def linedetection():
n = 716
dt = 1.0e-3
df = 1.0 / (dt * n)
npi = 4.0
nwin = 10
# line and noise components
fline = 50.0
aline = 10.0
noise_amplitude = 1.0
t = np.arange(n) * dt
lines = np.array([fline, fline + 2.0 * df])
nlines = len(lines)
y = noise_amplitude * normal(size = n) \
+ aline * np.cos(2.0 * pi * fline * t)
r = pymutt.mtft(series = y,
dt = dt,
npi = npi,
nwin = nwin,
kind = 1,
paddedlen = 10 * n,
dodof = 1,
)
Fsortidx = r['F'].argsort()
lidx = Fsortidx[-1]
linefs = [r['df'] * lidx]
# print >> sys.stderr, (linefs, r['df'], n * r['df'])
r = pymutt.mtft(series = y,
dt = dt,
npi = npi,
nwin = nwin,
kind = 1,
paddedlen = 10 * n,
dodof = 1,
lines = np.array(linefs),
)
f = r['df'] * np.arange(len(r['power']))
setout = file('lineprocmtft.dat', 'w')
setheader(setout,
title = 'line + noise',
subtitle = "npi = %.0f nwin = %d" % (npi, nwin)
)
for psdkey in ['power', 'reshaped', 'F']:
if not r.has_key(psdkey):
continue
setdata(setout, f, r[psdkey], legend = psdkey)
setout.close()
def mtanalyze(data,
dt = 1.0,
kind = 1, # adaptive: 2 for vanilla hi-res
npi = 3.0,
nwin = 5, # s.b. 2 * npi - 1
padby = 8, # pad to padby * power-of-2-holding-data
nlines = 0, # number of lines to find
linedomain = None, # could be a range of frequencies to search
doplot = 0,
title = None,
title2 = None,
verbose = 0,
):
if padby and padby > 1:
paddedlen = 2
while paddedlen < len(data):
paddedlen *= 2
paddedlen *= padby
else:
paddedlen = 0
if verbose:
print >> sys.stderr, "original length: %d padded to: %d" \
% (len(data), paddedlen)
r = pymutt.mtft(data, dt = dt, npi = npi, nwin = nwin,
paddedlen = paddedlen, dodof = (nlines > 0))
r['f'] = r['df'] * np.arange(len(r['power']))
if nlines:
# we operate on a copy of r['F'] so we can pass the original up
# unaltered
Fcpy = np.array(r['F'], copy = 1)
flines = []
Fmin = Fcpy.min() - 1.0
# For each line, find the maximum current value of the F-test.
# Then zero the F-test values in the region fline +- W/2 before
# searching for the next largest value.
if verbose:
print >> sys.stderr, "\nspectral lines:"
while len(flines) < nlines:
idxfmax = np.argsort(Fcpy)[-1]
fline = r['df'] * idxfmax
if not linedomain or \
(fline >= linedomain[0] and fline <= linedomain[1]):
flines.append(fline)
if verbose:
print >> sys.stderr, "%5d %13.6e" % (len(flines), fline)
wl = max(0, int(idxfmax - round(0.5 * r['W'] / r['df'])))
wr = min(r['n'] - 1, int(idxfmax + round(0.5 * r['W'] / r['df'])))
Fcpy[wl:wr] = Fmin
if len(flines) > 0:
reducedr = pymutt.mtft(data,
dt = dt,
npi = npi,
nwin = nwin,
kind = kind,
paddedlen = paddedlen,
dodof = 1,
lines = np.array(flines),
)
# added reshaped spectrum values to r
r['reshaped'] = reducedr['reshaped']
r['linea'] = reducedr['linea']
r['linevar'] = reducedr['linevar']
if doplot and mpl:
if not linedomain:
il = 0
ir = r['n'] - 1
else:
il = int(floor(linedomain[0] / r['df']))
ir = int(ceil(linedomain[1] / r['df']))
if nlines:
mpl.subplot(212)
if title2:
mpl.title(title2)
mpl.plot(r['f'][il:ir], r['F'][il:ir])
mpl.ylabel('F')
mpl.xlabel('frequency')
if nlines:
mpl.subplot(211)
if title:
mpl.title(title)
mpl.plot(r['f'][il:ir], 10.0 * np.log10(r['power'][il:ir]))
mpl.ylabel('dB')
if r.has_key('reshaped'):
mpl.plot(r['f'][il:ir], 10.0 * np.log10(reducedr['reshaped'][il:ir]))
mpl.show()
return r
#
# standard dataset: sine wave at 11.5 Hz plus noise (but it could be anything)
#
dt = 0.01
