






from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np



class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							float:
							return 0.0





def 					lowercase__				(					__snake_case   :							np.ndarray					,	__snake_case   :							int  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Any						=						min([-20, np.min(fft_results[1 : samplerate // 2 - 1]  )]  )
					UpperCAmelCase_   :				Optional[int]						=						max([20, np.max(fft_results[1 : samplerate // 2 - 1]  )]  )
					return lowest, highest




def 					lowercase__				(					__snake_case   :							FilterType					,	__snake_case   :							int  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Tuple						=						512
					UpperCAmelCase_   :				int						=						[1] + [0] * (size - 1)
					UpperCAmelCase_   :				Tuple						=						[filter_type.process(__snake_case  ) for item in inputs]

					UpperCAmelCase_   :				Any						=						[0] * (samplerate - size)  # zero-padding
					outputs += filler
					UpperCAmelCase_   :				Optional[int]						=						np.abs(np.fft.fft(__snake_case  )  )
					UpperCAmelCase_   :				List[str]						=						20 * np.logaa(__snake_case  )

					# 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
					UpperCAmelCase_   :				Tuple						=						get_bounds(__snake_case					,	__snake_case  )
					plt.ylim(max([-80, bounds[0]]  )					,	min([80, bounds[1]]  )  )
					plt.ylabel('Gain (dB)'  )

					plt.plot(__snake_case  )
					plt.show()






def 					lowercase__				(					__snake_case   :							FilterType					,	__snake_case   :							int  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Optional[int]						=						512
					UpperCAmelCase_   :				Any						=						[1] + [0] * (size - 1)
					UpperCAmelCase_   :				int						=						[filter_type.process(__snake_case  ) for item in inputs]

					UpperCAmelCase_   :				str						=						[0] * (samplerate - size)  # zero-padding
					outputs += filler
					UpperCAmelCase_   :				Any						=						np.angle(np.fft.fft(__snake_case  )  )

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














from __future__ import annotations




def 					lowercase__				(					__snake_case   :							list[int]					,	__snake_case   :							int  ):


					'''simple docstring'''


					if len(__snake_case  ) < k or k < 0:
										raise ValueError('Invalid Input'  )
					UpperCAmelCase_   :				int						=						sum(array[:k]  )
					for i in range(len(__snake_case  ) - k  ):
										UpperCAmelCase_   :				List[Any]						=						current_sum - array[i] + array[i + k]
										UpperCAmelCase_   :				List[Any]						=						max(__snake_case					,	__snake_case  )
					return max_sum


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

		testmod()
		__UpperCAmelCase     							=						[randint(-1000, 1000) for i in range(100)]
		__UpperCAmelCase     							=						randint(0, 110)
		print(F'The maximum sum of {k} consecutive elements is {max_sum_in_array(array,k)}')






