def test_mtm_cross_spectrum():
"""
Test the multi-taper cross-spectral estimation. Based on the example in
doc/examples/multi_taper_coh.py
"""
NW = 4
K = 2 * NW - 1
N = 2 ** 10
n_reps = 10
n_freqs = N
tapers, eigs = tsa.dpss_windows(N, NW, 2 * NW - 1)
est_psd = []
for k in xrange(n_reps):
data,nz,alpha = utils.ar_generator(N=N)
fgrid, hz = tsa.freq_response(1.0, a=np.r_[1, -alpha], n_freqs=n_freqs)
# 'one-sided', so multiply by 2:
psd = 2 * (hz * hz.conj()).real
tdata = tapers * data
tspectra = np.fft.fft(tdata)
L = N / 2 + 1
sides = 'onesided'
w, _ = utils.adaptive_weights(tspectra, eigs, sides=sides)
sxx = tsa.mtm_cross_spectrum(tspectra, tspectra, w, sides=sides)
est_psd.append(sxx)
fxx = np.mean(est_psd, 0)
psd_ratio = np.mean(fxx / psd)
# This is a rather lenient test, making sure that the average ratio is 1 to
# within an order of magnitude. That is, that they are equal on average:
npt.assert_array_almost_equal(psd_ratio, 1, decimal=1)
# Test raising of error in case the inputs don't make sense:
npt.assert_raises(ValueError,
tsa.mtm_cross_spectrum,
tspectra,np.r_[tspectra, tspectra],
(w, w))
def test_mtm_cross_spectrum():
"""
Test the multi-taper cross-spectral estimation. Based on the example in
doc/examples/multi_taper_coh.py
"""
NW = 4
K = 2 * NW - 1
N = 2**10
n_reps = 10
n_freqs = N
tapers, eigs = tsa.dpss_windows(N, NW, 2 * NW - 1)
est_psd = []
for k in range(n_reps):
data, nz, alpha = utils.ar_generator(N=N)
fgrid, hz = tsa.freq_response(1.0, a=np.r_[1, -alpha], n_freqs=n_freqs)
# 'one-sided', so multiply by 2:
psd = 2 * (hz * hz.conj()).real
tdata = tapers * data
tspectra = fftpack.fft(tdata)
L = N / 2 + 1
sides = 'onesided'
w, _ = utils.adaptive_weights(tspectra, eigs, sides=sides)
sxx = tsa.mtm_cross_spectrum(tspectra, tspectra, w, sides=sides)
est_psd.append(sxx)
fxx = np.mean(est_psd, 0)
psd_ratio = np.mean(fxx / psd)
# This is a rather lenient test, making sure that the average ratio is 1 to
# within an order of magnitude. That is, that they are equal on average:
npt.assert_array_almost_equal(psd_ratio, 1, decimal=1)
# Test raising of error in case the inputs don't make sense:
npt.assert_raises(ValueError, tsa.mtm_cross_spectrum, tspectra,
np.r_[tspectra, tspectra], (w, w))
def test_multi_taper_psd_csd():
"""
Test the multi taper psd and csd estimation functions.
Based on the example in
doc/examples/multi_taper_spectral_estimation.py
"""
N = 2**10
n_reps = 10
psd = []
est_psd = []
est_csd = []
for jk in [True, False]:
for k in range(n_reps):
for adaptive in [True, False]:
ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10)
ar_seq -= ar_seq.mean()
fgrid, hz = tsa.freq_response(1.0,
a=np.r_[1, -alpha],
n_freqs=N)
psd.append(2 * (hz * hz.conj()).real)
f, psd_mt, nu = tsa.multi_taper_psd(ar_seq,
adaptive=adaptive,
jackknife=jk)
est_psd.append(psd_mt)
f, csd_mt = tsa.multi_taper_csd(np.vstack([ar_seq, ar_seq]),
adaptive=adaptive)
# Symmetrical in this case, so take one element out:
est_csd.append(csd_mt[0][1])
fxx = np.mean(psd, axis=0)
fxx_est1 = np.mean(est_psd, axis=0)
fxx_est2 = np.mean(est_csd, axis=0)
# Tests the psd:
psd_ratio1 = np.mean(fxx_est1 / fxx)
npt.assert_array_almost_equal(psd_ratio1, 1, decimal=-1)
# Tests the csd:
psd_ratio2 = np.mean(fxx_est2 / fxx)
npt.assert_array_almost_equal(psd_ratio2, 1, decimal=-1)
def test_multi_taper_psd_csd():
"""
Test the multi taper psd and csd estimation functions.
Based on the example in
doc/examples/multi_taper_spectral_estimation.py
"""
N = 2 ** 10
n_reps = 10
psd = []
est_psd = []
est_csd = []
for jk in [True, False]:
for k in range(n_reps):
for adaptive in [True, False]:
ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10)
ar_seq -= ar_seq.mean()
fgrid, hz = tsa.freq_response(1.0, a=np.r_[1, -alpha],
n_freqs=N)
psd.append(2 * (hz * hz.conj()).real)
f, psd_mt, nu = tsa.multi_taper_psd(ar_seq, adaptive=adaptive,
jackknife=jk)
est_psd.append(psd_mt)
f, csd_mt = tsa.multi_taper_csd(np.vstack([ar_seq, ar_seq]),
adaptive=adaptive)
# Symmetrical in this case, so take one element out:
est_csd.append(csd_mt[0][1])
fxx = np.mean(psd, axis=0)
fxx_est1 = np.mean(est_psd, axis=0)
fxx_est2 = np.mean(est_csd, axis=0)
# Tests the psd:
psd_ratio1 = np.mean(fxx_est1 / fxx)
npt.assert_array_almost_equal(psd_ratio1, 1, decimal=-1)
# Tests the csd:
psd_ratio2 = np.mean(fxx_est2 / fxx)
npt.assert_array_almost_equal(psd_ratio2, 1, decimal=-1)
Next, we generate a sequence with known spectral properties: """ N = 512 ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10) ar_seq -= ar_seq.mean() """ This is the true PSD for this sequence: """ fgrid, hz = tsa.freq_response(1.0, a=np.r_[1, -alpha], n_freqs=N) psd = (hz * hz.conj()).real """ 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
""" Next, we generate a sequence with known spectral properties: """ N = 512 ar_seq, nz, alpha = utils.ar_generator(N=N, drop_transients=10) ar_seq -= ar_seq.mean() """ This is the true PSD for this sequence: """ fgrid, hz = tsa.freq_response(1.0, a=np.r_[1, -alpha], n_freqs=N) psd = (hz * hz.conj()).real """ 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.
