Python fftpack.ifft方法代码示例

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def quadrature_cc_1D(N):
    """ Computes the Clenshaw Curtis nodes and weights """
    N = np.int(N)        
    if N == 1:
        knots = 0
        weights = 2
    else:
        n = N - 1
        C = np.zeros((N,2))
        k = 2*(1+np.arange(np.floor(n/2)))
        C[::2,0] = 2/np.hstack((1, 1-k*k))
        C[1,1] = -n
        V = np.vstack((C,np.flipud(C[1:n,:])))
        F = np.real(ifft(V, n=None, axis=0))
        knots = F[0:N,1]
        weights = np.hstack((F[0,0],2*F[1:n,0],F[n,0]))
            
    return knots, weights 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def _centered(arr, newsize):
    # Return the center newsize portion of the array.
    newsize = numpy.asarray(newsize)
    currsize = numpy.array(arr.shape)
    startind = (currsize - newsize) // 2
    endind = startind + newsize
    myslice = [slice(startind[k], endind[k]) for k in range(len(endind))]
    return arr[tuple(myslice)]


#def _rfftn(a, s=None, axes=None):
#    s, axes = _cook_nd_args(a, s, axes);
#    a = fft.rfft(a, s[-1], axes[-1], overwrite_x = True)
#    for ii in range(len(axes)-1):
#        a = fft.fft(a, s[ii], axes[ii], overwrite_x = True)
#    return a

#def _irfftn(a, s=None, axes=None):   
#    #a = asarray(a).astype('complex64')
#    s, axes = _cook_nd_args(a, s, axes, invreal=1)
#    for ii in range(len(axes)-1):
#        a = fft.ifft(a, s[ii], axes[ii], overwrite_x = True);
#    a = fft.ifft(a, s[-1], axes[-1], overwrite_x = True);
#    a = a.real;
#    return a 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def spectralwhitening(stream):
    """
    Apply spectral whitening to data.
    Data is divided by its smoothed (Default: None) amplitude spectrum.
    """
    stream2 = copy.deepcopy(stream)

    for trace in arange(len(stream2)):
        data = stream2[trace].data

        n = len(data)
        nfft = nextpow2(n)

        spec = fft(data, nfft)
        spec_ampl = sqrt(abs(multiply(spec, conjugate(spec))))

        spec /= spec_ampl  # Do we need to do some smoothing here?
        ret = real(ifft(spec, nfft)[:n])

        stream2[trace].data = ret

    return stream2 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def spectralwhitening_smooth(stream, N):
    """
    Apply spectral whitening to data.
    Data is divided by its smoothed (Default: None) amplitude spectrum.
    """
    stream2 = copy.deepcopy(stream)

    for trace in arange(len(stream2)):
        data = stream2[trace].data

        n = len(data)
        nfft = nextpow2(n)

        spec = fft(data, nfft)
        spec_ampl = sqrt(abs(multiply(spec, conjugate(spec))))

        spec_ampl = smooth(spec_ampl, N)

        spec /= spec_ampl  # Do we need to do some smoothing here?
        ret = real(ifft(spec, nfft)[:n])

        stream2[trace].data = ret

    return stream2 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def carr_madan_fraction_fft_call_pricer(N, d_u, d_k, alpha, r, t, S0, q, chf_ln_st):
    rou = (d_u * d_k) / (2 * np.pi)
    beta = np.log(S0) - d_k * N / 2
    u_arr = np.arange(N) * d_u
    k_arr = beta + np.arange(N) * d_k
    delta_arr = np.zeros(N)
    delta_arr[0] = 1
    w_arr = d_u / 3 * (3 + (-1) ** (np.arange(N) + 1) - delta_arr)
    call_chf = (np.exp(-r * t) / ((alpha + 1j * u_arr) * (alpha + 1j * u_arr + 1))) * chf_ln_st(
        u_arr - (alpha + 1) * 1j,
        t, r, q=q, S0=S0)
    x_arr = np.exp(-1j * beta * u_arr) * call_chf * w_arr
    y_arr = np.zeros(2 * N) * 0j
    y_arr[:N] = np.exp(-1j * np.pi * rou * np.arange(N) ** 2) * x_arr
    z_arr = np.zeros(2 * N) * 0j
    z_arr[:N] = np.exp(1j * np.pi * rou * np.arange(N) ** 2)
    z_arr[N:] = np.exp(1j * np.pi * rou * np.arange(N - 1, -1, -1) ** 2)
    ffty = (fft(y_arr))
    fftz = (fft(z_arr))
    fftx = ffty * fftz
    fftpsi = ifft(fftx)
    fft_prices = np.exp(-1j * np.pi * (np.arange(N) ** 2) * rou) * fftpsi[:N]
    call_prices = (np.exp(-alpha * k_arr) / np.pi) * fft_prices.real
    return np.exp(k_arr), call_prices 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def test_definition(self):
        x1 = [1,2,3,4,1,2,3,4]
        x1_1 = [1,2+3j,4+1j,2+3j,4,2-3j,4-1j,2-3j]
        x2 = [1,2,3,4,1,2,3,4,5]
        x2_1 = [1,2+3j,4+1j,2+3j,4+5j,4-5j,2-3j,4-1j,2-3j]

