
'''simple docstring'''







from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A = 1 / sqrt(2	)	)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)

	_snake_case   						=		(1 - _cos) / 2
	_snake_case   						=		1 - _cos

	_snake_case   						=		1 + alpha
	_snake_case   						=		-2 * _cos
	_snake_case   						=		1 - alpha

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([aa, aa, aa]			,				[ba, ba, ba]	)
	return filt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A = 1 / sqrt(2	)	)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)

	_snake_case   						=		(1 + _cos) / 2
	_snake_case   						=		-1 - _cos

	_snake_case   						=		1 + alpha
	_snake_case   						=		-2 * _cos
	_snake_case   						=		1 - alpha

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([aa, aa, aa]			,				[ba, ba, ba]	)
	return filt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A = 1 / sqrt(2	)	)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)

	_snake_case   						=		_sin / 2
	_snake_case   						=		0
	_snake_case   						=		-ba

	_snake_case   						=		1 + alpha
	_snake_case   						=		-2 * _cos
	_snake_case   						=		1 - alpha

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([aa, aa, aa]			,				[ba, ba, ba]	)
	return filt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A = 1 / sqrt(2	)	)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)

	_snake_case   						=		1 - alpha
	_snake_case   						=		-2 * _cos
	_snake_case   						=		1 + alpha

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([ba, ba, ba]			,				[ba, ba, ba]	)
	return filt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A			,				__A = 1 / sqrt(2	)			,				)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)
	_snake_case   						=		10 ** (gain_db / 40)

	_snake_case   						=		1 + alpha * big_a
	_snake_case   						=		-2 * _cos
	_snake_case   						=		1 - alpha * big_a
	_snake_case   						=		1 + alpha / big_a
	_snake_case   						=		-2 * _cos
	_snake_case   						=		1 - alpha / big_a

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([aa, aa, aa]			,				[ba, ba, ba]	)
	return filt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A			,				__A = 1 / sqrt(2	)			,				)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)
	_snake_case   						=		10 ** (gain_db / 40)
	_snake_case   						=		(big_a + 1) - (big_a - 1) * _cos
	_snake_case   						=		(big_a + 1) + (big_a - 1) * _cos
	_snake_case   						=		(big_a - 1) - (big_a + 1) * _cos
	_snake_case   						=		(big_a - 1) + (big_a + 1) * _cos
	_snake_case   						=		2 * sqrt(__A	) * alpha

	_snake_case   						=		big_a * (pmc + aaa)
	_snake_case   						=		2 * big_a * mpc
	_snake_case   						=		big_a * (pmc - aaa)
	_snake_case   						=		ppmc + aaa
	_snake_case   						=		-2 * pmpc
	_snake_case   						=		ppmc - aaa

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([aa, aa, aa]			,				[ba, ba, ba]	)
	return filt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A			,				__A = 1 / sqrt(2	)			,				)       ->	IIRFilter:
	_snake_case   						=		tau * frequency / samplerate
	_snake_case   						=		sin(__A	)
	_snake_case   						=		cos(__A	)
	_snake_case   						=		_sin / (2 * q_factor)
	_snake_case   						=		10 ** (gain_db / 40)
	_snake_case   						=		(big_a + 1) - (big_a - 1) * _cos
	_snake_case   						=		(big_a + 1) + (big_a - 1) * _cos
	_snake_case   						=		(big_a - 1) - (big_a + 1) * _cos
	_snake_case   						=		(big_a - 1) + (big_a + 1) * _cos
	_snake_case   						=		2 * sqrt(__A	) * alpha

	_snake_case   						=		big_a * (ppmc + aaa)
	_snake_case   						=		-2 * big_a * pmpc
	_snake_case   						=		big_a * (ppmc - aaa)
	_snake_case   						=		pmc + aaa
	_snake_case   						=		2 * mpc
	_snake_case   						=		pmc - aaa

	_snake_case   						=		IIRFilter(2	)
	filt.set_coefficients([aa, aa, aa]			,				[ba, ba, ba]	)
	return filt







from __future__ import annotations




def 					lowerCamelCase__       (						A__       :					list[int | float]  ,			A__       :					int  ,			A__       :					int	):





       '''simple docstring'''



       if len(A__	) == 0:
              raise ValueError("""find_max() arg is an empty sequence"""	)
       if (
           left >= len(A__	)
           or left < -len(A__	)
           or right >= len(A__	)
           or right < -len(A__	)
       ):
              raise IndexError("""list index out of range"""	)
       if left == right:
              return nums[left]
       __lowerCamelCase   =						(left + right) >> 1  # the middle
       __lowerCamelCase   =						find_max(A__  ,			A__  ,			A__	)  # find max in range[left, mid]
       __lowerCamelCase   =						find_max(A__  ,			mid + 1  ,			A__	)  # find max in range[mid + 1, right]

       return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
       import doctest

       doctest.testmod(verbose=True)

