我们从Python开源项目中，提取了以下7个代码示例，用于说明如何使用numpy.fft.irfft()。
def make_residual_func(samples, indices, **params): 'closure for residual func' fft_size = 2 while fft_size < indices[-1]: fft_size *= 2 freqs = rfftfreq(fft_size, 5) ind_from = int(round(1/(params['t_max']*freqs[1]))) ind_to = ind_from+params['n_harm'] def make_series(x): 'Calculates time series from parameterized spectrum' nonlocal freqs, ind_from, ind_to, params spectrum = zeros_like(freqs, 'complex') sign_x0 = 0 if x[0] == 0.5 else abs(x[0]-0.5)/(x[0]-0.5) spectrum[0] = rect(sign_x0*exp(params['scale'][0]*abs(x[0]-0.5)), 0) for i in range(ind_from, ind_to): spectrum[i] = rect( exp(params['scale'][1]*x[1]+params['slope']*log(freqs[i])), params['scale'][2]*x[2+i-ind_from] ) return irfft(spectrum) def residual_func(x): 'calculates sum of squared residuals' nonlocal samples, indices series = make_series(x) sum_err = 0 for position, ind in enumerate(indices): sum_err += (series[ind]-samples[position])**2 return sum_err return make_series, residual_func
def single_step_propagation(self): """ Perform single step propagation. The final Wigner function is not normalized. :return: self.wignerfunction """ expV = self.get_expV(self.t) # p x -> theta x self.wignerfunction = fft.rfft(self.wignerfunction, axis=0) self.wignerfunction *= expV # theta x -> p x self.wignerfunction = fft.irfft(self.wignerfunction, axis=0) # p x -> p lambda self.wignerfunction = fft.rfft(self.wignerfunction, axis=1) self.wignerfunction *= self.get_expK(self.t) # p lambda -> p x self.wignerfunction = fft.irfft(self.wignerfunction, axis=1) # p x -> theta x self.wignerfunction = fft.rfft(self.wignerfunction, axis=0) self.wignerfunction *= expV # theta x -> p x self.wignerfunction = fft.irfft(self.wignerfunction, axis=0) # increment current time self.t += self.dt return self.wignerfunction
def single_step_propagation(self): """ Perform single step propagation. The final Wigner function is not normalized. :return: self.wignerfunction """ # p x -> theta x self.wignerfunction = fft.rfft(self.wignerfunction, axis=0) self.wignerfunction *= self.expV # theta x -> p x self.wignerfunction = fft.irfft(self.wignerfunction, axis=0) # p x -> p lambda self.wignerfunction = fft.rfft(self.wignerfunction, axis=1) self.wignerfunction *= self.expK # p lambda -> p x self.wignerfunction = fft.irfft(self.wignerfunction, axis=1) # p x -> theta x self.wignerfunction = fft.rfft(self.wignerfunction, axis=0) self.wignerfunction *= self.expV # theta x -> p x self.wignerfunction = fft.irfft(self.wignerfunction, axis=0) return self.wignerfunction
def istft(stft_signal, size=1024, shift=256, window=signal.blackman, fading=True, window_length=None): """ Calculated the inverse short time Fourier transform to exactly reconstruct the time signal. :param stft_signal: Single channel complex STFT signal with dimensions frames times size/2+1. :param size: Scalar FFT-size. :param shift: Scalar FFT-shift. Typically shift is a fraction of size. :param window: Window function handle. :param fading: Removes the additional padding, if done during STFT. :param window_length: Sometimes one desires to use a shorter window than the fft size. In that case, the window is padded with zeros. The default is to use the fft-size as a window size. :return: Single channel complex STFT signal :return: Single channel time signal. """ assert stft_signal.shape[1] == size // 2 + 1 if window_length is None: window = window(size) else: window = window(window_length) window = np.pad(window, (0, size - window_length), mode='constant') window = _biorthogonal_window_loopy(window, shift) # Why? Line created by Hai, Lukas does not know, why it exists. window *= size time_signal = scipy.zeros(stft_signal.shape[0] * shift + size - shift) for j, i in enumerate(range(0, len(time_signal) - size + shift, shift)): time_signal[i:i + size] += window * np.real(irfft(stft_signal[j])) # Compensate fade-in and fade-out if fading: time_signal = time_signal[ size - shift:len(time_signal) - (size - shift)] return time_signal
