def test_fstatisticsAndReshapedSpectrum(self):
"""
Test for mtspec_pad with jackknife interval errors. The result is
compared to the output of test_recreatePaperFigures.py in the same
directory. This is assumed to be correct because they are identical to
the figures in the paper on the machine that created these.
"""
data = load_mtdata('v22_174_series.dat.gz')
# Calculate the spectra.
spec, freq, jackknife, fstatistics, _ = mtspec(data, 4930., 3.5,
nfft=312, number_of_tapers=5, statistics=True,
rshape=0, fcrit=0.9)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
self.assertEqual(np.isnan(jackknife).any(), False)
self.assertEqual(np.isnan(fstatistics).any(), False)
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'fstatistics.npz')
record = np.load(datafile)
spec2 = record['spec']
jackknife2 = record['jackknife']
fstatistics2 = record['fstatistics']
freq2 = np.arange(157) * 6.50127447e-07
# Compare.
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec)
np.testing.assert_almost_equal(jackknife / jackknife,
jackknife2 / jackknife, 5)
np.testing.assert_almost_equal(fstatistics / fstatistics,
fstatistics2 / fstatistics, 5)
def test_figure1(self):
"""
Recreate Figure 1
"""
data = load_mtdata('v22_174_series.dat.gz')
spec, freq, jackknife, _, _ = mtspec(data, 4930., 3.5, number_of_tapers=5,
nfft=312, statistics=True)
fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1)
ax1.plot(data, color='black')
ax1.set_xlim(0, len(data))
ax2 = fig.add_subplot(2, 1, 2)
ax2.set_yscale('log')
ax2.plot(freq, spec, color='black')
try:
ax2.fill_between(freq, jackknife[:, 0], jackknife[:, 1], color='grey')
except:
ax2.plot(freq, jackknife[:, 0], '--', color = 'red')
ax2.plot(freq, jackknife[:, 1], '--', color = 'red')
ax2.set_xlim(freq[0], freq[-1])
outfile = os.path.join(self.outpath, 'fig1.pdf')
fig.savefig(outfile)
stat = os.stat(outfile)
self.assertTrue(abs(stat.st_mtime - time.time()) < 3)
def test_eigenspectraOutput(self):
"""
Tests the eigenspectra output using a nonadaptive spectra. This also at
least somewhat tests the weights.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq, eigspec, eigcoef, weights = \
mtspec(data, 1.0, 4.5, number_of_tapers=5, adaptive=False,
optional_output=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(eigspec).any(), False)
self.assertEqual(np.isnan(eigcoef).any(), False)
self.assertEqual(np.isnan(weights).any(), False)
# The weights should all be one for the nonadaptive spectrum.
np.testing.assert_almost_equal(weights, np.ones((43201, 5), 'float64'))
# Sum over the eigenspectra to get the nonadaptive spectrum.
new_spec = eigspec.sum(axis=1) / float(eigspec.shape[1])
new_spec[1:] *= 2.0
# Compare the output and the newly calculated spectrum. Normalize with
# the maximum values to avoid scaling issues.
np.testing.assert_almost_equal(spec[:10] / spec.max(),
new_spec[:10] / new_spec.max())
def test_eigenspectraOutput(self):
"""
Tests the eigenspectra output using a nonadaptive spectra. This also at
least somewhat tests the weights.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq, eigspec, eigcoef, weights = \
mtspec(data, 1.0, 4.5, number_of_tapers=5, adaptive=False,
optional_output=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(eigspec).any(), False)
self.assertEqual(np.isnan(eigcoef).any(), False)
self.assertEqual(np.isnan(weights).any(), False)
# The weights should all be one for the nonadaptive spectrum.
np.testing.assert_almost_equal(weights, np.ones((43201, 5),
'float64'))
