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Display frequency spectrum

**Library:**DSP System Toolbox / Sinks

The Spectrum Analyzer block, referred to here as the scope, displays the frequency spectra of signals.

You can use the Spectrum Analyzer block in models running in Normal or Accelerator simulation modes. You can also use the Spectrum Analyzer block in models running in Rapid Accelerator or External simulation modes, with some limitations.

You can use the Spectrum Analyzer block inside all subsystems and conditional subsystems. *Conditional
subsystems* include enabled subsystems, triggered subsystems, enabled and triggered subsystems, and
function-call subsystems. See Conditionally Executed Subsystems Overview (Simulink) for more information.

You can configure and display Spectrum Analyzer settings from the command line with `spbscopes.SpectrumAnalyzerConfiguration`

.

For information about the Spectrum Analyzer System
object™, see `dsp.SpectrumAnalyzer`

.

`Port_1`

— Signals to visualizescalar | vector | matrix | array

Connect the signals you want to visualize. You can have up to 96 input ports. Input signals can have these characteristics:

**Signal Domain**— Frequency or time signals**Type**— Discrete (sample-based and frame-based).**Data type**— Any data type that Simulink^{®}supports. See Data Types Supported by Simulink (Simulink).**Dimension**— One dimensional (vector), two dimensional (matrix), or multidimensional (array). Input must have fixed number of channels. See Signal Dimensions (Simulink) and Determine Output Signal Dimensions (Simulink).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `uint8`

| `uint16`

| `uint32`

| `fixed point`

**Complex Number Support: **Yes

The **Spectrum Settings** pane appears at the right side of the Spectrum Analyzer window. This
pane controls how the spectrum is calculated. To show the Spectrum Settings, in the Spectrum Analyzer menu, select **View** > **Spectrum Settings** or use the button in the toolbar.

`Input domain`

— Domain of the input signal`Time`

(default) | `Frequency`

The domain of the input signal you want to visualize. If you visualize time-domain signals, the signal is transformed to the frequency spectrum based on the algorithm specified by the Method parameter.

See InputDomain.

`Type`

— Type of spectrum to display`Power`

(default) | `Power density`

| `RMS`

`Power`

— Spectrum Analyzer shows the power spectrum.

`Power density`

— Spectrum Analyzer shows the power spectral density. The
power spectral density is the magnitude of the spectrum normalized to a bandwidth of 1 hertz.

`RMS`

— Spectrum Analyzer shows the root mean squared spectrum.

**Tunable: **Yes

To use this parameter, set Input domain to
`Time`

.

See SpectrumType.

`View`

— Spectrum view`Spectrum`

(default) | `Spectrogram`

| `Spectrum and spectrogram`

`Spectrum`

— Spectrum Analyzer shows the spectrum.

`Spectrogram`

— Spectrum Analyzer shows the spectrogram, which displays
frequency content over time. The most recent spectrogram update is at the bottom of the display, and
time scrolls from the bottom to the top of the display.

`Spectrum and spectrogram`

— Spectrum Analyzer shows both the spectrum and
spectrogram.

**Tunable: **Yes

See ViewType.

`Sample rate`

— Sample rate of the input signal in hertz`Inherited`

(default) | positive scalarSelect `Inherited`

to use the same sample rate as the input signal. To
specify a sample rate, delete `Inherited`

and enter a sample rate
value.

See SampleRate.

`Method`

— Spectrum estimation method`Welch`

(default) | `Filter Bank`

Select `Welch`

or `Filter Bank`

as the spectrum
estimation method. For more details about the two spectrum estimation algorithms, see Algorithms.

**Tunable: **No

To use this parameter, set Input domain to
`Time`

.

See Method.

`Full frequency span`

— Use entire Nyquist frequency intervalon (default) | off

Select this check box to compute and plot the spectrum over the entire Nyquist frequency interval.

**Tunable: **Yes

To use this parameter, set Input domain to
`Time`

.

See FrequencySpan.

`Span (Hz)`

— Frequency span in hertz `10e3`

(default) | real positive scalarSpecify the frequency span in hertz. Use this parameter with the CF (Hz) parameter to define the frequency span around a center frequency. This parameter defines the range of values shown on the Frequency axis in the Spectrum Analyzer window.

**Tunable: **Yes

To use this parameter, you must:

Set Input domain to

`Time`

.Clear the Full frequency span check box.

