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) 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 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.
The spectrum analyzer provides three units to specify the power spectral density:
dBW/Hz. Corresponding units of power are
dBW. For electrical engineering applications, you can also
view the RMS of your signal in
dBV. The default spectrum type is Power
dBW is given by:
dBm is given by:
For a sine wave signal with an amplitude of 1 V, the power of
a one-sided spectrum in
Watts is given
In this example, this power equals 0.5 W. Corresponding power in dBm is given by:
Here, the power equals 26.9897 dBm. To confirm this value with a peak finder, click Tools > Measurements > Peak Finder.
For a white noise signal, the spectrum is flat for all frequencies. The spectrum analyzer in this example shows a one-sided spectrum in the range [0 Fs/2]. For a white noise signal with a variance of 1e-4, the power per unit bandwidth (Punitbandwidth) is 1e-4. The total power of white noise in watts over the entire frequency range is given by:
The number of frequency bins is the ratio of total bandwidth to RBW. For a one-sided spectrum, the total bandwidth is half the sampling rate. RBW in this example is 21.53 Hz. With these values, the total power of white noise in watts is 0.1024 W. In dBm, the power of white noise can be calculated using 10*log10(0.1024/10^-3), which equals 20.103 dBm.
If you set the spectral units to
dBFS and set the full scale (
Auto, power in
dBFS is computed as:
Pwatts is the power in watts
For double and float signals, Full_Scale is the maximum value of the input signal.
For fixed point or integer signals, Full_Scale is the maximum value that can be represented.
If you specify a manual full scale (set
Property), power in
dBFS is given by:
FS is the full scaling factor specified in the
For a sine wave signal with an amplitude of 1 V, the power of a one-sided spectrum in
Watts is given by:
In this example, this power equals 0.5 W and the maximum input signal for a sine wave is 1 V. The corresponding power in dBFS is given by:
Here, the power equals -3.0103. To confirm this value in the spectrum analyzer, run these commands:
Fs = 1000; % Sampling frequency sinef = dsp.SineWave('SampleRate',Fs,'SamplesPerFrame',100); scope = dsp.SpectrumAnalyzer('SampleRate',Fs,... 'SpectrumUnits','dBFS','PlotAsTwoSidedSpectrum',false) %% for ii = 1:100000 xsine = sinef(); scope(xsine) end
dBm is given by:
Voltage in RMS is given by:
From the previous example, PdBm equals 26.9897 dBm. The Vrms is calculated as
which equals 0.7071.
To confirm this value:
Change Type to
Open the peak finder by clicking Tools > Measurements > Peak Finder.
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.