Cutting of unused frequencies in specgram matplotlib

Question

I have a signal with sampling rate 16e3, its frequency range is from 125 to 1000 Hz. So if i plot a specgram i get a pretty small colorrange because of all the unused frequencys

Answer 1

Here is an adapted version of this: http://matplotlib.org/examples/pylab_examples/specgram_demo.html which changes the range of frequencies that are plotted.

#!/usr/bin/env python
#### from the example
#### 
from pylab import *

dt = 0.0005
t = arange(0.0, 20.0, dt)
s1 = sin(2*pi*100*t)
s2 = 2*sin(2*pi*400*t)
mask = where(logical_and(t>10, t<12), 1.0, 0.0)
s2 = s2 * mask
nse = 0.01*randn(len(t))
x = s1 + s2 + nse # the signal

NFFT = 1024       # the length of the windowing segments
Fs = int(1.0/dt)  # the sampling frequency

ax1 = subplot(211)
plot(t, x)
subplot(212, sharex=ax1)
Pxx, freqs, bins, im = specgram(x, NFFT=NFFT, Fs=Fs, noverlap=900,
                                cmap=cm.gist_heat)

#### edited from the example
#### 
# here we get access to the axes
x1,x2,y1,y2 = axis()
# leave x range the same, change y (frequency) range
axis((x1,x2,25,500))

show()

Answer 2

These days, there's an easier way to do this than when the question was asked: you can use matplotlib.pyplot.axis to set ymin and ymax to your desired frequencies. It's quite easy; here's a snippet from my program:

plt.specgram(xmit, NFFT=65536, Fs=Fs)
plt.axis(ymin=Fc-Fa*10, ymax=Fc+Fa*10)
plt.show()

Answer 3

specgram() is doing all the work for you. If you look in axes.py at the specgram function you can see how it works. The original function is in Python27\Lib\site-packages\matplotlib\axes.py on my computer.

    <snip>  
    Pxx, freqs, bins = mlab.specgram(x, NFFT, Fs, detrend,
         window, noverlap, pad_to, sides, scale_by_freq)

    Z = 10. * np.log10(Pxx)
    Z = np.flipud(Z)

    if xextent is None: xextent = 0, np.amax(bins)
    xmin, xmax = xextent
    freqs += Fc
    extent = xmin, xmax, freqs[0], freqs[-1]
    im = self.imshow(Z, cmap, extent=extent, **kwargs)
    self.axis('auto')

    return Pxx, freqs, bins, im

You might have to make your own function modeled on this and clip the Pxx data to suit your needs.

    Pxx, freqs, bins = mlab.specgram(x, NFFT, Fs, detrend,
         window, noverlap, pad_to, sides, scale_by_freq)
    # ****************
    # create a new limited Pxx and freqs
    # 
    # ****************
    Z = 10. * np.log10(Pxx)
    Z = np.flipud(Z)

Pxx is a 2d array with a shape of (len(freqs),len(bins)

>>> Pxx.shape
(129, 311)
>>> freqs.shape
(129,)
>>> bins.shape
(311,)
>>> 

This will limit Pxx and freqs

Pxx = Pxx[(freqs >= 125) & (freqs <= 1000)]
freqs = freqs[(freqs >= 125) & (freqs <= 1000)]

Here is a complete solution - my_specgram() - used with the specgram_demo from the gallery.

from pylab import *
from matplotlib import *


# 100, 400 and 200 Hz sine 'wave'
dt = 0.0005
t = arange(0.0, 20.0, dt)
s1 = sin(2*pi*100*t)
s2 = 2*sin(2*pi*400*t)
s3 = 2*sin(2*pi*200*t)

# create a transient "chirp"
mask = where(logical_and(t>10, t<12), 1.0, 0.0)
s2 = s2 * mask

# add some noise into the mix
nse = 0.01*randn(len(t))

x = s1 + s2 + +s3 + nse # the signal
NFFT = 1024       # the length of the windowing segments
Fs = int(1.0/dt)  # the sampling frequency

# modified specgram()
def my_specgram(x, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
             window=mlab.window_hanning, noverlap=128,
             cmap=None, xextent=None, pad_to=None, sides='default',
             scale_by_freq=None, minfreq = None, maxfreq = None, **kwargs):
    """
    call signature::

      specgram(x, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
               window=mlab.window_hanning, noverlap=128,
               cmap=None, xextent=None, pad_to=None, sides='default',
               scale_by_freq=None, minfreq = None, maxfreq = None, **kwargs)

    Compute a spectrogram of data in *x*.  Data are split into
    *NFFT* length segments and the PSD of each section is
    computed.  The windowing function *window* is applied to each
    segment, and the amount of overlap of each segment is
    specified with *noverlap*.

    %(PSD)s

      *Fc*: integer
        The center frequency of *x* (defaults to 0), which offsets
        the y extents of the plot to reflect the frequency range used
        when a signal is acquired and then filtered and downsampled to
        baseband.

      *cmap*:
        A :class:`matplotlib.cm.Colormap` instance; if *None* use
        default determined by rc

      *xextent*:
        The image extent along the x-axis. xextent = (xmin,xmax)
        The default is (0,max(bins)), where bins is the return
        value from :func:`mlab.specgram`

      *minfreq, maxfreq*
        Limits y-axis. Both required

      *kwargs*:

        Additional kwargs are passed on to imshow which makes the
        specgram image

      Return value is (*Pxx*, *freqs*, *bins*, *im*):

      - *bins* are the time points the spectrogram is calculated over
      - *freqs* is an array of frequencies
      - *Pxx* is a len(times) x len(freqs) array of power
      - *im* is a :class:`matplotlib.image.AxesImage` instance

    Note: If *x* is real (i.e. non-complex), only the positive
    spectrum is shown.  If *x* is complex, both positive and
    negative parts of the spectrum are shown.  This can be
    overridden using the *sides* keyword argument.

    **Example:**

    .. plot:: mpl_examples/pylab_examples/specgram_demo.py

    """

    #####################################
    # modified  axes.specgram() to limit
    # the frequencies plotted
    #####################################

    # this will fail if there isn't a current axis in the global scope
    ax = gca()
    Pxx, freqs, bins = mlab.specgram(x, NFFT, Fs, detrend,
         window, noverlap, pad_to, sides, scale_by_freq)

    # modified here
    #####################################
    if minfreq is not None and maxfreq is not None:
        Pxx = Pxx[(freqs >= minfreq) & (freqs <= maxfreq)]
        freqs = freqs[(freqs >= minfreq) & (freqs <= maxfreq)]
    #####################################

    Z = 10. * np.log10(Pxx)
    Z = np.flipud(Z)

    if xextent is None: xextent = 0, np.amax(bins)
    xmin, xmax = xextent
    freqs += Fc
    extent = xmin, xmax, freqs[0], freqs[-1]
    im = ax.imshow(Z, cmap, extent=extent, **kwargs)
    ax.axis('auto')

    return Pxx, freqs, bins, im

# plot
ax1 = subplot(211)
plot(t, x)
subplot(212, sharex=ax1)

# the minfreq and maxfreq args will limit the frequencies 
Pxx, freqs, bins, im = my_specgram(x, NFFT=NFFT, Fs=Fs, noverlap=900, 
                                cmap=cm.Accent, minfreq = 180, maxfreq = 220)
show()
close()

Answer 4

specgram() returns (Pxx, freqs, bins, im), where im is AxesImage instance [1]. You could use it to set the limits of your plot:

Pxx, freqs, bins, im = plt.specgram(signal, Fs=fs)
im.set_ylim((125,1000))

[1] http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.specgram