Set the

**Span (Hz)/Fstart (Hz)**dropdown to`Span (Hz)`

.

See FrequencySpan and Span.

`CF (Hz)`

— Center frequency in hertz`0`

(default) | scalarSpecify the center frequency, in hertz. Use this parameter with the Span (Hz) parameter to define the frequency span around a center frequency. This parameter defines the value shown at the middle point of the Frequency axis on the Spectrum Analyzer window.

**Tunable: **Yes

To use this parameter, you must:

Set Input domain to

`Time`

.Clear the Full frequency span check box.

Set the

**Span (Hz)/Fstart (Hz)**dropdown to Span (Hz).

See CenterFrequency.

`FStart (Hz)`

— Start frequency in hertz`-5e3`

(default) | scalarSpecify the start frequency in hertz. Use this parameter with the FStop (Hz) parameter to define the range of frequency-axis values using start frequency and stop frequency. This parameter defines the value shown at the leftmost side of the Frequency axis on the Spectrum Analyzer window.

**Tunable: **Yes

To use this parameter, you must:

Set Input domain to

`Time`

.Clear the Full frequency span check box.

Set the

**Span (Hz)/FStart (Hz)**dropdown to`FStart (Hz)`

.

See StartFrequency.

`FStop (Hz)`

— Stop frequency in hertz`5e3`

(default) | scalarSpecify the stop frequency, in hertz. Use this parameter with the FStart (Hz) parameter to define the range of Frequency axis values. This parameter defines the value shown at the rightmost side of the Frequency axis on the Spectrum Analyzer window.

**Tunable: **Yes

To use this parameter, you must:

Set Input domain to

`Time`

.Clear the Full frequency span check box.

Set the

**Span (Hz)/FStart (Hz)**dropdown to FStart (Hz).

See StopFrequency.

`Frequency (Hz)`

— Frequency vector`Auto`

(default) | `Input port`

| monotonically increasing vectorSet the frequency vector which determines the *x*-axis of the display.

`Auto`

— The frequency vector is calculated from the length of the input. See Frequency Vector.`Input port`

— When selected, an input port appears on the block for the frequency vector input.Custom vector — Enter a custom vector as the frequency vector. The length of the custom vector must be equal to the frame size of the input signal.

**Tunable: **No

To use this parameter, set Input domain to
`Frequency`

.

See FrequencyVector.

`RBW (Hz)`

— Resolution bandwidth`Auto`

(default) | `Input port`

| positive scalarThe resolution bandwidth in hertz. This parameter defines the smallest positive frequency that can
be resolved. By default, this parameter is set to `Auto`

. In this case, the
Spectrum Analyzer determines the appropriate value to ensure that there are 1024
*RBW* intervals over the specified frequency span.

If you set this parameter to a numeric value, the value must allow at least two
*RBW* intervals over the specified frequency span. In other words, the ratio of the
overall frequency span to *RBW* must be at least two:

$$\frac{span}{RBW}>2$$ | (2-1) |

For frequency input only, you can use an input port to set the RBW value.

**Tunable: **Yes

To use this parameter, set either:

Input domain to

`Time`

and the**RBW (Hz)/Window length/Number of frequency bands**dropdown to`RBW (Hz)`

.Input domain to

`Frequency`

.

See RBW.

`Input units`

— Units of frequency input`Auto`

(default) | `dBm`

| `dBV`

| `dBW`

| `Vrms`

| `Watts`

Select the units of the frequency-domain input. This property allows the Spectrum Analyzer to scale frequency data if you choose a different display unit with the Units property.

**Tunable: **No

This option is only available for Input domain set to
`Frequency`

.

See `InputUnits`

.

`Window length`

— Length of window in samples`1024`

(default) | integer greater than 2The length of the window, in samples. The window length used to control the frequency resolution and compute the spectral estimates. The window length must be an integer greater than 2.

To use this parameter, set:

Method to

`Welch`

Set the

**RBW (Hz)/Window length/Number of frequency bands**dropdown to`Window Length`

To use this parameter, set Input domain to
`Time`

.

See WindowLength.

`Number of frequency bands`

— FFT length`Auto`

(default) | positive integerSpecify the fast Fourier transform (FFT) length to control the number of frequency bands. If the
value is `Auto`

, the Spectrum Analyzer uses the entire frame size to estimate
the spectrum. If you specify the number of frequency bands, you set the input buffer size.

