






from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np
class    _UpperCAmelCase      ( A__			):

				"""simple docstring"""




				def        lowercase__     (  self		:					str,						lowerCamelCase		:					float						):

								'''simple docstring'''
								return 0.0






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''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    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    512
				lowercase__     				=    [1] + [0] * (size - 1)
				lowercase__     				=    [filter_type.process(lowerCamelCase_       ) for item in inputs]

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

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

				plt.plot(lowerCamelCase_       )
				plt.show()






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    512
				lowercase__     				=    [1] + [0] * (size - 1)
				lowercase__     				=    [filter_type.process(lowerCamelCase_       ) for item in inputs]

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

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












def 						a    (		lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''

				if exponent == 1:
								return base
				if exponent % 2 == 0:
								lowercase__     				=    _modexpt(lowerCamelCase_	,     exponent // 2	,     lowerCamelCase_       ) % modulo_value
								return (x * x) % modulo_value
				else:
								return (base * _modexpt(lowerCamelCase_	,     exponent - 1	,     lowerCamelCase_       )) % modulo_value






def 						a    (		lowerCamelCase_ = 1777	,     lowerCamelCase_ = 1855	,     lowerCamelCase_ = 8       ):






				'''simple docstring'''
				lowercase__     				=    base
				for _ in range(1	,     lowerCamelCase_       ):
								lowercase__     				=    _modexpt(lowerCamelCase_	,     lowerCamelCase_	,     10**digits       )

				return result


if __name__ == "__main__":
							print(F"{solution() = }")




