
from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						)			->    List[Any]:
    __lowercase		:      int						     =							tau * frequency / samplerate
    __lowercase		:      Optional[int]						     =							sin(__A						)
    __lowercase		:      Tuple						     =							cos(__A						)
    __lowercase		:      Any						     =							_sin / (2 * q_factor)

    __lowercase		:      List[Any]						     =							(1 - _cos) / 2
    __lowercase		:      str						     =							1 - _cos

    __lowercase		:      Any						     =							1 + alpha
    __lowercase		:      Optional[Any]						     =							-2 * _cos
    __lowercase		:      List[str]						     =							1 - alpha

    __lowercase		:      Any						     =							IIRFilter(2						)
    filt.set_coefficients([aa, aa, aa]						,       [ba, ba, ba]						)
    return filt


def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						)			->    Tuple:
    __lowercase		:      Optional[int]						     =							tau * frequency / samplerate
    __lowercase		:      Dict						     =							sin(__A						)
    __lowercase		:      Dict						     =							cos(__A						)
    __lowercase		:      Optional[int]						     =							_sin / (2 * q_factor)

    __lowercase		:      Any						     =							(1 + _cos) / 2
    __lowercase		:      Optional[Any]						     =							-1 - _cos

    __lowercase		:      Optional[int]						     =							1 + alpha
    __lowercase		:      str						     =							-2 * _cos
    __lowercase		:      List[str]						     =							1 - alpha

    __lowercase		:      Optional[Any]						     =							IIRFilter(2						)
    filt.set_coefficients([aa, aa, aa]						,       [ba, ba, ba]						)
    return filt


def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						)			->    Dict:
    __lowercase		:      Optional[int]						     =							tau * frequency / samplerate
    __lowercase		:      Union[str, Any]						     =							sin(__A						)
    __lowercase		:      Optional[int]						     =							cos(__A						)
    __lowercase		:      Dict						     =							_sin / (2 * q_factor)

    __lowercase		:      Optional[int]						     =							_sin / 2
    __lowercase		:      Optional[int]						     =							0
    __lowercase		:      List[str]						     =							-ba

    __lowercase		:      List[str]						     =							1 + alpha
    __lowercase		:      Union[str, Any]						     =							-2 * _cos
    __lowercase		:      List[Any]						     =							1 - alpha

    __lowercase		:      Dict						     =							IIRFilter(2						)
    filt.set_coefficients([aa, aa, aa]						,       [ba, ba, ba]						)
    return filt


def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						)			->    Any:
    __lowercase		:      Any						     =							tau * frequency / samplerate
    __lowercase		:      Any						     =							sin(__A						)
    __lowercase		:      Dict						     =							cos(__A						)
    __lowercase		:      List[Any]						     =							_sin / (2 * q_factor)

    __lowercase		:      Any						     =							1 - alpha
    __lowercase		:      int						     =							-2 * _cos
    __lowercase		:      Any						     =							1 + alpha

    __lowercase		:      Dict						     =							IIRFilter(2						)
    filt.set_coefficients([ba, ba, ba]						,       [ba, ba, ba]						)
    return filt


def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						,       )			->    str:
    __lowercase		:      List[Any]						     =							tau * frequency / samplerate
    __lowercase		:      List[str]						     =							sin(__A						)
    __lowercase		:      Dict						     =							cos(__A						)
    __lowercase		:      Dict						     =							_sin / (2 * q_factor)
    __lowercase		:      Optional[int]						     =							10 ** (gain_db / 40)

    __lowercase		:      Optional[Any]						     =							1 + alpha * big_a
    __lowercase		:      Dict						     =							-2 * _cos
    __lowercase		:      Optional[int]						     =							1 - alpha * big_a
    __lowercase		:      Optional[int]						     =							1 + alpha / big_a
    __lowercase		:      Optional[int]						     =							-2 * _cos
    __lowercase		:      Union[str, Any]						     =							1 - alpha / big_a

    __lowercase		:      List[str]						     =							IIRFilter(2						)
    filt.set_coefficients([aa, aa, aa]						,       [ba, ba, ba]						)
    return filt


def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						,       )			->    Union[str, Any]:
    __lowercase		:      Tuple						     =							tau * frequency / samplerate
    __lowercase		:      Any						     =							sin(__A						)
    __lowercase		:      int						     =							cos(__A						)
    __lowercase		:      List[Any]						     =							_sin / (2 * q_factor)
    __lowercase		:      Any						     =							10 ** (gain_db / 40)
    __lowercase		:      Dict						     =							(big_a + 1) - (big_a - 1) * _cos
    __lowercase		:      List[str]						     =							(big_a + 1) + (big_a - 1) * _cos
    __lowercase		:      List[str]						     =							(big_a - 1) - (big_a + 1) * _cos
    __lowercase		:      List[Any]						     =							(big_a - 1) + (big_a + 1) * _cos
    __lowercase		:      Optional[Any]						     =							2 * sqrt(__A						) * alpha

