




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter





def __UpperCamelCase			(       _A ,  _A ,  _A = 1 / sqrt(2  )  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)

						lowerCAmelCase_      			=  (1 - _cos) / 2
						lowerCAmelCase_      			=  1 - _cos

						lowerCAmelCase_      			=  1 + alpha
						lowerCAmelCase_      			=  -2 * _cos
						lowerCAmelCase_      			=  1 - alpha

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([aa, aa, aa] ,  [ba, ba, ba]  )
						return filt





def __UpperCamelCase			(       _A ,  _A ,  _A = 1 / sqrt(2  )  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)

						lowerCAmelCase_      			=  (1 + _cos) / 2
						lowerCAmelCase_      			=  -1 - _cos

						lowerCAmelCase_      			=  1 + alpha
						lowerCAmelCase_      			=  -2 * _cos
						lowerCAmelCase_      			=  1 - alpha

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([aa, aa, aa] ,  [ba, ba, ba]  )
						return filt





def __UpperCamelCase			(       _A ,  _A ,  _A = 1 / sqrt(2  )  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)

						lowerCAmelCase_      			=  _sin / 2
						lowerCAmelCase_      			=  0
						lowerCAmelCase_      			=  -ba

						lowerCAmelCase_      			=  1 + alpha
						lowerCAmelCase_      			=  -2 * _cos
						lowerCAmelCase_      			=  1 - alpha

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([aa, aa, aa] ,  [ba, ba, ba]  )
						return filt





def __UpperCamelCase			(       _A ,  _A ,  _A = 1 / sqrt(2  )  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)

						lowerCAmelCase_      			=  1 - alpha
						lowerCAmelCase_      			=  -2 * _cos
						lowerCAmelCase_      			=  1 + alpha

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([ba, ba, ba] ,  [ba, ba, ba]  )
						return filt





def __UpperCamelCase			(       _A ,  _A ,  _A ,  _A = 1 / sqrt(2  ) ,  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)
						lowerCAmelCase_      			=  10 ** (gain_db / 40)

						lowerCAmelCase_      			=  1 + alpha * big_a
						lowerCAmelCase_      			=  -2 * _cos
						lowerCAmelCase_      			=  1 - alpha * big_a
						lowerCAmelCase_      			=  1 + alpha / big_a
						lowerCAmelCase_      			=  -2 * _cos
						lowerCAmelCase_      			=  1 - alpha / big_a

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([aa, aa, aa] ,  [ba, ba, ba]  )
						return filt





def __UpperCamelCase			(       _A ,  _A ,  _A ,  _A = 1 / sqrt(2  ) ,  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)
						lowerCAmelCase_      			=  10 ** (gain_db / 40)
						lowerCAmelCase_      			=  (big_a + 1) - (big_a - 1) * _cos
						lowerCAmelCase_      			=  (big_a + 1) + (big_a - 1) * _cos
						lowerCAmelCase_      			=  (big_a - 1) - (big_a + 1) * _cos
						lowerCAmelCase_      			=  (big_a - 1) + (big_a + 1) * _cos
						lowerCAmelCase_      			=  2 * sqrt(_A  ) * alpha

						lowerCAmelCase_      			=  big_a * (pmc + aaa)
						lowerCAmelCase_      			=  2 * big_a * mpc
						lowerCAmelCase_      			=  big_a * (pmc - aaa)
						lowerCAmelCase_      			=  ppmc + aaa
						lowerCAmelCase_      			=  -2 * pmpc
						lowerCAmelCase_      			=  ppmc - aaa

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([aa, aa, aa] ,  [ba, ba, ba]  )
						return filt






def __UpperCamelCase			(       _A ,  _A ,  _A ,  _A = 1 / sqrt(2  ) ,  ):
						lowerCAmelCase_      			=  tau * frequency / samplerate
						lowerCAmelCase_      			=  sin(_A  )
						lowerCAmelCase_      			=  cos(_A  )
						lowerCAmelCase_      			=  _sin / (2 * q_factor)
						lowerCAmelCase_      			=  10 ** (gain_db / 40)
						lowerCAmelCase_      			=  (big_a + 1) - (big_a - 1) * _cos
						lowerCAmelCase_      			=  (big_a + 1) + (big_a - 1) * _cos
						lowerCAmelCase_      			=  (big_a - 1) - (big_a + 1) * _cos
						lowerCAmelCase_      			=  (big_a - 1) + (big_a + 1) * _cos
						lowerCAmelCase_      			=  2 * sqrt(_A  ) * alpha

						lowerCAmelCase_      			=  big_a * (ppmc + aaa)
						lowerCAmelCase_      			=  -2 * big_a * pmpc
						lowerCAmelCase_      			=  big_a * (ppmc - aaa)
						lowerCAmelCase_      			=  pmc + aaa
						lowerCAmelCase_      			=  2 * mpc
						lowerCAmelCase_      			=  pmc - aaa

						lowerCAmelCase_      			=  IIRFilter(2  )
						filt.set_coefficients([aa, aa, aa] ,  [ba, ba, ba]  )
						return filt










import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute





def __UpperCamelCase			(       _A = 3  ):
						if isinstance(_A ,  _A  ):
												raise TypeError('''number of qubits must be a integer.'''  )
						if number_of_qubits <= 0:
												raise ValueError('''number of qubits must be > 0.'''  )
						if math.floor(_A  ) != number_of_qubits:
												raise ValueError('''number of qubits must be exact integer.'''  )
						if number_of_qubits > 10:
												raise ValueError('''number of qubits too large to simulate(>10).'''  )

						lowerCAmelCase_      			=  QuantumRegister(_A ,  '''qr'''  )
						lowerCAmelCase_      			=  ClassicalRegister(_A ,  '''cr'''  )

						lowerCAmelCase_      			=  QuantumCircuit(_A ,  _A  )

						lowerCAmelCase_      			=  number_of_qubits

						for i in range(_A  ):
												quantum_circuit.h(number_of_qubits - i - 1  )
												counter -= 1
												for j in range(_A  ):
																		quantum_circuit.cp(np.pi / 2 ** (counter - j) ,  _A ,  _A  )

						for k in range(number_of_qubits // 2  ):
												quantum_circuit.swap(_A ,  number_of_qubits - k - 1  )

						# measure all the qubits
						quantum_circuit.measure(_A ,  _A  )
						# simulate with 10000 shots
						lowerCAmelCase_      			=  Aer.get_backend('''qasm_simulator'''  )
						lowerCAmelCase_      			=  execute(_A ,  _A ,  shots=10000  )

						return job.result().get_counts(_A  )


if __name__ == "__main__":
						print(
						    f"Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}"
						)




