Matplotlib spectrogram intensity legend (colorbar)

Question

I'm using matplotlib's specgram function to generate a spectrogram. I've attempted to include a colorbar off to the right of the spectrogram to give an indication of dB-to-color-mapping.

For some reason though, the dB indicated by the colorbar do not make sense.

Perhaps I've not generated the colorbar correctly? Perhaps there is some parameter that I need to pass to specgram?

The signal I'm generating is a 1Khz, 2Vpp sine sampled at 32Khz.

I'm expecting that the dark red peak on the spectrogram corresponds to 0dB (Meaning that +1V is my reference)

Anybody have any idea what is wrong with my approach?

def plot_specgram(data, title='', x_label='', y_label='', fig_size=None):
    fig = plt.figure()
    if fig_size != None:
        fig.set_size_inches(fig_size[0], fig_size[1])
    ax = fig.add_subplot(111)
    ax.set_title(title)
    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label)
    pxx,  freq, t, cax = plt.specgram(data, Fs=32000)
    fig.colorbar(cax).set_label('Intensity [dB]')

plot_specgram(a,title='Spectrogram', x_label='time (in seconds)', y_label='frequency', fig_size=(14,8))

This is what I get as resulting spectrogram:

Solution

First of all, please supply your a vector, since it seems to have some kind of harmonics.

This is a bit trial and error, but this seems to produce the correct scaling:

NFFT = 256
ax.specgram(x/(NFFT/2), NFFT=NFFT, Fs=fs, mode='magnitude', window=plt.window_none)

Using a window seems to lose about 1/2 of the peak power, you can of course adjust for this.

A complete example where I have limited the dynamic range to 40dB (as an example, if you want to hide the small stuff).

import numpy as np
import pylab as plt

# generate a 1kHz sine wave
fs = 32e3
t = np.arange(0, 15, 1.0/fs)
f0 = 1e3
A = 1
x = A*np.sin(2*np.pi*f0*t)

fig, ax = plt.subplots()
cmap = plt.get_cmap('viridis')
vmin = 20*np.log10(np.max(x)) - 40  # hide anything below -40 dBc
cmap.set_under(color='k', alpha=None)

NFFT = 256
pxx,  freq, t, cax = ax.specgram(x/(NFFT/2), Fs=fs, mode='magnitude',
                                 NFFT=NFFT, noverlap=NFFT/2,
                                 vmin=vmin, cmap=cmap,
                                 window=plt.window_none)
fig.colorbar(cax)

print np.max(pxx) # should match A