





from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class    __SCREAMING_SNAKE_CASE			( UpperCamelCase_					):







       def 						__lowerCamelCase    (      self     :	Any		,					A     :	float			)   ->List[Any]:
          return 0.0



def        _a						(    UpperCAmelCase			,  UpperCAmelCase     )				->				List[Any]:







   """simple docstring"""
   lowerCamelCase__   :						Any					   =							min([-20, np.min(fft_results[1 : samplerate // 2 - 1]     )]     )
   lowerCamelCase__   :						Optional[Any]					   =							max([20, np.max(fft_results[1 : samplerate // 2 - 1]     )]     )
   return lowest, highest



def        _a						(    UpperCAmelCase			,  UpperCAmelCase     )				->				Union[str, Any]:







   """simple docstring"""
   lowerCamelCase__   :						List[Any]					   =							512
   lowerCamelCase__   :						Optional[Any]					   =							[1] + [0] * (size - 1)
   lowerCamelCase__   :						Tuple					   =							[filter_type.process(_lowercase     ) for item in inputs]

   lowerCamelCase__   :						Optional[int]					   =							[0] * (samplerate - size)  # zero-padding
   outputs += filler
   lowerCamelCase__   :						List[Any]					   =							np.abs(np.fft.fft(_lowercase     )     )
   lowerCamelCase__   :						Optional[int]					   =							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
   lowerCamelCase__   :						str					   =							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						(    UpperCAmelCase			,  UpperCAmelCase     )				->				List[str]:







   """simple docstring"""
   lowerCamelCase__   :						Any					   =							512
   lowerCamelCase__   :						int					   =							[1] + [0] * (size - 1)
   lowerCamelCase__   :						List[str]					   =							[filter_type.process(_lowercase     ) for item in inputs]

   lowerCamelCase__   :						Any					   =							[0] * (samplerate - size)  # zero-padding
   outputs += filler
   lowerCamelCase__   :						Dict					   =							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()




import math
def       A	(    _lowercase						):
						return math.sqrt(_lowercase						) * math.sqrt(_lowercase						) == num
def       A	(    _lowercase						):
						SCREAMING_SNAKE_CASE							:    Dict							=							0
						SCREAMING_SNAKE_CASE							:    Tuple							=							n
						while left <= right:
												SCREAMING_SNAKE_CASE							:    Union[str, Any]							=							(left + right) // 2
												if mid**2 == n:
																		return True
												elif mid**2 > n:
																		SCREAMING_SNAKE_CASE							:    Optional[Any]							=							mid - 1
												else:
																		SCREAMING_SNAKE_CASE							:    Optional[int]							=							mid + 1
						return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()





