

'''simple docstring'''




class 					__magic_name__		:







			def __init__(			self       :						Dict       ,    lowercase_       :						int       ,    lowercase_       :						Optional[Any]=None       ,    lowercase_       :						Any=None					):
										lowercase_      :    Optional[int]       		= data
										lowercase_      :    int       		= previous
										lowercase_      :    Optional[int]       		= next_node







			def __str__(			self       :						List[Any]					):
										return f'''{self.data}'''







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Tuple					):
										return self.data







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Union[str, Any]					):
										return self.next







			def 			SCREAMING_SNAKE_CASE_  (			self       :						int					):
										return self.previous





class 					__magic_name__		:







			def __init__(			self       :						int       ,    lowercase_       :						Union[str, Any]					):
										lowercase_      :    Optional[Any]       		= head







			def __iter__(			self       :						List[str]					):
										return self







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Union[str, Any]					):







										if not self.current:
																	raise StopIteration
										else:
																	lowercase_      :    int       		= self.current.get_data()
																	lowercase_      :    List[str]       		= self.current.get_next()
																	return value





class 					__magic_name__		:







			def __init__(			self       :						Dict					):
										lowercase_      :    Tuple       		= None  # First node in list
										lowercase_      :    Tuple       		= None  # Last node in list







			def __str__(			self       :						int					):
										lowercase_      :    str       		= self.head
										lowercase_      :    Any       		= []
										while current is not None:
																	nodes.append(current.get_data()					)
																	lowercase_      :    Any       		= current.get_next()
										return " ".join(str(lowerCAmelCase_					) for node in nodes					)







			def __contains__(			self       :						int       ,    lowercase_       :						int					):
										lowercase_      :    Optional[Any]       		= self.head
										while current:
																	if current.get_data() == value:
																								return True
																	lowercase_      :    List[Any]       		= current.get_next()
										return False







			def __iter__(			self       :						Optional[int]					):
										return LinkedListIterator(self.head					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Tuple					):







										if self.head:
																	return self.head.get_data()
										return None







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Optional[int]					):







										if self.tail:
																	return self.tail.get_data()
										return None







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Dict       ,    lowercase_       :						Node					):







										if self.head is None:
																	lowercase_      :    Union[str, Any]       		= node
																	lowercase_      :    str       		= node
										else:
																	self.insert_before_node(self.head       ,    lowerCAmelCase_					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Dict       ,    lowercase_       :						Node					):







										if self.head is None:
																	self.set_head(lowerCAmelCase_					)
										else:
																	self.insert_after_node(self.tail       ,    lowerCAmelCase_					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Tuple       ,    lowercase_       :						int					):
										lowercase_      :    int       		= Node(lowerCAmelCase_					)
										if self.head is None:
																	self.set_head(lowerCAmelCase_					)
										else:
																	self.set_tail(lowerCAmelCase_					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Optional[Any]       ,    lowercase_       :						Node       ,    lowercase_       :						Node					):
										lowercase_      :    List[Any]       		= node
										lowercase_      :    List[str]       		= node.previous

										if node.get_previous() is None:
																	lowercase_      :    Any       		= node_to_insert
										else:
																	lowercase_      :    List[str]       		= node_to_insert

										lowercase_      :    List[str]       		= node_to_insert







			def 			SCREAMING_SNAKE_CASE_  (			self       :						List[str]       ,    lowercase_       :						Node       ,    lowercase_       :						Node					):
										lowercase_      :    Union[str, Any]       		= node
										lowercase_      :    Any       		= node.next

										if node.get_next() is None:
																	lowercase_      :    int       		= node_to_insert
										else:
																	lowercase_      :    int       		= node_to_insert

										lowercase_      :    List[Any]       		= node_to_insert







			def 			SCREAMING_SNAKE_CASE_  (			self       :						List[Any]       ,    lowercase_       :						int       ,    lowercase_       :						int					):
										lowercase_      :    Union[str, Any]       		= 1
										lowercase_      :    Union[str, Any]       		= Node(lowerCAmelCase_					)
										lowercase_      :    Union[str, Any]       		= self.head
										while node:
																	if current_position == position:
																								self.insert_before_node(lowerCAmelCase_       ,    lowerCAmelCase_					)
																								return
																	current_position += 1
																	lowercase_      :    Optional[int]       		= node.next
										self.insert_after_node(self.tail       ,    lowerCAmelCase_					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						List[str]       ,    lowercase_       :						int					):
										lowercase_      :    List[str]       		= self.head
										while node:
																	if node.get_data() == item:
																								return node
																	lowercase_      :    Tuple       		= node.get_next()
										raise Exception("""Node not found"""					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						List[Any]       ,    lowercase_       :						Optional[int]					):







										if (node := self.get_node(lowerCAmelCase_					)) is not None:
																	if node == self.head:
																								lowercase_      :    List[Any]       		= self.head.get_next()

																	if node == self.tail:
																								lowercase_      :    Union[str, Any]       		= self.tail.get_previous()

																	self.remove_node_pointers(lowerCAmelCase_					)







