




'''simple docstring'''





from __future__ import annotations







def 		_A(       UpperCamelCase__							:			Dict				,       UpperCamelCase__							:			Union[str, Any] = None				,       UpperCamelCase__							:			str = None				,       UpperCamelCase__							:			Dict = False				,       )    -> tuple[int, float, str]:
							'''simple docstring'''


							__lowercase      =    cipher_alphabet or [chr(a__				) for i in range(97				,       123				)]

							# If the argument is None or the user provided an empty dictionary
							if not frequencies_dict:
														# Frequencies of letters in the english language (how much they show up)
														__lowercase      =    {
														    '''a''': 0.0_8497,
														    '''b''': 0.0_1492,
														    '''c''': 0.0_2202,
														    '''d''': 0.0_4253,
														    '''e''': 0.1_1162,
														    '''f''': 0.0_2228,
														    '''g''': 0.0_2015,
														    '''h''': 0.0_6094,
														    '''i''': 0.0_7546,
														    '''j''': 0.0_0153,
														    '''k''': 0.0_1292,
														    '''l''': 0.0_4025,
														    '''m''': 0.0_2406,
														    '''n''': 0.0_6749,
														    '''o''': 0.0_7507,
														    '''p''': 0.0_1929,
														    '''q''': 0.0_0095,
														    '''r''': 0.0_7587,
														    '''s''': 0.0_6327,
														    '''t''': 0.0_9356,
														    '''u''': 0.0_2758,
														    '''v''': 0.0_0978,
														    '''w''': 0.0_2560,
														    '''x''': 0.0_0150,
														    '''y''': 0.0_1994,
														    '''z''': 0.0_0077,
														}
							else:
														# Custom frequencies dictionary
														__lowercase      =    frequencies_dict

							if not case_sensitive:
														__lowercase      =    ciphertext.lower()

							# Chi squared statistic values
							__lowercase      =    {}

							# cycle through all of the shifts
							for shift in range(len(a__				)				):
														__lowercase      =    ''''''

														# decrypt the message with the shift
														for letter in ciphertext:
																					try:
																												# Try to index the letter in the alphabet
																												__lowercase      =    (alphabet_letters.index(letter.lower()				) - shift) % len(
																												    a__				)
																												decrypted_with_shift += (
																												    alphabet_letters[new_key].upper()
																												    if case_sensitive and letter.isupper()
																												    else alphabet_letters[new_key]
																												)
																					except ValueError:
																												# Append the character if it isn't in the alphabet
																												decrypted_with_shift += letter

														__lowercase      =    0.0

														# Loop through each letter in the decoded message with the shift
														for letter in decrypted_with_shift:
																					if case_sensitive:
																												__lowercase      =    letter.lower()
																												if letter in frequencies:
																																			# Get the amount of times the letter occurs in the message
																																			__lowercase      =    decrypted_with_shift.lower().count(a__				)

																																			# Get the excepcted amount of times the letter should appear based
																																			# on letter frequencies
																																			__lowercase      =    frequencies[letter] * occurrences

																																			# Complete the chi squared statistic formula
																																			__lowercase      =    ((occurrences - expected) ** 2) / expected

																																			# Add the margin of error to the total chi squared statistic
																																			chi_squared_statistic += chi_letter_value
																					else:
																												if letter.lower() in frequencies:
																																			# Get the amount of times the letter occurs in the message
																																			__lowercase      =    decrypted_with_shift.count(a__				)

																																			# Get the excepcted amount of times the letter should appear based
																																			# on letter frequencies
																																			__lowercase      =    frequencies[letter] * occurrences

																																			# Complete the chi squared statistic formula
																																			__lowercase      =    ((occurrences - expected) ** 2) / expected

																																			# Add the margin of error to the total chi squared statistic
																																			chi_squared_statistic += chi_letter_value

																												# Add the data to the chi_squared_statistic_values dictionary
														__lowercase      =    (
														    chi_squared_statistic,
														    decrypted_with_shift,
														)

							# Get the most likely cipher by finding the cipher with the smallest chi squared
							# statistic
							def chi_squared_statistic_values_sorting_key(UpperCamelCase__							:			List[str]				) -> tuple[float, str]:
														return chi_squared_statistic_values[key]

							__lowercase      =    min(
							    a__				,       key=a__				,       )

							# Get all the data from the most likely cipher (key, decoded message)
							(
							    (
							    __lowercase	
							)     ,     (
							    __lowercase	
							)     ,     	
							)      =    chi_squared_statistic_values[most_likely_cipher]

							# Return the data on the most likely shift
							return (
							    most_likely_cipher,
							    most_likely_cipher_chi_squared_value,
							    decoded_most_likely_cipher,
							)












from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np







class a (     __SCREAMING_SNAKE_CASE  ):
						"""simple docstring"""

						def     UpperCAmelCase_      ( self :     List[str]				,							lowerCamelCase__ :     float				)    ->						float:
													"""simple docstring"""


													return 0.0







def 		_A(       UpperCamelCase__							:			np.ndarray				,       UpperCamelCase__							:			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(       UpperCamelCase__							:			FilterType				,       UpperCamelCase__							:			int				)    -> None:
							'''simple docstring'''


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

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

							plt.plot(UpperCamelCase__				)
							plt.show()







def 		_A(       UpperCamelCase__							:			FilterType				,       UpperCamelCase__							:			int				)    -> None:
							'''simple docstring'''


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

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






