# -*- coding: utf-8 -*-
# ------------------------------------------------------------------
# Filename: spectrogram.py
# Purpose: Plotting spectrogram of Seismograms.
# Author: Christian Sippl, Moritz Beyreuther
# Email: sippl@geophysik.uni-muenchen.de
#
# Copyright (C) 2008-2012 Christian Sippl
# --------------------------------------------------------------------
"""
Plotting spectrogram of seismograms.
:copyright:
The ObsPy Development Team (devs@obspy.org)
:license:
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from future.builtins import * # NOQA @UnusedWildImport
import math
import numpy as np
from matplotlib import mlab
from matplotlib.colors import Normalize
from obspy.imaging.cm import obspy_sequential
[docs]def _nearest_pow_2(x):
"""
Find power of two nearest to x
>>> _nearest_pow_2(3)
2.0
>>> _nearest_pow_2(15)
16.0
:type x: float
:param x: Number
:rtype: Int
:return: Nearest power of 2 to x
"""
a = math.pow(2, math.ceil(np.log2(x)))
b = math.pow(2, math.floor(np.log2(x)))
if abs(a - x) < abs(b - x):
return a
else:
return b
[docs]def spectrogram(data, samp_rate, per_lap=0.9, wlen=None, log=False,
outfile=None, fmt=None, axes=None, dbscale=False,
mult=8.0, cmap=obspy_sequential, zorder=None, title=None,
show=True, sphinx=False, clip=[0.0, 1.0]):
"""
Computes and plots spectrogram of the input data.
:param data: Input data
:type samp_rate: float
:param samp_rate: Samplerate in Hz
:type per_lap: float
:param per_lap: Percentage of overlap of sliding window, ranging from 0
to 1. High overlaps take a long time to compute.
:type wlen: int or float
:param wlen: Window length for fft in seconds. If this parameter is too
small, the calculation will take forever. If None, it defaults to
(samp_rate/100.0).
:type log: bool
:param log: Logarithmic frequency axis if True, linear frequency axis
otherwise.
:type outfile: str
:param outfile: String for the filename of output file, if None
interactive plotting is activated.
:type fmt: str
:param fmt: Format of image to save
:type axes: :class:`matplotlib.axes.Axes`
:param axes: Plot into given axes, this deactivates the fmt and
outfile option.
:type dbscale: bool
:param dbscale: If True 10 * log10 of color values is taken, if False the
sqrt is taken.
:type mult: float
:param mult: Pad zeros to length mult * wlen. This will make the
spectrogram smoother.
:type cmap: :class:`matplotlib.colors.Colormap`
:param cmap: Specify a custom colormap instance. If not specified, then the
default ObsPy sequential colormap is used.
:type zorder: float
:param zorder: Specify the zorder of the plot. Only of importance if other
plots in the same axes are executed.
:type title: str
:param title: Set the plot title
:type show: bool
:param show: Do not call `plt.show()` at end of routine. That way, further
modifications can be done to the figure before showing it.
:type sphinx: bool
:param sphinx: Internal flag used for API doc generation, default False
:type clip: [float, float]
:param clip: adjust colormap to clip at lower and/or upper end. The given
percentages of the amplitude range (linear or logarithmic depending
on option `dbscale`) are clipped.
"""
import matplotlib.pyplot as plt
# enforce float for samp_rate
samp_rate = float(samp_rate)
# set wlen from samp_rate if not specified otherwise
if not wlen:
wlen = samp_rate / 100.
npts = len(data)
# nfft needs to be an integer, otherwise a deprecation will be raised
# XXX add condition for too many windows => calculation takes for ever
nfft = int(_nearest_pow_2(wlen * samp_rate))
if nfft > npts:
nfft = int(_nearest_pow_2(npts / 8.0))
if mult is not None:
mult = int(_nearest_pow_2(mult))
mult = mult * nfft
nlap = int(nfft * float(per_lap))
data = data - data.mean()
end = npts / samp_rate
# Here we call not plt.specgram as this already produces a plot
# matplotlib.mlab.specgram should be faster as it computes only the
# arrays
# XXX mlab.specgram uses fft, would be better and faster use rfft
specgram, freq, time = mlab.specgram(data, Fs=samp_rate, NFFT=nfft,
pad_to=mult, noverlap=nlap)
# db scale and remove zero/offset for amplitude
if dbscale:
specgram = 10 * np.log10(specgram[1:, :])
else:
specgram = np.sqrt(specgram[1:, :])
freq = freq[1:]
vmin, vmax = clip
if vmin < 0 or vmax > 1 or vmin >= vmax:
msg = "Invalid parameters for clip option."
raise ValueError(msg)
_range = float(specgram.max() - specgram.min())
vmin = specgram.min() + vmin * _range
vmax = specgram.min() + vmax * _range
norm = Normalize(vmin, vmax, clip=True)
if not axes:
fig = plt.figure()
ax = fig.add_subplot(111)
else:
ax = axes
# calculate half bin width
halfbin_time = (time[1] - time[0]) / 2.0
halfbin_freq = (freq[1] - freq[0]) / 2.0
# argument None is not allowed for kwargs on matplotlib python 3.3
kwargs = {k: v for k, v in (('cmap', cmap), ('zorder', zorder))
if v is not None}
if log:
# pcolor expects one bin more at the right end
freq = np.concatenate((freq, [freq[-1] + 2 * halfbin_freq]))
time = np.concatenate((time, [time[-1] + 2 * halfbin_time]))
# center bin
time -= halfbin_time
freq -= halfbin_freq
# Log scaling for frequency values (y-axis)
ax.set_yscale('log')
# Plot times
ax.pcolormesh(time, freq, specgram, norm=norm, **kwargs)
else:
# this method is much much faster!
specgram = np.flipud(specgram)
# center bin
extent = (time[0] - halfbin_time, time[-1] + halfbin_time,
freq[0] - halfbin_freq, freq[-1] + halfbin_freq)
ax.imshow(specgram, interpolation="nearest", extent=extent, **kwargs)
# set correct way of axis, whitespace before and after with window
# length
ax.axis('tight')
ax.set_xlim(0, end)
ax.grid(False)
if axes:
return ax
ax.set_xlabel('Time [s]')
ax.set_ylabel('Frequency [Hz]')
if title:
ax.set_title(title)
if not sphinx:
# ignoring all NumPy warnings during plot
with np.errstate(all='ignore'):
plt.draw()
if outfile:
if fmt:
fig.savefig(outfile, format=fmt)
else:
fig.savefig(outfile)
elif show:
plt.show()
else:
return fig