n = 430
t = dt * np.arange(n)
data = np.random.randn(n) + 0.6 * np.sin(2.0 * 3.141592654 * 11.5 * t)
# mpl.plot(data)
# mpl.figure()
#
# simplest processing: assume dt = 1 so frequency domain is [0, 0.5]
#
r = pymutt.mtft(data)
# mpl.plot(r['power'])
#
# next simplest: use correct dt so frequency has true domain and use
# correct frequency in the plot
#
r = pymutt.mtft(data,
dt = dt
)
f = np.arange(r['nspec']) * r['df']
# mpl.plot(f, r['power'])
#
def main(argv = None):
import getopt
import traceback
if argv is None:
argv = sys.argv
try:
npi = 4.0
nwin = 6
kind = 2
nlines_to_find = 2
padfactor = 8
arglist = "vhW:K:k:l:z:"
try:
opts, args = getopt.getopt(argv[1:], arglist)
except getopt.error, msg:
raise Usage(msg)
for opt, v in opts:
if opt == "-v":
pass
elif opt == "-h":
print >> sys.stdout, __doc__
return 0
elif opt == "-W":
npi = float(v)
elif opt == "-K":
nwin = int(v)
elif opt == "-k":
kind = int(v)
elif opt == "-z":
padfactor = int(v)
elif opt == "-l":
nlines_to_find = int(v)
lines = []
dodof = 1
doweights = 1
seriesname = args[0] if len(args) > 0 else "willamette"
ts, dt, dtu = getseries(seriesname)
serieslength = len(ts)
paddedlen = 2
while paddedlen < serieslength:
paddedlen *= 2
paddedlen *= padfactor
print >> sys.stdout, "dataset %s has %d (%d) samples at %s %s" \
% (seriesname, len(ts), paddedlen, dt, dtu)
print >> sys.stdout, " npi: %.1f K: %d lines: %d %s" \
% (npi, nwin, nlines_to_find, ("?", "high-res", "adaptive")[kind])
ts -= nx.mean(ts)
plotseries(ts, dx = dt, xunits = dtu, title = seriesname)
r = pymutt.mtft(series = ts,
dt = dt,
npi = npi,
nwin = nwin,
kind = kind,
paddedlen = paddedlen,
dodof = dodof,
doweights = doweights,
lines = nx.array(lines),
)
show_contents(r, "original")
basetitle = seriesname + (" W %.1f K %d a %d n %d (%d)"
% (r['npi'], r['nwin'], r['kind'], len(ts), r['n']))
mtpanel(r, title = basetitle + ": original")
tlen = len(ts)
t = dt * nx.arange(tlen)
A = nx.zeros((tlen, 2 * nlines_to_find + 1))
A[:,0] = 1
flines = []
Fcpy = nx.array(r['F'], copy = 1)
for l in range(nlines_to_find):
idxfmax = nx.argsort(Fcpy)[-1]
fline = r['df'] * idxfmax
flines.append(fline)
ir = max(0, int(idxfmax + round(r['W'] / r['df'])))
il = min(r['n'] - 1, int(idxfmax - round(r['W'] / r['df'])))
Fcpy[il:ir] = 0.0
reducedr = pymutt.mtft(series = ts,
dt = dt,
npi = npi,
nwin = nwin,
kind = kind,
paddedlen = paddedlen,
dodof = dodof,
lines = nx.array(flines))
show_contents(reducedr, "reshaped")
if nlines_to_find > 0:
if 0:
plotseries(ts, dx = dt, xunits = dtu,
title = seriesname + ": reshaped")
mtpanel(reducedr, title = basetitle + ": reshaped")
mpl.show()
return 0
def doit(verbose = 0):
# pick a miscellaneous length and then find a much bigger power-of-2
n = 716
dt = 1.0
df = 1.0 / (dt * n)
pow2 = ceil(log(5 * n) / log(2.0))
paddedlen = int(pow(2, pow2))
print __doc__
print "here are the actual results for this run:\n"
print " test series length padded from %d to %d" % (n, paddedlen)
# line and noise components
fline = 50 * df
aline = 10.0
noise_amplitude = 1.0
t = np.arange(n) * dt
lines = np.array([fline, fline + 4.0 * df])
nlines = len(lines)
suma = complex(0.0, 0.0) * np.zeros([nlines])
sumF = None
sumv = np.zeros([nlines])
trials = 20
print " averaging over %d trials" % trials
for i in range(trials):
y = noise_amplitude * normal(size = n) \
