

from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np





class 					__lowerCAmelCase	(   UpperCAmelCase__				):




  def     A__	(							self				,  lowerCAmelCase   )    ->					float:
        '''simple docstring'''






        return 0.0
def 	a (     A__      :  np.ndarray ,  A__      :  int	)       -> tuple[int | float, int | float]:





      """simple docstring"""



      _lowercase      			=min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
      _lowercase      			=max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
      return lowest, highest
def 	a (     A__      :  FilterType ,  A__      :  int	)       -> None:





      """simple docstring"""



      _lowercase      			=512
      _lowercase      			=[1] + [0] * (size - 1)
      _lowercase      			=[filter_type.process(A__	) for item in inputs]

      _lowercase      			=[0] * (samplerate - size)  # zero-padding
      outputs += filler
      _lowercase      			=np.abs(np.fft.fft(A__	)	)
      _lowercase      			=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
      _lowercase      			=get_bounds(A__ ,  A__	)
      plt.ylim(max([-80, bounds[0]]	) ,  min([80, bounds[1]]	)	)
      plt.ylabel('Gain (dB)'	)

      plt.plot(A__	)
      plt.show()







def 	a (     A__      :  FilterType ,  A__      :  int	)       -> None:





      """simple docstring"""



      _lowercase      			=512
      _lowercase      			=[1] + [0] * (size - 1)
      _lowercase      			=[filter_type.process(A__	) for item in inputs]

      _lowercase      			=[0] * (samplerate - size)  # zero-padding
      outputs += filler
      _lowercase      			=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()






from __future__ import annotations






def 					UpperCamelCase   (      __magic_name__	:				list[int]	)  ->    list[int]:  # This function is recursive
		"""simple docstring"""




		lowercase__	     =						len(__magic_name__	)
		# If the array contains only one element, we return it (it's the stop condition of
		# recursion)
		if array_length <= 1:
				return array
				# Else
		lowercase__	     =						array[0]
		lowercase__	     =						False
		lowercase__	     =						1
		lowercase__	     =						[]
		while not is_found and i < array_length:
				if array[i] < pivot:
						lowercase__	     =						True
						lowercase__	     =						[element for element in array[i:] if element >= array[i]]
						lowercase__	     =						longest_subsequence(__magic_name__	)
						if len(__magic_name__	) > len(__magic_name__	):
								lowercase__	     =						temp_array
				else:
						i += 1

		lowercase__	     =						[element for element in array[1:] if element >= pivot]
		lowercase__	     =						[pivot, *longest_subsequence(__magic_name__	)]
		if len(__magic_name__	) > len(__magic_name__	):
				return temp_array
		else:
				return longest_subseq


if __name__ == "__main__":
	import doctest

	doctest.testmod()