# Sum over the eigenspectra to get the nonadaptive spectrum.
new_spec = eigspec.sum(axis=1) / float(eigspec.shape[1])
new_spec[1:] *= 2.0
# Compare the output and the newly calculated spectrum. Normalize with
# the maximum values to avoid scaling issues.
np.testing.assert_almost_equal(spec[:10] / spec.max(),
new_spec[:10] / new_spec.max())
def test_figure1(self):
"""
Recreate Figure 1
"""
data = load_mtdata('v22_174_series.dat.gz')
spec, freq, jackknife, _, _ = mtspec(data,
4930.,
3.5,
number_of_tapers=5,
nfft=312,
statistics=True)
fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1)
ax1.plot(data, color='black')
ax1.set_xlim(0, len(data))
ax2 = fig.add_subplot(2, 1, 2)
ax2.set_yscale('log')
ax2.plot(freq, spec, color='black')
try:
ax2.fill_between(freq,
jackknife[:, 0],
jackknife[:, 1],
color='grey')
except:
ax2.plot(freq, jackknife[:, 0], '--', color='red')
ax2.plot(freq, jackknife[:, 1], '--', color='red')
ax2.set_xlim(freq[0], freq[-1])
outfile = os.path.join(self.outpath, 'fig1.pdf')
fig.savefig(outfile)
stat = os.stat(outfile)
self.assertTrue(abs(stat.st_mtime - time.time()) < 3)
def test_figure2(self):
"""
Recreate Figure 2
"""
data = load_mtdata('v22_174_series.dat.gz')
spec, freq, jackknife, fstatistics, _ = mtspec(data,
4930.,
3.5,
number_of_tapers=5,
nfft=312,
statistics=True,
rshape=0,
fcrit=0.9)
fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1)
ax1.plot(freq, fstatistics, color='black')
ax1.set_xlim(freq[0], freq[-1])
ax2 = fig.add_subplot(2, 1, 2)
ax2.set_yscale('log')
ax2.plot(freq, spec, color='black')
ax2.set_xlim(freq[0], freq[-1])
outfile = os.path.join(self.outpath, 'fig2.pdf')
fig.savefig(outfile)
stat = os.stat(outfile)
self.assertTrue(abs(stat.st_mtime - time.time()) < 3)
def test_paddedMultitaperSpectrumWithErrors(self):
"""
Test for mtspec_pad with jackknife interval errors. The result is
compared to the output of test_recreatePaperFigures.py in the same
directory. This is assumed to be correct because they are identical to
the figures in the paper on the machine that created these.
"""
data = load_mtdata('v22_174_series.dat.gz')
# Calculate the spectra.
spec, freq, jackknife, _, _ = mtspec(data,
4930.,
3.5,
nfft=312,
number_of_tapers=5,
statistics=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(jackknife).any(), False)
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'mtspec_pad_with_errors.npz')
record = np.load(datafile)
spec2 = record['spec']
jackknife2 = record['jackknife']
