tau * frequency / samplerate
   UpperCAmelCase_					:					Union[str, Any]			     =    sin(__lowerCamelCase  )
   UpperCAmelCase_					:					int			     =    cos(__lowerCamelCase  )
   UpperCAmelCase_					:					Optional[int]			     =    _sin / (2 * q_factor)
   UpperCAmelCase_					:					List[str]			     =    10 ** (gain_db / 40)

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

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







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

   UpperCAmelCase_					:					List[str]			     =    big_a * (pmc + aaa)
   UpperCAmelCase_					:					int			     =    2 * big_a * mpc
   UpperCAmelCase_					:					int			     =    big_a * (pmc - aaa)
   UpperCAmelCase_					:					Dict			     =    ppmc + aaa
   UpperCAmelCase_					:					Any			     =    -2 * pmpc
   UpperCAmelCase_					:					List[str]			     =    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  ),		):
   UpperCAmelCase_					:					int			     =    tau * frequency / samplerate
   UpperCAmelCase_					:					Optional[Any]			     =    sin(__lowerCamelCase  )
   UpperCAmelCase_					:					Optional[Any]			     =    cos(__lowerCamelCase  )
   UpperCAmelCase_					:					Optional[Any]			     =    _sin / (2 * q_factor)
   UpperCAmelCase_					:					Tuple			     =    10 ** (gain_db / 40)
   UpperCAmelCase_					:					Tuple			     =    (big_a + 1) - (big_a - 1) * _cos
   UpperCAmelCase_					:					Optional[Any]			     =    (big_a + 1) + (big_a - 1) * _cos
   UpperCAmelCase_					:					List[Any]			     =    (big_a - 1) - (big_a + 1) * _cos
   UpperCAmelCase_					:					Any			     =    (big_a - 1) + (big_a + 1) * _cos
   UpperCAmelCase_					:					Dict			     =    2 * sqrt(__lowerCamelCase  ) * alpha

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

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


