



from __future__ import annotations



def 					lowercase				(      SCREAMING_SNAKE_CASE__				:		int )     ->   list[int]:  # This function is recursive
 _snake_case			:     List[Any] 		=    len(__A )
 # If the array contains only one element, we return it (it's the stop condition of
 # recursion)
 if array_length <= 1:
  return array
  # Else
 _snake_case			:     Any 		=    array[0]
 _snake_case			:     str 		=    False
 _snake_case			:     Union[str, Any] 		=    1
 _snake_case			:     Any 		=    []
 while not is_found and i < array_length:
  if array[i] < pivot:
   _snake_case			:     Tuple 		=    True
   _snake_case			:     Dict 		=    [element for element in array[i:] if element >= array[i]]
   _snake_case			:     Optional[int] 		=    longest_subsequence(__A )
   if len(__A ) > len(__A ):
    _snake_case			:     int 		=    temp_array
  else:
   i += 1

 _snake_case			:     List[Any] 		=    [element for element in array[1:] if element >= pivot]
 _snake_case			:     Optional[int] 		=    [pivot, *longest_subsequence(__A )]
 if len(__A ) > len(__A ):
  return temp_array
 else:
  return longest_subseq


if __name__ == "__main__":
  import doctest

  doctest.testmod()


'''simple docstring'''







from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class 						__UpperCAmelCase      (					_lowerCamelCase						):


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								return 0.0







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	tuple[int | float, int | float]:
	_snake_case   						=		min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
	_snake_case   						=		max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
	return lowest, highest







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	None:
	_snake_case   						=		512
	_snake_case   						=		[1] + [0] * (size - 1)
	_snake_case   						=		[filter_type.process(__A	) for item in inputs]

	_snake_case   						=		[0] * (samplerate - size)  # zero-padding
	outputs += filler
	_snake_case   						=		np.abs(np.fft.fft(__A	)	)
	_snake_case   						=		20 * np.logaa(__A	)

	# 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
	_snake_case   						=		get_bounds(__A			,				__A	)
	plt.ylim(max([-80, bounds[0]]	)			,				min([80, bounds[1]]	)	)
	plt.ylabel('Gain (dB)'	)

	plt.plot(__A	)
	plt.show()







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	None:
	_snake_case   						=		512
	_snake_case   						=		[1] + [0] * (size - 1)
	_snake_case   						=		[filter_type.process(__A	) for item in inputs]

	_snake_case   						=		[0] * (samplerate - size)  # zero-padding
	outputs += filler
	_snake_case   						=		np.angle(np.fft.fft(__A	)	)

	# 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(__A			,				-2 * pi	)	)
	plt.show()

