

'''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 (							UpperCAmelCase__    ):

		'''simple docstring'''






		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_		)  ->     float:






							'''simple docstring'''



							return 0.0







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







def   _UpperCamelCase	(		__UpperCamelCase    ,__UpperCamelCase	)       ->			None:
					lowerCamelCase_  				=      5_12
					lowerCamelCase_  				=      [1] + [0] * (size - 1)
					lowerCamelCase_  				=      [filter_type.process(__UpperCamelCase	) for item in inputs]

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

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

					plt.plot(__UpperCamelCase	)
					plt.show()







def   _UpperCamelCase	(		__UpperCamelCase    ,__UpperCamelCase	)       ->			None:
					lowerCamelCase_  				=      5_12
					lowerCamelCase_  				=      [1] + [0] * (size - 1)
					lowerCamelCase_  				=      [filter_type.process(__UpperCamelCase	) for item in inputs]

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

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







from __future__ import annotations






def 						a__			(				A__,      A__ = None,      A__ = None				):
			if start is None:
						SCREAMING_SNAKE_CASE_		:     List[str]					=					0

			if end is None:
						SCREAMING_SNAKE_CASE_		:     Optional[Any]					=					len(A__				) - 1

			if start >= end:
						return

			SCREAMING_SNAKE_CASE_		:     Tuple					=					(start + end) // 2

			slowsort(A__,      A__,      A__				)
			slowsort(A__,      mid + 1,      A__				)

			if sequence[end] < sequence[mid]:
						SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     Optional[Any]					=					sequence[mid], sequence[end]

			slowsort(A__,      A__,      end - 1				)


if __name__ == "__main__":
				from doctest import testmod

				testmod()





