


"""simple docstring"""




from __future__ import annotations
class    lowerCAmelCase      :




		'''simple docstring'''







		def __init__(      self		,			lowerCAmelCase__							)	->				None:
								SCREAMING_SNAKE_CASE						=   order

								# a_{0} ... a_{k}
								SCREAMING_SNAKE_CASE						=   [1.0] + [0.0] * order
								# b_{0} ... b_{k}
								SCREAMING_SNAKE_CASE						=   [1.0] + [0.0] * order

								# x[n-1] ... x[n-k]
								SCREAMING_SNAKE_CASE						=   [0.0] * self.order
								# y[n-1] ... y[n-k]
								SCREAMING_SNAKE_CASE						=   [0.0] * self.order







		def 				__A		(      self		,			lowerCAmelCase__		,			lowerCAmelCase__							)	->				None:
								if len(_lowercase							) < self.order:
														SCREAMING_SNAKE_CASE						=   [1.0, *a_coeffs]

								if len(_lowercase							) != self.order + 1:
														SCREAMING_SNAKE_CASE						=   (
														    F'Expected a_coeffs to have {self.order + 1} elements '
														    F'for {self.order}-order filter, got {len(_lowercase							)}'
														)
														raise ValueError(_lowercase							)

								if len(_lowercase							) != self.order + 1:
														SCREAMING_SNAKE_CASE						=   (
														    F'Expected b_coeffs to have {self.order + 1} elements '
														    F'for {self.order}-order filter, got {len(_lowercase							)}'
														)
														raise ValueError(_lowercase							)

								SCREAMING_SNAKE_CASE						=   a_coeffs
								SCREAMING_SNAKE_CASE						=   b_coeffs







		def 				__A		(      self		,			lowerCAmelCase__							)	->				float:
								SCREAMING_SNAKE_CASE						=   0.0

								# Start at index 1 and do index 0 at the end.
								for i in range(1		,			self.order + 1							):
														result += (
														    self.b_coeffs[i] * self.input_history[i - 1]
														    - self.a_coeffs[i] * self.output_history[i - 1]
														)

								SCREAMING_SNAKE_CASE						=   (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

								SCREAMING_SNAKE_CASE						=   self.input_history[:-1]
								SCREAMING_SNAKE_CASE						=   self.output_history[:-1]

								SCREAMING_SNAKE_CASE						=   sample
								SCREAMING_SNAKE_CASE						=   result

								return result





'''simple docstring'''

def 							_UpperCamelCase				(   lowerCAmelCase__:					int		,lowerCAmelCase__:					int   )      -> str:
							if a < 0 or b < 0:
														raise ValueError('the value of both inputs must be positive'   )
							SCREAMING_SNAKE_CASE_				=				str(bin(lowerCAmelCase__   )   )[2:]  # remove the leading "0b"
							SCREAMING_SNAKE_CASE_				=				str(bin(lowerCAmelCase__   )   )[2:]
							SCREAMING_SNAKE_CASE_				=				max(len(lowerCAmelCase__   )		,len(lowerCAmelCase__   )   )
							return "0b" + "".join(
							    str(int('1' in (char_a, char_b)   )   )
							    for char_a, char_b in zip(a_binary.zfill(lowerCAmelCase__   )		,b_binary.zfill(lowerCAmelCase__   )   )   )


if __name__ == "__main__":
							import doctest

							doctest.testmod()





