def viz(wavelet, scales, scaletype, show_last, nv):
plot(scales,
show=1,
title="scales | scaletype=%s, nv=%s" % (scaletype, nv))
if scaletype == 'log-piecewise':
extra = ", logscale_transition_idx=%s" % logscale_transition_idx(
scales)
else:
extra = ""
print("n_scales={}, max(scales)={:.1f}{}".format(len(scales), scales.max(),
extra))
psih = wavelet(scale=scales)
last_psihs = psih[-show_last:]
# find xmax of plot
least_large = last_psihs[0]
mx_idx = np.argmax(least_large)
last_nonzero_idx = np.where(
least_large[mx_idx:] < least_large.max() * .1)[0][0]
last_nonzero_idx += mx_idx + 2
plot(last_psihs.T[:last_nonzero_idx],
color='tab:blue',
show=1,
title="Last %s largest scales" % show_last)
def viz(x,
Tf,
ridge_idxs,
yticks=None,
ssq=False,
transform='cwt',
show_x=True):
if show_x:
plot(x,
title="x(t)",
show=1,
xlabel="Time [samples]",
ylabel="Signal Amplitude [A.U.]")
ylabel = ("Frequency scales [1/Hz]" if
(transform == 'cwt' and not ssq) else "Frequencies [Hz]")
title = "abs({}{}) w/ ridge_idxs".format("SSQ_" if ssq else "",
transform.upper())
ikw = dict(abs=1, cmap='turbo', yticks=yticks, title=title)
pkw = dict(linestyle='--',
color='k',
xlabel="Time [samples]",
ylabel=ylabel,
xlims=(0, Tf.shape[1]))
imshow(Tf, **ikw, show=0)
plot(ridge_idxs, **pkw, show=1)
def test_visuals():
os.environ['SSQ_GPU'] = '0'
x = np.random.randn(10)
visuals.hist(x, show=1, stats=1)
y = x * (1 + 1j)
visuals.plot(y,
complex=1,
c_annot=1,
vlines=1,
ax_equal=1,
xticks=np.arange(len(y)),
yticks=y)
visuals.plot(y, abs=1, vert=1, dx1=1, ticks=0)
visuals.scat(x, vlines=1, hlines=1)
visuals.scat(y, complex=1, ticks=0)
visuals.plotscat(y, show=1, xlims=(-1, 1), dx1=1, ylabel="5")
visuals.plots([y, y], tight=1, show=1)
visuals.plots([y, y], nrows=2)
visuals.plots([y, y], ncols=2)
g = np.random.randn(4, 4)
visuals.imshow(g * (1 + 2j), complex=1)
visuals.imshow(g, ridge=1, ticks=0)
pass_on_error(visuals.plot, None, None)
pass_on_error(visuals.wavelet_tf, 'morlet', notext=True)
def test_visuals():
x = np.random.randn(10)
hist(x, show=1, stats=1)
y = x * (1 + 1j)
plot(y,
complex=1,
c_annot=1,
vlines=1,
ax_equal=1,
xticks=np.arange(len(y)),
yticks=y)
plot(y, abs=1, vert=1, dx1=1, ticks=0)
scat(x, vlines=1, hlines=1)
scat(y, complex=1, ticks=0)
plotscat(y, show=1, xlims=(-1, 1), dx1=1, ylabel="5")
plots([y, y], tight=1, show=1)
plots([y, y], nrows=2)
plots([y, y], ncols=2)
g = np.random.randn(4, 4)
imshow(g * (1 + 2j), complex=1)
imshow(g, ridge=1, ticks=0)
_pass_on_error(plot, None, None)
def _maybe_viz(Wx, xo, xrec, title, err):
if not VIZ:
return
mx = np.abs(Wx).max()
if 'SSQ' in title:
Wx = np.pad(np.flipud(Wx), [[5], [0]])
mx = .1*mx
else:
mx = .9*mx
imshow(Wx, abs=1, norm=(0, mx), cmap='jet', show=1, title=title)
plot(xo, title="Original vs reconstructed | MAD/RMS=%.4f" % err)
plot(xrec, show=1)
#%%
row_anim(Wxz, idxs, scales)
#%%## Superimpose ####
row_anim(Wxz, idxs, scales, superposed=True)
#%%## Synchrosqueeze
Tx, _, ssq_freqs, *_ = ssq_cwt(x, wavelet, t=_t(0, 1, N))
#%%
imshow(Tx, abs=1, title="abs(SSWT)", yticks=ssq_freqs, show=1)
#%%# Damped pendulum example ################################################
N, w0 = 4096, 25
t = _t(0, 6, N)
s = np.exp(-t) * np.cos(w0 * t)
w = np.linspace(-40, 40, N)
S = (1 + 1j * w) / ((1 + 1j * w)**2 + w0**2)
#%%# Plot ####
plot(s, title="s(t)", show=1)
plot(w, np.abs(S), title="abs(FT(s(t)))", show=1)
#%%# Now SSWT ##
wavelet = ('morlet', {'mu': 5})
Tx, *_ = ssq_cwt(s, wavelet, t=t)
#%%# 'cheat' a little; could use boundary wavelets instead (not implemented)
aTxz = np.abs(Tx)[:, len(t) // 8:]
imshow(aTxz, abs=1, title="abs(SSWT(s(t)))", show=1, cmap='bone')
#%%
mxidx = np.where(np.abs(aTxz) == np.abs(aTxz).max())[0][0]
plot(aTxz[mxidx], title="max row of abs(SSWT(s(t)))", show=1)
#%%## Configure signal #######################################################
N = 2048
noise_var = 6 # noise variance; compare error against = 12
x, ts = echirp(N)
x *= (1 + .3 * cos_f([1], N)) # amplitude modulation
xo = x.copy()
np.random.seed(4)
x += np.sqrt(noise_var) * np.random.randn(len(x))
#### Show signal & its global spectrum #######################################
axf = np.abs(rfft(x))
plot(xo)
scat(xo, s=8, show=1)
plot(x)
scat(x, s=8, show=1)
plot(axf, show=1)
#%%# Synchrosqueeze ##########################################################
kw = dict(wavelet=('morlet', {'mu': 4.5}), nv=32, scales='log')
Tx, *_ = ssq_cwt(x, t=ts, **kw)
Wx, *_ = cwt(x, t=ts, **kw)
#%%# Visualize ###############################################################
pkw = dict(abs=1, cmap='bone')
_Tx = np.pad(Tx, [[4, 4]]) # improve display of top- & bottom-most freqs
imshow(Wx, **pkw)
imshow(np.flipud(_Tx), norm=(0, 4e-1), **pkw)