freq2 = np.arange(157) * 6.50127447e-07
# Compare.
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 6)
np.testing.assert_almost_equal(jackknife / jackknife,
jackknife2 / jackknife, 6)
def test_figure3(self):
"""
Recreate Figure 2
"""
data = load_mtdata('PASC.dat.gz')
fig = plt.figure()
ax1 = fig.add_subplot(3, 1, 1)
ax1.plot(data, color='black')
ax1.set_xlim(0, len(data))
spec, freq = mtspec(data, 1.0, 1.5, number_of_tapers=1)
ax2 = fig.add_subplot(3, 2, 3)
ax2.set_yscale('log')
ax2.set_xscale('log')
ax2.plot(freq, spec, color='black')
ax2.set_xlim(freq[0], freq[-1])
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5)
ax3 = fig.add_subplot(3, 2, 4)
ax3.set_yscale('log')
ax3.set_xscale('log')
ax3.plot(freq, spec, color='black')
ax3.set_xlim(freq[0], freq[-1])
spec, freq = sine_psd(data, 1.0)
ax4 = fig.add_subplot(3, 2, 5)
ax4.set_yscale('log')
ax4.set_xscale('log')
ax4.plot(freq, spec, color='black')
ax4.set_xlim(freq[0], freq[-1])
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5, quadratic=True)
ax5 = fig.add_subplot(3, 2, 6)
ax5.set_yscale('log')
ax5.set_xscale('log')
ax5.plot(freq, spec, color='black')
ax5.set_xlim(freq[0], freq[-1])
outfile = os.path.join(self.outpath, 'fig3.pdf')
fig.savefig(outfile)
stat = os.stat(outfile)
self.assertTrue(abs(stat.st_mtime - time.time()) < 3)
def test_figure3(self):
"""
Recreate Figure 2
"""
data = load_mtdata('PASC.dat.gz')
fig = plt.figure()
ax1 = fig.add_subplot(3, 1, 1)
ax1.plot(data, color='black')
ax1.set_xlim(0, len(data))
spec, freq = mtspec(data, 1.0, 1.5, number_of_tapers=1)
ax2 = fig.add_subplot(3, 2, 3)
ax2.set_yscale('log')
ax2.set_xscale('log')
ax2.plot(freq, spec, color='black')
ax2.set_xlim(freq[0], freq[-1])
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5)
ax3 = fig.add_subplot(3, 2, 4)
ax3.set_yscale('log')
ax3.set_xscale('log')
ax3.plot(freq, spec, color='black')
ax3.set_xlim(freq[0], freq[-1])
spec, freq = sine_psd(data, 1.0)
ax4 = fig.add_subplot(3, 2, 5)
ax4.set_yscale('log')
ax4.set_xscale('log')
ax4.plot(freq, spec, color='black')
ax4.set_xlim(freq[0], freq[-1])
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5, quadratic=True)
ax5 = fig.add_subplot(3, 2, 6)
ax5.set_yscale('log')
ax5.set_xscale('log')
ax5.plot(freq, spec, color='black')
ax5.set_xlim(freq[0], freq[-1])
outfile = os.path.join(self.outpath, 'fig3.pdf')
fig.savefig(outfile)
stat = os.stat(outfile)
self.assertTrue(abs(stat.st_mtime - time.time()) < 3)
def test_quadraticMultitaperIsDifferent(self):
"""
The quadratic and the normal multitaper spectra look quite similar.
Check that they are different.
"""
data = load_mtdata('v22_174_series.dat.gz')
# Calculate the spectra.
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=2)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
spec2, freq2 = mtspec(data, 1.0, 4.5, number_of_tapers=2,
quadratic=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec2).any(), False)
self.assertEqual(np.isnan(freq2).any(), False)
# Test that these are not equal.
self.assertRaises(AssertionError, np.testing.assert_almost_equal,
spec, spec2)
def test_multitaperSpectrum(self):
"""
Test for mtspec. The result is compared to the output of
test_recreatePaperFigures.py in the same directory. This is assumed to
be correct because they are identical to the figures in the paper on
the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'multitaper.npz')
spec2 = np.load(datafile)['spec']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare, normalize for subdigit comparision
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 5)
def test_sinePSD(self):
"""
Test for the sine_psd spectra. The result is compared to the output of
test_recreatePaperFigures.py in the same directory. This is assumed to
be correct because they are identical to the figures in the paper on
the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq = sine_psd(data, 1.0)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'sine_psd.npz')
spec2 = np.load(datafile)['spec']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare.
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 2)
def test_sinePSD(self):
"""
Test for the sine_psd spectra. The result is compared to the output of
test_recreatePaperFigures.py in the same directory. This is assumed to
be correct because they are identical to the figures in the paper on
the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq = sine_psd(data, 1.0)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'sine_psd.npz')
spec2 = np.load(datafile)['spec']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare.
