



'''simple docstring'''






import random


def  snake_case_     (					_lowerCAmelCase  :						list   ,      _lowerCAmelCase  :						str  )      ->   tuple:
							UpperCAmelCase							,		UpperCAmelCase							,		UpperCAmelCase :       Tuple 							=		[], [], []
							for element in data:
														if element < pivot:
																					less.append(_lowerCAmelCase  )
														elif element > pivot:
																					greater.append(_lowerCAmelCase  )
														else:
																					equal.append(_lowerCAmelCase  )
							return less, equal, greater




def  snake_case_     (					_lowerCAmelCase  :						list   ,      _lowerCAmelCase  :						int  )      ->   Dict:
							# index = len(items) // 2 when trying to find the median
							#   (value of index when items is sorted)

							# invalid input
							if index >= len(_lowerCAmelCase  ) or index < 0:
														return None

							UpperCAmelCase :       int 							=		items[random.randint(0   ,      len(_lowerCAmelCase  ) - 1  )]
							UpperCAmelCase :       List[Any] 							=		0
							UpperCAmelCase							,		UpperCAmelCase							,		UpperCAmelCase :       Any 							=		_partition(_lowerCAmelCase   ,      _lowerCAmelCase  )
							UpperCAmelCase :       List[str] 							=		len(_lowerCAmelCase  )
							UpperCAmelCase :       str 							=		len(_lowerCAmelCase  )

							# index is the pivot
							if m <= index < m + count:
														return pivot
							# must be in smaller
							elif m > index:
														return quick_select(_lowerCAmelCase   ,      _lowerCAmelCase  )
							# must be in larger
							else:
														return quick_select(_lowerCAmelCase   ,      index - (m + count)  )










'''simple docstring'''






from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Optional[int] 							=		tau * frequency / samplerate
							UpperCAmelCase :       List[Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       int 							=		_sin / (2 * q_factor)

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

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

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


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Any 							=		tau * frequency / samplerate
							UpperCAmelCase :       Tuple 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Tuple 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Dict 							=		_sin / (2 * q_factor)

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

							UpperCAmelCase :       Tuple 							=		1 + alpha
							UpperCAmelCase :       List[str] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha

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


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Optional[int] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Optional[int] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Tuple 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[int] 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       Union[str, Any] 							=		_sin / 2
							UpperCAmelCase :       Any 							=		0
							UpperCAmelCase :       int 							=		-ba

							UpperCAmelCase :       Optional[Any] 							=		1 + alpha
							UpperCAmelCase :       List[Any] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha

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


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

							UpperCAmelCase :       List[str] 							=		1 - alpha
							UpperCAmelCase :       Any 							=		-2 * _cos
							UpperCAmelCase :       Optional[int] 							=		1 + alpha

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


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       Optional[Any] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[int] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Dict 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       str 							=		10 ** (gain_db / 40)

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

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


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

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

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




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

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

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