To use this parameter, set:

Method to

`Filter Bank`

Set the

**RBW (Hz)/Window length/Number of frequency bands**dropdown to`Number of frequency bands`

See FFTLength

`Taps per band`

— Number of filter taps`12`

(default) | positive even integerSpecify the number of filter taps or coefficients for each frequency band. This number must be a
positive even integer. This value corresponds to the number of filter coefficients per polyphase
branch. The total number of filter coefficients is equal to *Taps Per Band* +
*FFT Length*.

To use this parameter, you must set the **RBW (Hz)/Window length/Number of frequency
bands** dropdown to Number of frequency bands.

See NumTapsPerBand.

`NFFT`

— Number of FFT points`Auto`

(default) | positive integerSpecify the length of the FFT that Spectrum Analyzer uses to compute spectral estimates. Acceptable
options are `Auto`

or a positive integer.

The **NFFT** value must be greater than or equal to the value of the
**Window length** parameter. By default, when **NFFT** is set to
`Auto`

, the Spectrum Analyzer sets **NFFT** equal to the
value of **Window length**. When in RBW mode, the specified RBW value is used to
calculate an FFT length that equals the window length.

When this parameter is set to a positive integer, this parameter is equivalent to the
`n`

parameter of the `fft`

function.

To use this parameter, you must set the **RBW (Hz)/Window length/Number of frequency
bands** dropdown to Window length.

See FFTLength.

`Samples/update`

— Required number of input samplespositive scalar

This property is read-only.

The number of input samples required to compute one spectral update. You cannot modify this
parameter; it is shown in the spectrum analyzer for informational purposes only. This parameter is
directly related to **RBW (Hz)/Window length/Number of frequency bands**. For more
details, see Algorithms.

If the input does not have enough samples to achieve the resolution bandwidth that you specify, Spectrum Analyzer produces a message on the display.

`Channel`

— Spectrogram channelchannel name

Select the signal channel for which the spectrogram settings apply.

To use this option:

Set View to

`Spectrogram`

or`Spectrum and spectrogram`

.There must be more than one signal channel input.

`Time res. (s)`

— Time resolution in seconds`Auto`

(default) | positive numberTime resolution is the amount of data, in seconds, used to compute a spectrogram line. The minimum attainable resolution is the amount of time it takes to compute a single spectral estimate. The tooltip displays the minimum attainable resolution given the current settings.

The time resolution value is determined based on frequency resolution method, the RBW setting, and the time resolution setting.

Method | Frequency Resolution Method | Frequency Resolution Setting | Time Resolution Setting | Resulting Time Resolution in Seconds |
---|---|---|---|---|

`Welch` or `Filter Bank` | `RBW (Hz)` | `Auto` | `Auto` | 1/RBW |

`Welch` or `Filter Bank` | `RBW (Hz)` | `Auto` | Manually entered | Time Resolution |

`Welch` or `Filter Bank` | `RBW (Hz)` | Manually entered | `Auto` | 1/RBW |

`Welch` or `Filter Bank` | `RBW (Hz)` | Manually entered | Manually entered | Must be equal to or greater than the minimum attainable time resolution, 1/RBW. Several spectral estimates are combined into one spectrogram line to obtain the desired time resolution. Interpolation is used to obtain time resolution values that are not integer multiples of 1/RBW. |

`Welch` | `Window length` | — | `Auto` | 1/RBW |

`Welch` | `Window length` | — | Manually entered | Must be equal to or greater than the minimum attainable time resolution. Several spectral estimates are combined into one spectrogram line to obtain the desired time resolution. Interpolation is used to obtain time resolution values that are not integer multiples of 1/RBW. |

`Filter Bank` | `Number of frequency bands` | — | `Auto` | 1/RBW |

`Filter Bank` | `Number of frequency bands` | — | Manually entered | Must be equal to or greater than the minimum attainable time resolution, 1/RBW. |

**Tunable: **Yes

To use this option, set View to
`Spectrogram`

or ```
Spectrum and
spectrogram
```

.

See TimeResolution.

`Time span`

— Time span in seconds`Auto`

(default) | positive scalar The time span over which the Spectrum Analyzer displays the spectrogram specified in seconds. The
time span is the product of the desired number of spectral lines and the time resolution. The tooltip
displays the minimum allowable time span, given the current settings. If the time span is set to
`Auto`

, 100 spectral lines are used.

**Tunable: **Yes

To use this option, set View to
`Spectrogram`

or ```
Spectrum and
spectrogram
```

.