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 2)
def test_multitaperSpectrum(self):
"""
Test for mtspec. The result is compared to the output of
test_recreatePaperFigures.py in the same directory. This is assumed to
be correct because they are identical to the figures in the paper on
the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'multitaper.npz')
spec2 = np.load(datafile)['spec']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare, normalize for subdigit comparision
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 5)
def test_quadraticMultitaperIsDifferent(self):
"""
The quadratic and the normal multitaper spectra look quite similar.
Check that they are different.
"""
data = load_mtdata('v22_174_series.dat.gz')
# Calculate the spectra.
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=2)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
spec2, freq2 = mtspec(data,
1.0,
4.5,
number_of_tapers=2,
quadratic=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec2).any(), False)
self.assertEqual(np.isnan(freq2).any(), False)
# Test that these are not equal.
self.assertRaises(AssertionError, np.testing.assert_almost_equal, spec,
spec2)
def test_multitaperSpectrumOptionalOutput(self):
"""
Test for mtspec. The result is compared to the output of
test_recreatePaperFigures.py in the same directory. This is assumed to
be correct because they are identical to the figures in the paper on
the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq, eigspec, eigcoef, weights = \
mtspec(data, 1.0, 4.5, number_of_tapers=5,
optional_output=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(eigspec).any(), False)
self.assertEqual(np.isnan(eigcoef).any(), False)
self.assertEqual(np.isnan(weights).any(), False)
#XXX: Verify if this is correct, if so savez the data
#import matplotlib.pyplot as plt
#plt.plot(np.abs(eigcoef[:,0]))
#plt.show()
#import ipdb; ipdb.set_trace()
#np.savez('data/multitaper.npz', spec=spec.astype('float32'),
# eigspec=eigspec.astype('float32'),
# eigcoef=eigcoef.astype('float32'),
# weights=weights.astype('float32'))
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'multitaper.npz')
record = np.load(datafile)
spec2 = record['spec']
#eigspec2 = record['eigspec']
#eigcoef2 = record['eigcoef']
#weights2 = record['weights']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare, normalize for subdigit comparision
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 5)
def test_multitaperSpectrumOptionalOutput(self):
"""
Test for mtspec. The result is compared to the output of
test_recreatePaperFigures.py in the same directory. This is assumed to
be correct because they are identical to the figures in the paper on
the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq, eigspec, eigcoef, weights = \
mtspec(data, 1.0, 4.5, number_of_tapers=5,
optional_output=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(eigspec).any(), False)
self.assertEqual(np.isnan(eigcoef).any(), False)
self.assertEqual(np.isnan(weights).any(), False)
#XXX: Verify if this is correct, if so savez the data
#import matplotlib.pyplot as plt
#plt.plot(np.abs(eigcoef[:,0]))
#plt.show()
#import ipdb; ipdb.set_trace()
#np.savez('data/multitaper.npz', spec=spec.astype('float32'),
# eigspec=eigspec.astype('float32'),
# eigcoef=eigcoef.astype('float32'),
# weights=weights.astype('float32'))
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'multitaper.npz')
record = np.load(datafile)
spec2 = record['spec']
#eigspec2 = record['eigspec']
#eigcoef2 = record['eigcoef']
#weights2 = record['weights']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare, normalize for subdigit comparision
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 5)
def test_figure2(self):
"""
Recreate Figure 2
"""
data = load_mtdata('v22_174_series.dat.gz')
spec, freq, jackknife, fstatistics, _ = mtspec(data, 4930., 3.5,
number_of_tapers=5, nfft=312, statistics=True, rshape=0,
fcrit=0.9)
fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1)
ax1.plot(freq, fstatistics, color='black')
ax1.set_xlim(freq[0], freq[-1])
ax2 = fig.add_subplot(2, 1, 2)
ax2.set_yscale('log')
ax2.plot(freq, spec, color='black')
ax2.set_xlim(freq[0], freq[-1])
outfile = os.path.join(self.outpath, 'fig2.pdf')
fig.savefig(outfile)
stat = os.stat(outfile)
self.assertTrue(abs(stat.st_mtime - time.time()) < 3)
def test_sinePSDStatistics(self):
"""
Test for the sine_psd spectra with optional output. The result is
compared to the output of test_recreatePaperFigures.py in the same
directory. This is assumed to be correct because they are identical
to the figures in the paper on the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq, errors, tapers = sine_psd(data, 1.0, statistics=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
self.assertEqual(np.isnan(errors).any(), False)
self.assertEqual(np.isnan(tapers).any(), False)
#XXX: assert for errors and tapers is missing
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'sine_psd.npz')
spec2 = np.load(datafile)['spec']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare #XXX really bad precision for spec (linux 64bit)
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 2)
def test_sinePSDStatistics(self):
"""
Test for the sine_psd spectra with optional output. The result is
compared to the output of test_recreatePaperFigures.py in the same
directory. This is assumed to be correct because they are identical
to the figures in the paper on the machine that created these.
