def test_fftcoef_detrend():
for n in (50, 51):
t = np.arange(n) / n
x = np.random.randn(n)
xd = signal.detrend(x)
mag, phase, frq = dsp.fftcoef(x, 1 / t[1], dodetrend=True)
A, B, frq = dsp.fftcoef(x,
1 / t[1],
coef="ab",
window=np.ones(x.shape),
dodetrend=True)
w = 2 * np.pi * frq[1]
# reconstruct with magnitude and phase:
x2 = 0.0
for k, (m, p, f) in enumerate(zip(mag, phase, frq)):
x2 = x2 + m * np.sin(k * w * t - p)
assert np.allclose(xd, x2)
# reconstruct with A and B:
x3 = 0.0
for k, (a, b, f) in enumerate(zip(A, B, frq)):
x3 = x3 + a * np.cos(k * w * t) + b * np.sin(k * w * t)
assert np.allclose(xd, x3)
assert_raises(ValueError,
dsp.fftcoef,
x,
1 / t[1],
window=np.ones(x.size - 1))
def test_fftcoef_maxdf():
n = 16
t = np.arange(n) / n
x = np.random.randn(n)
mag, phase, frq = dsp.fftcoef(x, 1 / t[1])
mag1, phase1, frq1 = dsp.fftcoef(x, 1 / t[1], maxdf=0.6)
assert frq1[1] <= 0.6
assert np.allclose(mag1[::2], mag)
def test_fftcoef_fold():
for n in (10, 11):
t = np.arange(n) / n
x = np.random.randn(n)
mag, phase, frq = dsp.fftcoef(x, 1 / t[1], fold=True)
mag1, phase1, frq = dsp.fftcoef(x, 1 / t[1], fold=False)
if not (n & 1):
mag1[1:-1] *= 2.0
else:
mag1[1:] *= 2.0
assert np.allclose(mag, mag1)
assert np.allclose(phase, phase1)
def test_fftcoef_recon():
for n in (50, 51):
t = np.arange(n) / n
x = np.random.randn(n)
mag, phase, frq = dsp.fftcoef(x, 1 / t[1])
A, B, frq = dsp.fftcoef(x, 1 / t[1], coef="ab", window=np.ones(x.shape))
w = 2 * np.pi * frq[1]
# reconstruct with magnitude and phase:
x2 = 0.0
for k, (m, p, f) in enumerate(zip(mag, phase, frq)):
x2 = x2 + m * np.sin(k * w * t - p)
assert np.allclose(x, x2)
# reconstruct with A and B:
x3 = 0.0
for k, (a, b, f) in enumerate(zip(A, B, frq)):
x3 = x3 + a * np.cos(k * w * t) + b * np.sin(k * w * t)
assert np.allclose(x, x3)
def test_fftcoef():
for n in (50, 51):
t = np.arange(n) / n
x = 4.0 * np.sin(2 * np.pi * 4 * t)
mag, phase, frq = dsp.fftcoef(x, 1 / t[1])
# lowest frequency = 1/T = 1.0
# highest frequency = sr/2 = 500.0
nfrq = (n // 2) + 1
assert np.allclose(frq, 0.0 + np.arange(nfrq))
x2 = np.zeros(len(frq))
x2[4] = 4.0
assert np.allclose(mag, x2)
assert np.allclose(phase[4], 0.0)
x = 4.0 * np.cos(2 * np.pi * 4 * t)
mag, phase, frq = dsp.fftcoef(x, 1 / t[1])
# lowest frequency = 1/T = 1.0
# highest frequency = sr/2 = 500.0
nfrq = (n // 2) + 1
assert np.allclose(frq, 0.0 + np.arange(nfrq))
x2 = np.zeros(len(frq))
x2[4] = 4.0
assert np.allclose(mag, x2)
assert np.allclose(phase[4], -np.pi / 2)
sig = np.column_stack((x, x, x))
mag1, phase1, frq1 = dsp.fftcoef(sig, 1 / t[1], axis=0)
assert np.allclose(frq, frq1)
for i in range(3):
assert np.allclose(mag1[:, i], mag)
assert np.allclose(phase1[:, i], phase)
sig = sig.reshape(1, 1, -1, 3, 1)
mag2, phase2, frq2 = dsp.fftcoef(sig, 1 / t[1], axis=2)
assert np.allclose(frq, frq2)
assert np.allclose(mag1, mag2.reshape(-1, 3))
assert np.allclose(phase1, phase2.reshape(-1, 3))
def _plot_era(self):
"""
Plots input data against reduced model.
