コード例 #1
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ファイル: test_spectral.py プロジェクト: arokem/nitime
def test_periodogram_spectral_normalization():
    """
    Check that the spectral estimators are normalized in the
    correct Watts/Hz fashion
    """

    x = np.random.randn(1024)
    f1, Xp1 = tsa.periodogram(x)
    f2, Xp2 = tsa.periodogram(x, Fs=100)
    f3, Xp3 = tsa.periodogram(x, N=2**12)

    p1 = np.sum(Xp1) * 2 * np.pi / 2**10
    p2 = np.sum(Xp2) * 100 / 2**10
    p3 = np.sum(Xp3) * 2 * np.pi / 2**12
    npt.assert_( np.abs(p1 - p2) < 1e-14,
                    'Inconsistent frequency normalization in periodogram (1)' )
    npt.assert_( np.abs(p3 - p2) < 1e-8,
                    'Inconsistent frequency normalization in periodogram (2)' )

    td_var = np.var(x)
    # assure that the estimators are at least in the same
    # order of magnitude as the time-domain variance
    npt.assert_( np.abs(np.log10(p1/td_var)) < 1,
                    'Incorrect frequency normalization in periodogram' )

    # check the freq vector while we're here
    npt.assert_( f2.max() == 50, 'Periodogram returns wrong frequency bins' )
コード例 #2
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def test_periodogram_spectral_normalization():
    """
    Check that the spectral estimators are normalized in the
    correct Watts/Hz fashion
    """

    x = np.random.randn(1024)
    f1, Xp1 = tsa.periodogram(x)
    f2, Xp2 = tsa.periodogram(x, Fs=100)
    f3, Xp3 = tsa.periodogram(x, N=2**12)

    p1 = np.sum(Xp1) * 2 * np.pi / 2**10
    p2 = np.sum(Xp2) * 100 / 2**10
    p3 = np.sum(Xp3) * 2 * np.pi / 2**12
    nt.assert_true(
        np.abs(p1 - p2) < 1e-14,
        'Inconsistent frequency normalization in periodogram (1)')
    nt.assert_true(
        np.abs(p3 - p2) < 1e-8,
        'Inconsistent frequency normalization in periodogram (2)')

    td_var = np.var(x)
    # assure that the estimators are at least in the same
    # order of magnitude as the time-domain variance
    nt.assert_true(
        np.abs(np.log10(p1 / td_var)) < 1,
        'Incorrect frequency normalization in periodogram')

    # check the freq vector while we're here
    nt.assert_true(f2.max() == 50, 'Periodogram returns wrong frequency bins')
コード例 #3
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ファイル: test_algorithms.py プロジェクト: zyq11223/nitime
def test_periodogram():
    arsig, _, _ = ut.ar_generator(N=512)
    avg_pwr = (arsig * arsig.conjugate()).mean()
    f, psd = tsa.periodogram(arsig, N=2048)
    df = 2. * np.pi / 2048
    avg_pwr_est = np.trapz(psd, dx=df)
    npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=1)
コード例 #4
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ファイル: test_algorithms.py プロジェクト: TomDLT/nitime
def test_periodogram():
    arsig, _, _ = ut.ar_generator(N=512)
    avg_pwr = (arsig * arsig.conjugate()).mean()
    f, psd = tsa.periodogram(arsig, N=2048)
    df = 2. * np.pi / 2048
    avg_pwr_est = np.trapz(psd, dx=df)
    npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=1)
コード例 #5
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ファイル: test_algorithms.py プロジェクト: slnovak/nitime
def test_periodogram():
    arsig,_,_ = ut.ar_generator(N=512)
    avg_pwr = (arsig*arsig.conjugate()).mean()
    f, psd = tsa.periodogram(arsig, N=2048)
    # for efficiency, let's leave out the 2PI in the numerator and denominator
    # for the following integral
    dw = 1./2048
    avg_pwr_est = np.trapz(psd, dx=dw)
    npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=1)
コード例 #6
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def test_periodogram():
    arsig, _, _ = ut.ar_generator(N=512)
    avg_pwr = (arsig * arsig.conjugate()).mean()
    f, psd = tsa.periodogram(arsig, N=2048)
    # for efficiency, let's leave out the 2PI in the numerator and denominator
    # for the following integral
    dw = 1. / 2048
    avg_pwr_est = np.trapz(psd, dx=dw)
    npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=1)
コード例 #7
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def test_periodogram():
    """Test some of the inputs to periodogram """

    arsig, _, _ = utils.ar_generator(N=1024)
    Sk = fftpack.fft(arsig)

    f1, c1 = tsa.periodogram(arsig)
    f2, c2 = tsa.periodogram(arsig, Sk=Sk)

    npt.assert_equal(c1, c2)

    # Check that providing a complex signal does the right thing
    # (i.e. two-sided spectrum):
    N = 1024
    r, _, _ = utils.ar_generator(N=N)
    c, _, _ = utils.ar_generator(N=N)
    arsig = r + c * scipy.sqrt(-1)

    f, c = tsa.periodogram(arsig)
    npt.assert_equal(f.shape[0], N)  # Should be N, not the one-sided N/2 + 1
コード例 #8
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ファイル: test_spectral.py プロジェクト: ilustreous/nitime
def test_periodogram():
    """Test some of the inputs to periodogram """

    arsig, _, _ = utils.ar_generator(N=1024)
    Sk = np.fft.fft(arsig)

    f1, c1 = tsa.periodogram(arsig)
    f2, c2 = tsa.periodogram(arsig, Sk=Sk)

    npt.assert_equal(c1, c2)

