

import math

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



def 				snake_case_(_UpperCamelCase = 3					)							->     qiskit.result.counts.Counts:



  """simple docstring"""






  if isinstance(_UpperCamelCase			,	_UpperCamelCase					):
    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(_UpperCamelCase					) != 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).'''					)

  _snake_case						=							QuantumRegister(_UpperCamelCase			,	'''qr'''					)
  _snake_case						=							ClassicalRegister(_UpperCamelCase			,	'''cr'''					)

  _snake_case						=							QuantumCircuit(_UpperCamelCase			,	_UpperCamelCase					)

  _snake_case						=							number_of_qubits

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

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

  # measure all the qubits
  quantum_circuit.measure(_UpperCamelCase			,	_UpperCamelCase					)
  # simulate with 10000 shots
  _snake_case						=							Aer.get_backend('''qasm_simulator'''					)
  _snake_case						=							execute(_UpperCamelCase			,	_UpperCamelCase			,	shots=10_000					)

  return job.result().get_counts(_UpperCamelCase					)


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





from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

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

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

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



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

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

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

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



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							_sin / 2
  _snake_case						=							0
  _snake_case						=							-ba

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

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



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

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

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



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)

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

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



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)
  _snake_case						=							(big_a + 1) - (big_a - 1) * _cos
  _snake_case						=							(big_a + 1) + (big_a - 1) * _cos
  _snake_case						=							(big_a - 1) - (big_a + 1) * _cos
  _snake_case						=							(big_a - 1) + (big_a + 1) * _cos
  _snake_case						=							2 * sqrt(_UpperCamelCase					) * alpha

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

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



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)
  _snake_case						=							(big_a + 1) - (big_a - 1) * _cos
  _snake_case						=							(big_a + 1) + (big_a - 1) * _cos
  _snake_case						=							(big_a - 1) - (big_a + 1) * _cos
  _snake_case						=							(big_a - 1) + (big_a + 1) * _cos
  _snake_case						=							2 * sqrt(_UpperCamelCase					) * alpha

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

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