def istft(stft_signal, signal_len, size=1024, shift=256, window=signal.blackman, fading=True, window_length=None): """ Calculated the inverse short time Fourier transform to exactly reconstruct the time signal. :param stft_signal: Single channel complex STFT signal with dimensions frames times size/2+1. :param size: Scalar FFT-size. :param shift: Scalar FFT-shift. Typically shift is a fraction of size. :param window: Window function handle. :param fading: Removes the additional padding, if done during STFT. :param window_length: Sometimes one desires to use a shorter window than the fft size. In that case, the window is padded with zeros. The default is to use the fft-size as a window size. :return: Single channel complex STFT signal :return: Single channel time signal. """ assert stft_signal.shape[1] == size // 2 + 1 if window_length is None: window = window(size) else: window = window(window_length) window = np.pad(window, (0, size - window_length), mode='constant') window = _biorthogonal_window_loopy(window, shift) # Why? Line created by Hai, Lukas does not know, why it exists. window *= size time_signal = scipy.zeros(stft_signal.shape[0] * shift + size - shift) for j, i in enumerate(range(0, len(time_signal) - size + shift, shift)): time_signal[i:i + size] += window * np.real(irfft(stft_signal[j])) time_signal = time_signal[0:signal_len] # Compensate fade-in and fade-out #if fading: # time_signal = time_signal[ # size - shift:len(time_signal) - (size - shift)] return time_signal
def single_step_propagation(self): """ Perform single step propagation. The final Wigner functions are not normalized. """ ################ p x -> theta x ################ self.wigner_ge = fftpack.fft(self.wigner_ge, axis=0, overwrite_x=True) self.wigner_g = fftpack.fft(self.wigner_g, axis=0, overwrite_x=True) self.wigner_e = fftpack.fft(self.wigner_e, axis=0, overwrite_x=True) # Construct T matricies TgL, TgeL, TeL = self.get_T_left(self.t) TgR, TgeR, TeR = self.get_T_right(self.t) # Save previous version of the Wigner function Wg, Wge, We = self.wigner_g, self.wigner_ge, self.wigner_e # First update the complex valued off diagonal wigner function self.wigner_ge = (TgL*Wg + TgeL*Wge.conj())*TgeR + (TgL*Wge + TgeL*We)*TeR # Slice arrays to employ the symmetry (savings in speed) TgL, TgeL, TeL = self.theta_slice(TgL, TgeL, TeL) TgR, TgeR, TeR = self.theta_slice(TgR, TgeR, TeR) Wg, Wge, We = self.theta_slice(Wg, Wge, We) # Calculate the remaning real valued Wigner functions self.wigner_g = (TgL*Wg + TgeL*Wge.conj())*TgR + (TgL*Wge + TgeL*We)*TgeR self.wigner_e = (TgeL*Wg + TeL*Wge.conj())*TgeR + (TgeL*Wge + TeL*We)*TeR ################ Apply the phase factor ################ self.wigner_ge *= self.expV self.wigner_g *= self.expV[:(1 + self.P_gridDIM//2), :] self.wigner_e *= self.expV[:(1 + self.P_gridDIM//2), :] ################ theta x -> p x ################ self.wigner_ge = fftpack.ifft(self.wigner_ge, axis=0, overwrite_x=True) self.wigner_g = fft.irfft(self.wigner_g, axis=0) self.wigner_e = fft.irfft(self.wigner_e, axis=0) ################ p x -> p lambda ################ self.wigner_ge = fftpack.fft(self.wigner_ge, axis=1, overwrite_x=True) self.wigner_g = fft.rfft(self.wigner_g, axis=1) self.wigner_e = fft.rfft(self.wigner_e, axis=1) ################ Apply the phase factor ################ self.wigner_ge *= self.expK self.wigner_g *= self.expK[:, :(1 + self.X_gridDIM//2)] self.wigner_e *= self.expK[:, :(1 + self.X_gridDIM//2)] ################ p lambda -> p x ################ self.wigner_ge = fftpack.ifft(self.wigner_ge, axis=1, overwrite_x=True) self.wigner_g = fft.irfft(self.wigner_g, axis=1) self.wigner_e = fft.irfft(self.wigner_e, axis=1) #self.normalize_wigner_matrix()
