



from __future__ import annotations

class 					_A :



       def __init__(	self							:  Dict  ,	__SCREAMING_SNAKE_CASE							:  int):


           '''simple docstring'''

           __a		 =       order

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

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



       def 	_lowerCamelCase    (	self							:  Optional[Any]  ,	__SCREAMING_SNAKE_CASE							:  Any  ,	__SCREAMING_SNAKE_CASE							:  Dict):


           '''simple docstring'''

           if len(A_) < self.order:
               __a		 =       [1.0, *a_coeffs]

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

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

           __a		 =       a_coeffs
           __a		 =       b_coeffs





       def 	_lowerCamelCase    (	self							:  Dict  ,	__SCREAMING_SNAKE_CASE							:  str):


           '''simple docstring'''

           __a		 =       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]
               )

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

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

           __a		 =       sample
           __a		 =       result

           return result










def   __snake_case			(    _UpperCAmelCase     ,				_UpperCAmelCase = False       ):

    if not isinstance(_UpperCAmelCase     ,				_UpperCAmelCase       ):
        __a		 =       f'Expected string as input, found {type(_UpperCAmelCase       )}'
        raise ValueError(_UpperCAmelCase       )
    if not isinstance(_UpperCAmelCase     ,				_UpperCAmelCase       ):
        __a		 =       f'Expected boolean as use_pascal parameter, found {type(_UpperCAmelCase       )}'
        raise ValueError(_UpperCAmelCase       )

    __a		 =       input_str.split('''_'''       )

    __a		 =       0 if use_pascal else 1

    __a		 =       words[start_index:]

    __a		 =       [word[0].upper() + word[1:] for word in words_to_capitalize]

    __a		 =       '''''' if use_pascal else words[0]

    return "".join([initial_word, *capitalized_words]       )


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

 testmod()





