





"""simple docstring"""




from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np




class 			_a						(				_lowerCAmelCase    ):






				def     snake_case     (			self		:   Optional[int],			lowerCAmelCase__		:   float							)     ->				float:




										'''simple docstring'''



										return 0.0





def 	a_    (							_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Tuple         =   min([-20, np.min(fft_results[1 : samplerate // 2 - 1]       )]       )
						_UpperCamelCase      : str         =   max([20, np.max(fft_results[1 : samplerate // 2 - 1]       )]       )
						return lowest, highest





def 	a_    (							_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Optional[int]         =   512
						_UpperCamelCase      : Union[str, Any]         =   [1] + [0] * (size - 1)
						_UpperCamelCase      : Optional[Any]         =   [filter_type.process(_lowercase       ) for item in inputs]

						_UpperCamelCase      : Dict         =   [0] * (samplerate - size)  # zero-padding
						outputs += filler
						_UpperCamelCase      : Dict         =   np.abs(np.fft.fft(_lowercase       )       )
						_UpperCamelCase      : Tuple         =   20 * np.logaa(_lowercase       )

						# Frequencies on log scale from 24 to nyquist frequency
						plt.xlim(24	,						samplerate / 2 - 1       )
						plt.xlabel('''Frequency (Hz)'''       )
						plt.xscale('''log'''       )

						# Display within reasonable bounds
						_UpperCamelCase      : int         =   get_bounds(_lowercase	,						_lowercase       )
						plt.ylim(max([-80, bounds[0]]       )	,						min([80, bounds[1]]       )       )
						plt.ylabel('''Gain (dB)'''       )

						plt.plot(_lowercase       )
						plt.show()






def 	a_    (							_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Tuple         =   512
						_UpperCamelCase      : Any         =   [1] + [0] * (size - 1)
						_UpperCamelCase      : Union[str, Any]         =   [filter_type.process(_lowercase       ) for item in inputs]

						_UpperCamelCase      : Union[str, Any]         =   [0] * (samplerate - size)  # zero-padding
						outputs += filler
						_UpperCamelCase      : str         =   np.angle(np.fft.fft(_lowercase       )       )

						# Frequencies on log scale from 24 to nyquist frequency
						plt.xlim(24	,						samplerate / 2 - 1       )
						plt.xlabel('''Frequency (Hz)'''       )
						plt.xscale('''log'''       )

						plt.ylim(-2 * pi	,						2 * pi       )
						plt.ylabel('''Phase shift (Radians)'''       )
						plt.plot(np.unwrap(_lowercase	,						-2 * pi       )       )
						plt.show()










"""simple docstring"""




from __future__ import annotations

from random import choice





def 	a_    (							_lowercase       ):
						return choice(_lowercase       )





def 	a_    (							_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Optional[int]         =   random_pivot(_lowercase       )

						# partition based on pivot
						# linear time
						_UpperCamelCase      : Union[str, Any]         =   [e for e in lst if e < pivot]
						_UpperCamelCase      : int         =   [e for e in lst if e > pivot]

						# if we get lucky, pivot might be the element we want.
						# we can easily see this:
						# small (elements smaller than k)
						# + pivot (kth element)
						# + big (elements larger than k)
						if len(_lowercase       ) == k - 1:
												return pivot
						# pivot is in elements bigger than k
						elif len(_lowercase       ) < k - 1:
												return kth_number(_lowercase	,						k - len(_lowercase       ) - 1       )
						# pivot is in elements smaller than k
						else:
												return kth_number(_lowercase	,						_lowercase       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



