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. Note that Simulink^{®} models are not supported in MATLAB
Online.

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 `Spectrum Analyzer Configuration`

object and
run the `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 `jet(256)`

.

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
various frequencies.

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 scope.

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 F_{s}/1024, while in a one-sided spectrum, it is (F_{s}/2)/1024. In this example, RBW is (44100/2)/1024 or 21.53 Hz.

If the **Method** is set to ```
Filter
bank
```

, using this value of *RBW*, the number of
input samples used to compute one spectral update is given by N_{samples} =
F_{s}/RBW, which is 44100/21.53 or 2048 in this example.

If the **Method** is set to `Welch`

,
using this value of *RBW*, the window length
(N_{samples}) is computed iteratively using this
relationship:

$${N}_{samples}=\frac{\left(1-\frac{{O}_{p}}{100}\right)\times NENBW\times {F}_{s}}{RBW}$$

*O _{p}* is the amount of overlap between
the previous and current buffered data segments.

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:
`Watts/Hz`

, `dBm/Hz`

, and
`dBW/Hz`

. Corresponding units of power are
`Watts`

, `dBm`

, and
`dBW`

. For electrical engineering applications, you can also
view the RMS of your signal in `Vrms`

or
`dBV`

. The default spectrum type is **Power**
in `dBm`

.

Power in `dBW`

is given by:

$${P}_{dBW}=10\mathrm{log}10(power\text{\hspace{0.17em}}in\text{\hspace{0.17em}}watt/1\text{\hspace{0.17em}}watt)$$

Power in `dBm`

is given by:

$${P}_{dBm}=10\mathrm{log}10(power\text{\hspace{0.17em}}in\text{\hspace{0.17em}}watt/1\text{\hspace{0.17em}}milliwatt)$$

For a sine wave signal with an amplitude of 1 V, the power of
a one-sided spectrum in `Watts`

is given
by:

$$\begin{array}{l}{P}_{Watts}={A}^{2}/2\\ {P}_{Watts}=1/2\end{array}$$

In this example, this power equals 0.5 W. Corresponding power in dBm is given by:

$$\begin{array}{l}{P}_{dBm}=10\mathrm{log}10(power\text{\hspace{0.17em}}in\text{\hspace{0.17em}}watt/1\text{\hspace{0.17em}}milliwatt)\\ {P}_{dBm}=10\mathrm{log}10(0.5/{10}^{-3})\end{array}$$

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 (P_{unitbandwidth})
is 1e-4. The total power of white noise in **watts** over
the entire frequency range is given by:

$$\begin{array}{l}{P}_{whitenoise}={P}_{unitbandwidth}*number\text{\hspace{0.17em}}of\text{\hspace{0.17em}}frequency\text{\hspace{0.17em}}bins,\\ {P}_{whitenoise}=({10}^{-4})*\left(\frac{Fs/2}{RBW}\right),\\ {P}_{whitenoise}=({10}^{-4})*\left(\frac{22050}{21.53}\right)\end{array}$$

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 (`FullScaleSource`

) to
`Auto`

, power in `dBFS`

is computed as:

$${P}_{dBFS}=20\cdot {\mathrm{log}}_{10}\left(\sqrt{{P}_{watts}}/Full\_Scale\right)$$

where:

`P`

is the power in watts_{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 `FullScaleSource`

to
`Property`

), power in `dBFS`

is given by:

$${P}_{FS}=20\cdot {\mathrm{log}}_{10}\left(\sqrt{{P}_{watts}}/FS\right)$$

Where `FS`

is the full scaling factor specified in the `FullScale`

property.

For a sine wave signal with an amplitude of 1 V, the power of a one-sided spectrum in
`Watts`

is given by:

$$\begin{array}{l}{P}_{Watts}={A}^{2}/2\\ {P}_{Watts}=1/2\end{array}$$

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:

$${P}_{FS}=20\cdot {\mathrm{log}}_{10}\left(\sqrt{1/2}/1\right)$$

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

Power in `dBm`

is given by:

$${P}_{dBm}=10\mathrm{log}10(power\text{\hspace{0.17em}}in\text{\hspace{0.17em}}watt/1\text{\hspace{0.17em}}milliwatt)$$

Voltage in RMS is given by:

$${V}_{rms}={10}^{{P}_{dBm}/20}\sqrt{{10}^{-3}}$$

From the previous example, P_{dBm} equals
26.9897 dBm. The V_{rms} is calculated as

$${V}_{rms}={10}^{26.9897/20}\sqrt{0.001}$$

which equals 0.7071.

To confirm this value:

Change

**Type**to`RMS`

.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.