    # Check that providing a complex signal does the right thing
    # (i.e. two-sided spectrum): 
    N = 1024 
    r, _, _ = utils.ar_generator(N=N)
    c, _, _ = utils.ar_generator(N=N)
    arsig = r + c * scipy.sqrt(-1)

    f, c = tsa.periodogram(arsig)
    npt.assert_equal(f.shape[0], N) # Should be N, not the one-sided N/2 + 1
コード例 #9
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    def periodogram(self):
        """

        This is the spectrum estimated as the FFT of the time-series

        Returns
        -------
        (f,spectrum): f is an array with the frequencies and spectrum is the
        complex-valued FFT.
        """
        return tsa.periodogram(self.input.data, Fs=self.input.sampling_rate)
コード例 #10
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ファイル: spectral.py プロジェクト: agramfort/nitime
    def periodogram(self):
        """

        This is the spectrum estimated as the FFT of the time-series

        Returns
        -------
        (f,spectrum): f is an array with the frequencies and spectrum is the
        complex-valued FFT.
        """
        return tsa.periodogram(self.input.data, Fs=self.input.sampling_rate)
コード例 #11
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def test_hermitian_periodogram_csd():
    """
    Make sure CSD matrices returned by various methods have
    Hermitian symmetry.
    """

    sig = np.random.randn(4, 256)

    _, csd1 = tsa.periodogram_csd(sig)

    for i in range(4):
        for j in range(i + 1):
            xc1 = csd1[i, j]
            xc2 = csd1[j, i]
            npt.assert_equal(xc1,
                             xc2.conj(),
                             err_msg='Periodogram CSD not Hermitian')

    _, psd = tsa.periodogram(sig)
    for i in range(4):
        npt.assert_almost_equal(
            psd[i],
            csd1[i, i].real,
            err_msg='Periodgram CSD diagonal inconsistent with real PSD')
コード例 #12
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ファイル: test_spectral.py プロジェクト: arokem/nitime
def test_hermitian_periodogram_csd():
    """
    Make sure CSD matrices returned by various methods have
    Hermitian symmetry.
    """

    sig = np.random.randn(4,256)

    _, csd1 = tsa.periodogram_csd(sig)

    for i in range(4):
        for j in range(i+1):
            xc1 = csd1[i,j]
            xc2 = csd1[j,i]
            npt.assert_equal(
                xc1, xc2.conj(), err_msg='Periodogram CSD not Hermitian'
                )

    _, psd = tsa.periodogram(sig)
    for i in range(4):
        npt.assert_almost_equal(
            psd[i], csd1[i,i].real,
            err_msg='Periodgram CSD diagonal inconsistent with real PSD'
            )
コード例 #13
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ファイル: mea.py プロジェクト: rajatsaxena/Ephys
def get_psd_v2(data, fs):
    freq, psd = tsa.periodogram(data,fs,normalize=True)  
    return freq, psd
コード例 #14
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"""

psd *= 2
dB(psd, psd)


"""

We begin by using the naive periodogram function (:func:`tsa.periodogram` in
order to calculate the PSD and compare that to the true PSD calculated above.


"""

freqs, d_psd = tsa.periodogram(ar_seq)
dB(d_psd, d_psd)

fig03 = plot_spectral_estimate(freqs, psd, (d_psd,), elabels=("Periodogram",))

"""

.. image:: fig/multi_taper_spectral_estimation_03.png


Next, we use Welch's periodogram, by applying :func:`tsa.get_spectra`. Note
that we explicitely provide the function with a 'method' dict, which specifies
the method used in order to calculate the PSD, but the default method is 'welch'.


"""
コード例 #15
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This is a one-sided spectrum, so we double the power:

"""

psd *= 2
dB(psd, psd)
"""

We begin by using the naive periodogram function (:func:`tsa.periodogram` in
order to calculate the PSD and compare that to the true PSD calculated above.


"""

freqs, d_psd = tsa.periodogram(ar_seq)
dB(d_psd, d_psd)

fig03 = plot_spectral_estimate(freqs,
                               psd, (d_psd, ),
                               elabels=("Periodogram", ))
"""

.. image:: fig/multi_taper_spectral_estimation_03.png

Next, we use Welch's periodogram, by applying :func:`tsa.get_spectra`. Note
that we explicitly provide the function with a 'method' dict, which specifies
the method used in order to calculate the PSD, but the default method is 'welch'.

"""
コード例 #16
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ファイル: multi_taper_sdf.py プロジェクト: fperez/nitime
    ar_seq = foo["arr_0"]
    nz = foo["arr_1"]
    alpha = foo["arr_2"]
else:
    ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10)
    ar_seq -= ar_seq.mean()
    np.savez("example_arrs", ar_seq, nz, alpha)
# --- True SDF
fgrid, hz = alg.my_freqz(1.0, a=np.r_[1, -alpha], Nfreqs=N)
sdf = (hz * hz.conj()).real
# onesided spectrum, so double the power
sdf[1:-1] *= 2
dB(sdf, sdf)

# --- Direct Spectral Estimator
freqs, d_sdf = alg.periodogram(ar_seq)
dB(d_sdf, d_sdf)

# --- Welch's Overlapping Periodogram Method via mlab
mlab_sdf, mlab_freqs = pp.mlab.psd(ar_seq, NFFT=N)
mlab_freqs *= np.pi / mlab_freqs.max()
mlab_sdf = mlab_sdf.squeeze()
dB(mlab_sdf, mlab_sdf)


### Taper Bandwidth Adjustments
NW = 4

# --- Regular Multitaper Estimate
f, sdf_mt, nu = alg.multi_taper_psd(ar_seq, width=NW, adaptive=False, jackknife=False)
dB(sdf_mt, sdf_mt)