Python fft.irfft方法代码示例

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def pink(N):
    """
    Pink noise.

    :param N: Amount of samples.

    Pink noise has equal power in bands that are proportionally wide.
    Power density decreases with 3 dB per octave.

    """
    # This method uses the filter with the following coefficients.
    # b = np.array([0.049922035, -0.095993537, 0.050612699, -0.004408786])
    # a = np.array([1, -2.494956002, 2.017265875, -0.522189400])
    # return lfilter(B, A, np.random.randn(N))
    # Another way would be using the FFT
    # x = np.random.randn(N)
    # X = rfft(x) / N
    uneven = N % 2
    X = np.random.randn(N // 2 + 1 + uneven) + 1j * np.random.randn(N // 2 + 1 + uneven)
    S = np.sqrt(np.arange(len(X)) + 1.)  # +1 to avoid divide by zero
    y = (irfft(X / S)).real
    if uneven:
        y = y[:-1]
    return normalize(y) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def mass(query, ts):
    """
    >>> np.round(mass(np.array([0.0, 1.0, -1.0, 0.0]), np.array([-1, 1, 0, 0, -1, 1])), 3)
    array([ 2.   ,  2.828,  2.   ])
    """
    query = zNormalize(query)
    m = len(query)
    n = len(ts)

    stdv = movstd(ts, m)
    query = query[::-1]
    query = np.pad(query, (0, n - m), 'constant')
    dots = fft.irfft(fft.rfft(ts) * fft.rfft(query))
    return np.sqrt(2 * (m - (dots[m - 1 :] / stdv))) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def impedance2wake(f, y):
    """
    Fourier transform with exp(-iwt)
                f -    Hz
                y -    Om
                s    - Meter
                w -    V/C
    """
    df = f[1] - f[0]
    n = len(f)
    s = 1./df*np.arange(n)/n*speed_of_light
    w = n*df*irfft(y, n)
    return s, w 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def bench_random(self):
        from numpy.fft import irfft as numpy_irfft

        print()
        print('Inverse Fast Fourier Transform (real data)')
        print('==================================')
        print(' size |  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()

            x = random([size]).astype(double)
            x1 = zeros(size/2+1,dtype=cdouble)
            x1[0] = x[0]
            for i in range(1,size/2):
                x1[i] = x[2*i-1] + 1j * x[2*i]
            if not size % 2:
                x1[-1] = x[-1]
            y = irfft(x)

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

            assert_array_almost_equal(numpy_irfft(x1,size),y)
            print('|%8.2f' % measure('numpy_irfft(x1,size)',repeat), end=' ')
            sys.stdout.flush()

            print(' (secs for %s calls)' % (repeat))

        sys.stdout.flush() 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_gaussian_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type in [numpy.float32, numpy.float64]:
                a = numpy.zeros(shape, type)
                a[0, 0] = 1.0
                a = fft.rfft(a, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_gaussian(a, [5.0, 2.5],
                                                       shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_almost_equal(ndimage.sum(a), 1) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_uniform_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type in [numpy.float32, numpy.float64]:
                a = numpy.zeros(shape, type)
                a[0, 0] = 1.0
                a = fft.rfft(a, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_uniform(a, [5.0, 2.5],
                                                      shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_almost_equal(ndimage.sum(a), 1.0) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_shift_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for dtype in [numpy.float32, numpy.float64]:
                expected = numpy.arange(shape[0] * shape[1], dtype=dtype)
                expected.shape = shape
                a = fft.rfft(expected, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_shift(a, [1, 1], shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_array_almost_equal(a[1:, 1:], expected[:-1, :-1])
                assert_array_almost_equal(a.imag, numpy.zeros(shape)) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_ellipsoid_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type in [numpy.float32, numpy.float64]:
                a = numpy.zeros(shape, type)
                a[0, 0] = 1.0
                a = fft.rfft(a, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_ellipsoid(a, [5.0, 2.5],
                                              shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_almost_equal(ndimage.sum(a), 1.0) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_gaussian_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type_, dec in zip([numpy.float32, numpy.float64], [6, 14]):
                a = numpy.zeros(shape, type_)
                a[0, 0] = 1.0
                a = fft.rfft(a, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_gaussian(a, [5.0, 2.5], shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_almost_equal(ndimage.sum(a), 1, decimal=dec) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_uniform_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type_, dec in zip([numpy.float32, numpy.float64], [6, 14]):
                a = numpy.zeros(shape, type_)
                a[0, 0] = 1.0
                a = fft.rfft(a, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_uniform(a, [5.0, 2.5], shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_almost_equal(ndimage.sum(a), 1.0, decimal=dec) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_shift_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type_, dec in zip([numpy.float32, numpy.float64], [4, 11]):
                expected = numpy.arange(shape[0] * shape[1], dtype=type_)
                expected.shape = shape
                a = fft.rfft(expected, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_shift(a, [1, 1], shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_array_almost_equal(a[1:, 1:], expected[:-1, :-1],
                                          decimal=dec)
                assert_array_almost_equal(a.imag, numpy.zeros(shape),
                                          decimal=dec) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def test_fourier_ellipsoid_real01(self):
        for shape in [(32, 16), (31, 15)]:
            for type_, dec in zip([numpy.float32, numpy.float64], [5, 14]):
                a = numpy.zeros(shape, type_)
                a[0, 0] = 1.0
                a = fft.rfft(a, shape[0], 0)
                a = fft.fft(a, shape[1], 1)
                a = ndimage.fourier_ellipsoid(a, [5.0, 2.5],
                                              shape[0], 0)
                a = fft.ifft(a, shape[1], 1)
                a = fft.irfft(a, shape[0], 0)
                assert_almost_equal(ndimage.sum(a), 1.0, decimal=dec) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def lpc_python(x, order):
    def levinson(R,order):
        """ input: autocorrelation and order, output: LPC coefficients """
        a   = np.zeros(order+2)
        a[0] = -1
        k = np.zeros(order+1)
        # step 1: initialize prediction error "e" to R[0]
        e = R[0]
        # step 2: iterate over [1:order]
        for i in range(1,order+1):
            # step 2-1: calculate PARCOR coefficients
            k[i]= (R[i] - np.sum(a[1:i] * R[i-1:0:-1])) / e
            # step 2-2: update LPCs
            a[i] = np.copy(k[i])
            a_old = np.copy(a) 
            for j in range(1,i):
                a[j] -=  k[i]* a_old[i-j] 
            # step 2-3: update prediction error "e" 
            e = e * (1.0 - k[i]**2)
        return -1*a[0:order+1], e, -1*k[1:]
    # N: compute next power of 2
    n = x.shape[0]
    N = int(np.power(2, np.ceil(np.log2(2 * n - 1))))
    # calculate autocorrelation using FFT
    X = rfft(x, N)
    r = irfft(abs(X) ** 2)[:order+1]
    return levinson(r, order) 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def multS(s, v, L, TP=False):

    N = s.shape[0]
    vp = prepare_v(v, N, L, TP=TP)
    p = irfft(rfft(vp) * rfft(s))
    if not TP:
        return p[:L]
    return p[L - 1:] 

# 需要导入模块: from numpy import fft [as 别名]
# 或者: from numpy.fft import irfft [as 别名]
def autocorr(x):
    """ Fast autocorrelation computation using the FFT """
    
    X = fft.rfft(x, n=2*x.shape[0])
    r = fft.irfft(np.abs(X)**2)
    
    return r[:x.shape[0]] / (x.shape[0] - 1)