View the Spectrogram Using Spectrum Analyzer
Spectrograms are a two-dimensional representation of the power spectrum of a signal as this signal sweeps through time. They give a visual understanding of the frequency content of your signal. Each line of the spectrogram is one periodogram computed using either the filter bank approach or the Welch’s algorithm of averaging modified periodogram.
To show the concepts of the spectrogram, this example uses the model
ex_psd_sa as the starting point.
Open the model and double-click the Spectrum Analyzer block. In the
Spectrum Settings pane, change View to
Spectrogram. The Method is set to
Filter bank. Run the model. You can see the spectrogram
output in the spectrum analyzer window. To acquire and store the data for further
processing, create a
SpectrumAnalyzerConfiguration object and run
getSpectrumData function on this object.
Power spectrum is computed as a function of frequency
f and is
plotted as a horizontal line. Each point on this line is given a specific color
based on the value of the power at that particular frequency. The color is chosen
based on the colormap seen at the top of the display. To change the colormap, click View > Configuration Properties, and choose one of the options in color
map. Make sure View is set to
Spectrogram. By default, color
map is set to
The two frequencies of the sine wave are distinctly visible at 5 kHz and 10 kHz. Since the spectrum analyzer uses the filter bank approach, there is no spectral leakage at the peaks. The sine wave is embedded in Gaussian noise, which has a variance of 0.0001. This value corresponds to a power of -40 dBm. The color that maps to -40 dBm is assigned to the noise spectrum. The power of the sine wave is 26.9 dBm at 5 kHz and 10 kHz. The color used in the display at these two frequencies corresponds to 26.9 dBm on the colormap. For more information on how the power is computed in dBm, see 'Conversion of power in watts to dBW and dBm'.
To confirm the dBm values, change View to
Spectrum. This view shows the power of the signal at
You can see that the two peaks in the power display have an amplitude of about 26 dBm and the white noise is averaging around -40 dBm.
In the spectrogram display, time scrolls from top to bottom, so the most recent
data is shown at the top of the display. As the simulation time increases, the
offset time also increases to keep the vertical axis limits constant while
accounting for the incoming data. The
Offset value, along with
the simulation time, is displayed at the bottom-right corner of the spectrogram
Resolution Bandwidth (RBW)
Resolution Bandwidth (RBW) is the minimum frequency bandwidth that can be resolved
by the spectrum analyzer. By default, RBW (Hz) is set to
Auto. In the auto mode, RBW is
the ratio of the frequency span to 1024. In a two-sided spectrum, this value is Fs/1024, while in a one-sided spectrum, it is (Fs/2)/1024. In this example, RBW is (44100/2)/1024 or 21.53 Hz.
If the Method is set to
bank, using this value of RBW, the number of
input samples used to compute one spectral update is given by Nsamples =
Fs/RBW, which is 44100/21.53 or 2048 in this example.
If the Method is set to
using this value of RBW, the window length
(Nsamples) is computed iteratively using this
Op is the amount of overlap between the previous and current buffered data segments. NENBW is the equivalent noise bandwidth of the window.
For more information on the details of the spectral estimation algorithm, see Spectral Analysis.
To distinguish between two frequencies in the display, the distance between the two frequencies must be at least RBW. In this example, the distance between the two peaks is 5000 Hz, which is greater than RBW. Hence, you can see the peaks distinctly.
Change the frequency of the second sine wave from 10000 Hz to 5015 Hz. The difference between the two frequencies is 15 Hz, which is less than RBW.
On zooming, you can see that the peaks at 5000 Hz and 5015 Hz are not distinguishable.
To increase the frequency resolution, decrease RBW to 1 Hz and run the simulation. On zooming, the two peaks, which are 15 Hz apart, are now distinguishable
Time resolution is the distance between two spectral lines in the vertical axis.
By default, Time res (s) is set to
Auto. In this mode, the value of time resolution is
1/RBW s, which is the minimum attainable resolution. When you
increase the frequency resolution, the time resolution decreases. To maintain a good
balance between the frequency resolution and time resolution, change the
RBW (Hz) to
Auto. You can also
specify the Time res (s) as a numeric value.
Scale Color Limits
When you run the model and do not see the spectrogram colors, click the Scale Color Limits button. This option autoscales the colors.
The spectrogram updates in real time. During simulation, if you change any of the tunable parameters in the model, the changes are effective immediately in the spectrogram.