+ aline * np.cos(2.0 * pi * fline * t)
r = pymutt.mtft(series = y,
dt = dt,
npi = 2,
nwin = 8,
kind = 1,
paddedlen = paddedlen,
dodof = 1,
lines = lines,
)
suma += r['linea']
sumv += r['linevar']
if sumF is None:
sumF = r['F']
else:
sumF += r['F']
print " frequency real imag abs F line var"
for i, f in enumerate(lines):
amp = suma[i] / trials
var = sumv[i] / trials
ifrq = int(round(f / r['df']))
Ftest = sumF[ifrq] / trials
print " %8.5f %8.3f %8.3f %8.4f %8.1f %10.3e" \
% (f, amp.real, amp.imag, abs(amp), Ftest, var)
return 0
def filteredprocess():
n = 937
dt = 1e-3
fu = 80.0
fs = 90.0
yr = bandlimited(n, dt, fu, fs)
setout = file('ranproc.dat', 'w')
setheader(setout,
title = 'filtered normal series',
subtitle = "fpass = %.1f fstop = %.1f" % (fu, fs)
)
setdata(setout, dt * np.arange(n), yr, legend = 'y(t)')
setout.close()
npi = 4.0
nwin = 10
setout = file('ranprocmtft.dat', 'w')
setheader(setout,
title = 'filtered normal series',
subtitle = "npi = %.0f nwin = %d" % (npi, nwin)
)
r = pymutt.mtft(series = yr,
dt = dt,
npi = npi,
nwin = nwin,
kind = 1,
paddedlen = 4 * n,
dodof = 1,
)
f = r['df'] * np.arange(len(r['power']))
for psdkey in ['power', 'dof']:
if not r.has_key(psdkey):
continue
setdata(setout, f, r[psdkey], legend = 'hires ' + psdkey)
r = pymutt.mtft(series = yr,
dt = dt,
npi = npi,
nwin = nwin,
kind = 2,
paddedlen = 4 * n,
dodof = 1,
)
for psdkey in ['power', 'dof']:
if not r.has_key(psdkey):
continue
setdata(setout, f, r[psdkey], legend = 'adaptive ' + psdkey)
yrp = dt * abs(dft.rfft(yr, n = n)) ** 2
df = 1.0 / (n * dt)
f = df * np.arange(len(yrp))
setdata(setout, f, yrp / n, legend = 'raw')
tscale = 1.0 /np.hanning(n).mean()
yrph = dt * abs(dft.rfft(tscale * np.hanning(n) * yr, n = n)) ** 2
setdata(setout, f, yrph / n, legend = 'hanning taper')
setout.close()
def doit(verbose = 0):
'''This code reproduces figure 512 in Percival and Walden. It (1)
analyzes the time series and applies the F-test for spectral
lines, (2) extracts the two lines with largest F-test values, and
(3) computes the reshaped spectrum. It then displays the F-test
and the original and reshaped spectra as in P&W figure 512.
'''
print doit.__doc__
global dt, data
ts = np.array(data)
ts -= ts.mean()
paddedlen = 1024
r = pymutt.mtft(series = ts,
dt = dt,
npi = 4,
nwin = 5,
kind = 1,
paddedlen = paddedlen,
dodof = 1,
)
Fcpy = np.array(r['F'], copy = 1)
flines = []
nlines_to_find = 2
# For each line, find the maximum current value of the F-test.
# Then zero the F-test values in the region fline +- W/2 before
# searching for the next largest value.
for l in range(nlines_to_find):
idxfmax = np.argsort(Fcpy)[-1]
fline = r['df'] * idxfmax
flines.append(fline)
ir = max(0, int(idxfmax + round(0.5 * r['W'] / r['df'])))
il = min(r['n'] - 1, int(idxfmax - round(0.5 * r['W'] / r['df'])))
Fcpy[il:ir] = 0.0
reducedr = pymutt.mtft(series = ts,
dt = dt,
npi = 4,
nwin = 5,
kind = 2,
paddedlen = paddedlen,
dodof = 1,
lines = np.array(flines),
)
f = r['df'] * np.arange(len(r['power']))
mpl.subplot(211)
mpl.title("Compare with Percival and Walden, figure 512")
mpl.plot(f, r['F'])
for level in (8.6, 18.5):
y = level + 0.0 * r['power']
mpl.plot(f, y)
mpl.ylabel("F-test")
mpl.subplot(212)
mpl.plot(f, 10.0 * np.log10(r['power']))
mpl.plot(f, 10.0 * np.log10(reducedr['reshaped']))
mpl.xlabel("f (cycles/year)")
mpl.ylabel("dB")
mpl.show()