        def _test(x, xr):
            y = irfft(np.array(x, dtype=self.rdt))
            y1 = direct_irdft(x)
            self.assertTrue(y.dtype == self.rdt,
                    "Output dtype is %s, expected %s" % (y.dtype, self.rdt))
            assert_array_almost_equal(y,y1, decimal=self.ndec)
            assert_array_almost_equal(y,ifft(xr), decimal=self.ndec)

        _test(x1, x1_1)
        _test(x2, x2_1) 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def test_pdos_1d():
    pad=lambda x: pad_zeros(x, nadd=len(x)-1)
    n=500; w=welch(n)
    # 1 second signal
    t=np.linspace(0,1,n); dt=t[1]-t[0]
    # sum of sin()s with random freq and phase shift, 10 frequencies from
    # f=0...100 Hz
    v=np.array([np.sin(2*np.pi*f*t + rand()*2*np.pi) for f in rand(10)*100]).sum(0)
    f=np.fft.fftfreq(2*n-1, dt)[:n]

    c1=mirror(ifft(abs(fft(pad(v)))**2.0)[:n].real)
    c2=correlate(v,v,'full')
    c3=mirror(acorr(v,norm=False))
    assert np.allclose(c1, c2)
    assert np.allclose(c1, c3)

    p1=(abs(fft(pad(v)))**2.0)[:n]
    p2=(abs(fft(mirror(acorr(v,norm=False)))))[:n]
    assert np.allclose(p1, p2)

    p1=(abs(fft(pad(v*w)))**2.0)[:n]
    p2=(abs(fft(mirror(acorr(v*w,norm=False)))))[:n]
    assert np.allclose(p1, p2) 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def istft(X, fftsize=128, step="half", wsola=False, mean_normalize=True,
          real=False, compute_onesided=True):
    """
    Compute ISTFT for STFT transformed X
    """
    if real:
        local_ifft = fftpack.irfft
        X_pad = np.zeros((X.shape[0], X.shape[1] + 1)) + 0j
        X_pad[:, :-1] = X
        X = X_pad
    else:
        local_ifft = fftpack.ifft
    if compute_onesided:
        X_pad = np.zeros((X.shape[0], 2 * X.shape[1])) + 0j
        X_pad[:, :fftsize // 2 + 1] = X
        X_pad[:, fftsize // 2 + 1:] = 0
        X = X_pad
    X = local_ifft(X).astype("float64")
    if step == "half":
        X = invert_halfoverlap(X)
    else:
        X = overlap_add(X, step, wsola=wsola)
    if mean_normalize:
        X -= np.mean(X)
    return X 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def test_size_accuracy(self):
        # Sanity check for the accuracy for prime and non-prime sized inputs
        if self.rdt == np.float32:
            rtol = 1e-5
        elif self.rdt == np.float64:
            rtol = 1e-10

        for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
            np.random.seed(1234)
            x = np.random.rand(size).astype(self.rdt)
            y = ifft(fft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)
            y = fft(ifft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)

            x = (x + 1j*np.random.rand(size)).astype(self.cdt)
            y = ifft(fft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)
            y = fft(ifft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt) 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def polyval(self, chebcoeff):
        """
        Compute the interpolation values at Chebyshev points.
        chebcoeff: Chebyshev coefficients
        """
        N = len(chebcoeff)
        if N == 1:
            return chebcoeff

        data = even_data(chebcoeff)/2
        data[0] *= 2
        data[N-1] *= 2

        fftdata = 2*(N-1)*fftpack.ifft(data, axis=0)
        complex_values = fftdata[:N]
        # convert to real if input was real
        if np.isrealobj(chebcoeff):
            values = np.real(complex_values)
        else:
            values = complex_values
        return values 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def idft(modes, null_hypothesis, counts=1):
    """
    Inverts the dft function.

    Parameters
    ----------
    modes : array
        The fourier modes to be transformed to the time domain.

    null_hypothesis : array
        The array that was used in the normalization before the dct. This is
        commonly the mean of the time-domain data vector. All elements of this
        array must be in (0,1).

     counts : int, optional
        A factor in the normalization, that should correspond to the counts-per-timestep (so
        for full time resolution this is 1).