"""
data = load_mtdata('PASC.dat.gz')
# Calculate the spectra.
spec, freq, errors, tapers = sine_psd(data, 1.0, statistics=True)
# No NaNs are supposed to be in the output.
self.assertEqual(np.isnan(spec).any(), False)
self.assertEqual(np.isnan(freq).any(), False)
self.assertEqual(np.isnan(errors).any(), False)
self.assertEqual(np.isnan(tapers).any(), False)
#XXX: assert for errors and tapers is missing
# Load the good data.
datafile = os.path.join(os.path.dirname(__file__), 'data',
'sine_psd.npz')
spec2 = np.load(datafile)['spec']
freq2 = np.arange(43201) * 1.15740741e-05
# Compare #XXX really bad precision for spec (linux 64bit)
np.testing.assert_almost_equal(freq, freq2)
np.testing.assert_almost_equal(spec / spec, spec2 / spec, 2)
import matplotlib as mpl
mpl.rcParams['font.size'] = 9.0
import matplotlib.pyplot as plt
from mtspec import mtspec
from mtspec.util import load_mtdata
data = load_mtdata('v22_174_series.dat.gz')
spec, freq, jackknife, _, _ = mtspec(data, 4930., 3.5, number_of_tapers=5,
nfft=312, statistics=True)
fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1)
ax1.plot(data, color='black')
ax1.set_xlim(0, len(data))
ax2 = fig.add_subplot(2, 1, 2)
ax2.set_yscale('log')
ax2.plot(freq, spec, color='black')
ax2.plot(freq, jackknife[:, 0], '--', color = 'red')
ax2.plot(freq, jackknife[:, 1], '--', color = 'red')
ax2.set_xlim(freq[0], freq[-1])
import matplotlib as mpl
mpl.rcParams['font.size'] = 9.0
import matplotlib.pyplot as plt
from mtspec import mtspec, sine_psd
from mtspec.util import load_mtdata
data = load_mtdata('PASC.dat.gz')
fig = plt.figure()
ax1 = fig.add_subplot(3, 1, 1)
ax1.plot(data, color='black')
ax1.set_xlim(0, len(data))
spec, freq = mtspec(data, 1.0, 1.5, number_of_tapers=1)
ax2 = fig.add_subplot(3, 2, 3)
ax2.set_yscale('log')
ax2.set_xscale('log')
ax2.plot(freq, spec, color='black')
ax2.set_xlim(freq[0], freq[-1])
spec, freq = mtspec(data, 1.0, 4.5, number_of_tapers=5)
ax3 = fig.add_subplot(3, 2, 4)
ax3.set_yscale('log')
ax3.set_xscale('log')
ax3.plot(freq, spec, color='black')
ax3.set_xlim(freq[0], freq[-1])
spec, freq = sine_psd(data, 1.0)