Notes
-----
If the parameter `input_labels` is left empty, the approximate
fit plot will not have a corresponding legend. Otherwise, the
data and its approximations will appear with a corresponding
legend. If the number of input labels provided does not match
the number of input signals, this will return an error.
If the parameter `FFT` is set to True, this function will
generate an FFT plot of the input data in the corresponding
color coding of the approximate fit plot. This will appear
below the approximate fit plot and serves as a helpful
comparison of detected modal data. If the scaling of the FFT
plot is suboptimal, it can be adjusted by changing the values
input to `FFT_range`, which will serve as a maximum cutoff or
minimum/maximum cutoff pair, depending on whether one or two
values are given.
"""
if not self.show_plot:
return
y = self.resp_era
if not hasattr(self, "time"):
self.time = np.arange(0, self.n_tsteps) / self.sr + self.t0
# plot each input in its own window
for j in range(self.n_inputs):
fig = plt.figure(f"ERA Fit, input {j}", clear=True)
if self.FFT:
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
else:
ax1 = fig.add_subplot(111)
# Will execute if the user has specified signal labels
if self.input_labels:
# Plot original data
for i in range(self.resp.shape[0]):
ax1.plot(
self.time,
self.resp[i, :, j],
label=f"{self.input_labels[i]} (Data)",
)
# reset color cycle so that the colors line up
ax1.set_prop_cycle(None)
# Plot ERA fit to data
for i in range(self.resp.shape[0]):
ax1.plot(
self.time,
y[i, :, j],
"--",
label=f"{self.input_labels[i]} (ERA Fit)",
)
# Legend will appear next to plot
ax1.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
else:
# Plot original data
ax1.plot(self.time, self.resp[:, :, j].T, label="Data")
# reset color cycle so that the colors line up
ax1.set_prop_cycle(None)
# Plot ERA fit to data
ax1.plot(self.time, y[:, :, j].T, "--", label="ERA fit")
# Labeling plot
ax1.set_xlabel("Time (s)")
ax1.set_ylabel("Response")
ax1.set_title("Data (solid) vs. ERA Reduced Model (dashed)")
# Will execute if the user requests an FFT
if self.FFT:
# Recovering magnitude, phase, and frequency FFT data
mag, phase, frq = dsp.fftcoef(self.resp[:, :, j].T,
self.sr,
axis=0,
maxdf=0.2)
# No defined limits will plot entire FFT
if not self.FFT_range:
ax2.plot(frq, mag)
# In the case of defined limits, they will be processed
else:
# Converts integer/float input to a list for indexing purposes
if isinstance(self.FFT_range, numbers.Real):
self.FFT_range = [self.FFT_range]
# If only one limit is provided, it is taken as a maximum limit
if len(self.FFT_range) == 1:
maxlim = max(np.where(frq <= self.FFT_range[0])[0])
ax2.plot(frq[:maxlim], mag[:maxlim])
# If a pair of limits is provided, it will be used
# as minimum/maximum limits
elif len(self.FFT_range) == 2:
minlim = max(np.where(frq <= self.FFT_range[0])[0])
maxlim = max(np.where(frq <= self.FFT_range[1])[0])
ax2.plot(frq[minlim:maxlim], mag[minlim:maxlim])
# Labeling FFT plot
ax2.set_xlabel("Frequency (Hz)")
ax2.set_ylabel("Magnitude")
ax2.set_title("Magnitude of Frequency Responses of Data")
fig.tight_layout()
fig.canvas.draw()
plt.show()