    Returns
    -------
    array
        Inverse of the dft function

    """
    z = _np.sqrt(len(modes)) * _ifft(modes)  # TIM CHECK THIS: len(*modes*) correct?
    x = unstandardizer(z, null_hypothesis, counts)
    return x 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def compute_beat_spectrum(power_spectrogram):
        """ Computes the beat spectrum averages (over freq's) the autocorrelation matrix of a one-sided spectrogram.

        The autocorrelation matrix is computed by taking the autocorrelation of each row of the spectrogram and
        dismissing the symmetric half.

        Args:
            power_spectrogram (:obj:`np.array`): 2D matrix containing the one-sided power spectrogram of an audio signal
            
        Returns:
            (:obj:`np.array`): array containing the beat spectrum based on the power spectrogram
            
        See Also:
            J Foote's original derivation of the Beat Spectrum: 
            Foote, Jonathan, and Shingo Uchihashi. "The beat spectrum: A new approach to rhythm analysis." 
            Multimedia and Expo, 2001. ICME 2001. IEEE International Conference on. IEEE, 2001.
            (`See PDF here <http://rotorbrain.com/foote/papers/icme2001.pdf>`_)
            
        """
        freq_bins, time_bins = power_spectrogram.shape

        # row-wise autocorrelation according to the Wiener-Khinchin theorem
        power_spectrogram = np.vstack([power_spectrogram, np.zeros_like(power_spectrogram)])

        nearest_power_of_two = 2 ** np.ceil(np.log(power_spectrogram.shape[0]) / np.log(2))
        pad_amount = int(nearest_power_of_two - power_spectrogram.shape[0])
        power_spectrogram = np.pad(power_spectrogram, ((0, pad_amount), (0, 0)), 'constant')
        fft_power_spec = scifft.fft(power_spectrogram, axis=0)
        abs_fft = np.abs(fft_power_spec) ** 2
        autocorrelation_rows = np.real(
            scifft.ifft(abs_fft, axis=0)[:freq_bins, :])  # ifft over columns

        # normalization factor
        norm_factor = np.tile(np.arange(freq_bins, 0, -1), (time_bins, 1)).T
        autocorrelation_rows = autocorrelation_rows / norm_factor

        # compute the beat spectrum
        beat_spectrum = np.mean(autocorrelation_rows, axis=1)
        # average over frequencies

        return beat_spectrum 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def bench_random(self):
        from numpy.fft import ifft as numpy_ifft
        print()
        print('       Inverse Fast Fourier Transform')
        print('===============================================')
        print('      |     real input    |    complex input   ')
        print('-----------------------------------------------')
        print(' size |  scipy  |  numpy  |  scipy  |  numpy  ')
        print('-----------------------------------------------')
        for size,repeat in [(100,7000),(1000,2000),
                            (256,10000),
                            (512,10000),
                            (1024,1000),
                            (2048,1000),
                            (2048*2,500),
                            (2048*4,500),
                            ]:
            print('%5s' % size, end=' ')
            sys.stdout.flush()

            for x in [random([size]).astype(double),
                      random([size]).astype(cdouble)+random([size]).astype(cdouble)*1j
                      ]:
                if size > 500:
                    y = ifft(x)
                else:
                    y = direct_idft(x)
                assert_array_almost_equal(ifft(x),y)
                print('|%8.2f' % measure('ifft(x)',repeat), end=' ')
                sys.stdout.flush()

                assert_array_almost_equal(numpy_ifft(x),y)
                print('|%8.2f' % measure('numpy_ifft(x)',repeat), end=' ')
                sys.stdout.flush()

            print(' (secs for %s calls)' % (repeat))
        sys.stdout.flush() 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def direct_diff(x,k=1,period=None):
    fx = fft(x)
    n = len(fx)
    if period is None:
        period = 2*pi
    w = fftfreq(n)*2j*pi/period*n
    if k < 0:
        w = 1 / w**k
        w[0] = 0.0
    else:
        w = w**k
    if n > 2000:
        w[250:n-250] = 0.0
    return ifft(w*fx).real 

# 需要导入模块: from scipy import fftpack [as 别名]
# 或者: from scipy.fftpack import ifft [as 别名]
def direct_tilbert(x,h=1,period=None):
    fx = fft(x)
    n = len(fx)
    if period is None:
        period = 2*pi
    w = fftfreq(n)*h*2*pi/period*n
    w[0] = 1
    w = 1j/tanh(w)
    w[0] = 0j
    return ifft(w*fx)