			@staticmethod
			def 			SCREAMING_SNAKE_CASE_  (			lowercase_       :						Node					):







										if node.get_next():
																	lowercase_      :    Any       		= node.previous

										if node.get_previous():
																	lowercase_      :    Optional[Any]       		= node.next

										lowercase_      :    Optional[Any]       		= None
										lowercase_      :    Optional[Any]       		= None







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Dict					):
										return self.head is None




def 							lowerCamelCase			(   )    ->   None:
							pass




if __name__ == "__main__":
						import doctest

						doctest.testmod()






'''simple docstring'''




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    Tuple       		= sin(UpperCAmelCase__				)
							lowercase_      :    int       		= cos(UpperCAmelCase__				)
							lowercase_      :    Any       		= _sin / (2 * q_factor)

							lowercase_      :    Dict       		= (1 - _cos) / 2
							lowercase_      :    Optional[int]       		= 1 - _cos

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

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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    Optional[int]       		= sin(UpperCAmelCase__				)
							lowercase_      :    Dict       		= cos(UpperCAmelCase__				)
							lowercase_      :    Optional[int]       		= _sin / (2 * q_factor)

							lowercase_      :    Dict       		= (1 + _cos) / 2
							lowercase_      :    str       		= -1 - _cos

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    Optional[Any]       		= -2 * _cos
							lowercase_      :    List[Any]       		= 1 - alpha

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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    int       		= tau * frequency / samplerate
							lowercase_      :    int       		= sin(UpperCAmelCase__				)
							lowercase_      :    Union[str, Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    str       		= _sin / (2 * q_factor)

							lowercase_      :    str       		= _sin / 2
							lowercase_      :    Any       		= 0
							lowercase_      :    Optional[Any]       		= -ba

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    Union[str, Any]       		= -2 * _cos
							lowercase_      :    Union[str, Any]       		= 1 - alpha

							lowercase_      :    Tuple       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    List[str]       		= tau * frequency / samplerate
							lowercase_      :    Any       		= sin(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    Optional[Any]       		= _sin / (2 * q_factor)

							lowercase_      :    Any       		= 1 - alpha
							lowercase_      :    Optional[Any]       		= -2 * _cos
							lowercase_      :    Optional[int]       		= 1 + alpha

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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    Dict       		= tau * frequency / samplerate
							lowercase_      :    Tuple       		= sin(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= _sin / (2 * q_factor)
							lowercase_      :    Any       		= 10 ** (gain_db / 40)

							lowercase_      :    List[str]       		= 1 + alpha * big_a
							lowercase_      :    List[Any]       		= -2 * _cos
							lowercase_      :    Dict       		= 1 - alpha * big_a
							lowercase_      :    str       		= 1 + alpha / big_a
							lowercase_      :    List[str]       		= -2 * _cos
							lowercase_      :    Tuple       		= 1 - alpha / big_a

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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    Dict       		= tau * frequency / samplerate
							lowercase_      :    Union[str, Any]       		= sin(UpperCAmelCase__				)
							lowercase_      :    Any       		= cos(UpperCAmelCase__				)
							lowercase_      :    Any       		= _sin / (2 * q_factor)
							lowercase_      :    Any       		= 10 ** (gain_db / 40)
							lowercase_      :    Any       		= (big_a + 1) - (big_a - 1) * _cos
							lowercase_      :    int       		= (big_a + 1) + (big_a - 1) * _cos
							lowercase_      :    Tuple       		= (big_a - 1) - (big_a + 1) * _cos
							lowercase_      :    Optional[Any]       		= (big_a - 1) + (big_a + 1) * _cos
							lowercase_      :    int       		= 2 * sqrt(UpperCAmelCase__				) * alpha

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

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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    int       		= sin(UpperCAmelCase__				)
							lowercase_      :    int       		= cos(UpperCAmelCase__				)
							lowercase_      :    Dict       		= _sin / (2 * q_factor)
							lowercase_      :    Union[str, Any]       		= 10 ** (gain_db / 40)
							lowercase_      :    Union[str, Any]       		= (big_a + 1) - (big_a - 1) * _cos
							lowercase_      :    Optional[int]       		= (big_a + 1) + (big_a - 1) * _cos
							lowercase_      :    Any       		= (big_a - 1) - (big_a + 1) * _cos
							lowercase_      :    str       		= (big_a - 1) + (big_a + 1) * _cos
							lowercase_      :    Optional[int]       		= 2 * sqrt(UpperCAmelCase__				) * alpha

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

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