    __lowercase		:      int						     =							big_a * (pmc + aaa)
    __lowercase		:      Tuple						     =							2 * big_a * mpc
    __lowercase		:      Any						     =							big_a * (pmc - aaa)
    __lowercase		:      Tuple						     =							ppmc + aaa
    __lowercase		:      List[Any]						     =							-2 * pmpc
    __lowercase		:      Union[str, Any]						     =							ppmc - aaa

    __lowercase		:      int						     =							IIRFilter(2						)
    filt.set_coefficients([aa, aa, aa]						,       [ba, ba, ba]						)
    return filt





def      UpperCAmelCase_	(    __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase						,       __lowerCAmelCase = 1 / sqrt(2						)						,       )			->    Optional[int]:
    __lowercase		:      str						     =							tau * frequency / samplerate
    __lowercase		:      Any						     =							sin(__A						)
    __lowercase		:      List[Any]						     =							cos(__A						)
    __lowercase		:      List[Any]						     =							_sin / (2 * q_factor)
    __lowercase		:      Optional[int]						     =							10 ** (gain_db / 40)
    __lowercase		:      Dict						     =							(big_a + 1) - (big_a - 1) * _cos
    __lowercase		:      Optional[int]						     =							(big_a + 1) + (big_a - 1) * _cos
    __lowercase		:      Union[str, Any]						     =							(big_a - 1) - (big_a + 1) * _cos
    __lowercase		:      Tuple						     =							(big_a - 1) + (big_a + 1) * _cos
    __lowercase		:      Tuple						     =							2 * sqrt(__A						) * alpha

    __lowercase		:      List[Any]						     =							big_a * (ppmc + aaa)
    __lowercase		:      List[str]						     =							-2 * big_a * pmpc
    __lowercase		:      Tuple						     =							big_a * (ppmc - aaa)
    __lowercase		:      Optional[Any]						     =							pmc + aaa
    __lowercase		:      int						     =							2 * mpc
    __lowercase		:      Dict						     =							pmc - aaa

    __lowercase		:      Any						     =							IIRFilter(2						)
    filt.set_coefficients([aa, aa, aa]						,       [ba, ba, ba]						)
    return filt










'''simple docstring'''







def 		_UpperCAmelCase (				__A				: int   ):
				a_		:	Optional[Any]									=   []
				a_		:	Optional[Any]									=   []
				a_		:	List[str]									=   {
				    '''^''': 3,
				    '''*''': 2,
				    '''/''': 2,
				    '''%''': 2,
				    '''+''': 1,
				    '''-''': 1,
				}  # Priority of each operator
				a_		:	int									=   len(__A   ) if (len(__A   ) > 7) else 7

				# Print table header for output
				print(
				    '''Symbol'''.center(8   )    ,		'''Stack'''.center(__A   )    ,		'''Postfix'''.center(__A   )    ,		sep=''' | '''    ,		)
				print('''-''' * (print_width * 3 + 7)   )

				for x in infix:
								if x.isalpha() or x.isdigit():
												post_fix.append(__A   )  # if x is Alphabet / Digit, add it to Postfix
								elif x == "(":
												stack.append(__A   )  # if x is "(" push to Stack
								elif x == ")":  # if x is ")" pop stack until "(" is encountered
												while stack[-1] != "(":
																post_fix.append(stack.pop()   )  # Pop stack & add the content to Postfix
												stack.pop()
								else:
												if len(__A   ) == 0:
																stack.append(__A   )  # If stack is empty, push x to stack
												else:  # while priority of x is not > priority of element in the stack
																while len(__A   ) > 0 and priority[x] <= priority[stack[-1]]:
																				post_fix.append(stack.pop()   )  # pop stack & add to Postfix
																stack.append(__A   )  # push x to stack

								print(
								    x.center(8   )    ,		(''''''.join(__A   )).ljust(__A   )    ,		(''''''.join(__A   )).ljust(__A   )    ,		sep=''' | '''    ,		)  # Output in tabular format

				while len(__A   ) > 0:  # while stack is not empty
								post_fix.append(stack.pop()   )  # pop stack & add to Postfix
								print(
								    ''' '''.center(8   )    ,		(''''''.join(__A   )).ljust(__A   )    ,		(''''''.join(__A   )).ljust(__A   )    ,		sep=''' | '''    ,		)  # Output in tabular format

				return "".join(__A   )  # return Postfix as str





def 		_UpperCAmelCase (				__A				: Tuple   ):
				a_		:	Union[str, Any]									=   list(infix[::-1]   )  # reverse the infix equation

				for i in range(len(__A   )   ):
								if infix[i] == "(":
												a_		:	List[str]									=   ''')'''  # change "(" to ")"
								elif infix[i] == ")":
												a_		:	str									=   '''('''  # change ")" to "("

				return (infix_2_postfix(''''''.join(__A   )   ))[
				    ::-1
				]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
		__lowerCAmelCase									=   input('\nEnter an Infix Equation = ')  # Input an Infix equation
		__lowerCAmelCase									=   ''.join(Infix.split())  # Remove spaces from the input
		print('\n\t', Infix, '(Infix) -> ', infix_2_prefix(Infix), '(Prefix)')