See TimeSpan.

`Overlap (%)`

— Segment overlap percentage0 (default) | scalar between 0 and 100

This parameter defines the amount of overlap between the previous and current buffered data segments. The overlap creates a window segment that is used to compute a spectral estimate. The value must be greater than or equal to zero and less than 100.

**Tunable: **Yes

See OverlapPercent.

`Window`

— Windowing method`Hann`

(default) | `Rectangular`

| `Blackman-Harris`

| `Chebyshev`

| `Flat Top`

| `Hamming`

| `Kaiser`

| custom window function nameThe windowing method to apply to the spectrum. Windowing is used to control the effect of sidelobes in spectral estimation. The window you specify affects the window length required to achieve a resolution bandwidth and the required number of samples per update. For more information about windowing, see Windows (Signal Processing Toolbox).

**Tunable: **Yes

See Window.

`Attenuation`

— Sidelobe attenuation`60`

(default) | scalar greater than or equal to `45`

The sidelobe attenuation in decibels (dB). The value must be greater than or equal to
`45`

.

This parameter applies only when you set the **Window** parameter to
`Chebyshev`

or `Kaiser`

.

See SidelobeAttenuation.

`NENBW`

— Normalized effective noise bandwidthscalar

This property is read-only.

The normalized effective noise bandwidth of the window. You cannot modify this parameter; it is shown for informational purposes only. This parameter is a measure of the noise performance of the window. The value is the width of a rectangular filter that accumulates the same noise power with the same peak power gain.

The rectangular window has the smallest NENBW, with a value of 1. All other windows have a larger NENBW value. For example, the Hann window has an NENBW value of approximately 1.5.

`Units`

— Spectrum units`dBm`

(default) | `dBW`

| `Watts`

| `Vrms`

| `dBV`

| `dBFS`

The units of the spectrum. The available values depend on the value of the Type parameter.

**Tunable: **Yes

See SpectrumUnits.

`Full scale`

— Full scale for dBFS units`Auto`

(default) | positive real scalarThe full scale used for the dBFS units. By default, the Spectrum Analyzer uses the entire spectrum scale. Specify a positive real scalar for the dBFS full scale.

**Tunable: **Yes

To enable this parameter, set:

Input domain to

`Time`

Units to

`dBFS`

See FullScale.

`Averages`

— Number of spectral averages`1`

(default) | positive integerSpecify the number of spectral averages as a positive integer. The spectrum analyzer computes the
current power spectrum estimate by computing a running average of the last *N* power
spectrum estimates. This parameter defines the number of spectral averages,
*N*.

This parameter applies only when the View parameter is
`Spectrum`

or `Spectrum and spectrogram`

.

See SpectralAverages.

`Reference load`

— Reference load`1`

(default) | positive real scalarThe reference load in ohms that the Spectrum Analyzer uses as a reference to compute power values.

To use this parameter, set Input domain to
`Time`

.

See ReferenceLoad.

`Scale`

— Scale of frequency axis`Linear`

(default) | `Logarithmic`

Choose a linear or logarithm scale for the frequency axis. When the frequency span contains negative frequency values, you cannot choose the logarithmic option.

See FrequencyScale.

`Offset`

— Constant frequency offset`0`

(default) | scalarThe constant frequency offset to apply to the entire spectrum, or a vector of frequencies to apply
to each spectrum for multiple inputs. The offset parameter is added to the values on the Frequency
axis in the Spectrum Analyzer window. This parameter is not used in any spectral computations. You
must take the parameter into consideration when you set the **Span (Hz)** and
**CF (Hz)** parameters to ensure that the frequency span is within the Nyquist frequency interval.

To use this parameter, set Input domain to
`Time`

.

See FrequencyOffset.

`Normal trace`

— Normal trace viewon (default) | off

When this check box is selected, the Spectrum Analyzer calculates and plots the power spectrum or power spectrum density. Spectrum Analyzer performs a smoothing operation by averaging several spectral estimates.

To clear this check box, you must first select either the Max hold trace or the Min hold trace parameter. This parameter applies
only when View is
`Spectrum`

or `Spectrum and spectrogram`

.

See PlotNormalTrace.

`Max hold trace`

— Maximum hold trace viewoff (default) | on

Select this check box to enable Spectrum Analyzer to plot the maximum spectral values of all the estimates obtained.

This parameter applies only when View is
`Spectrum`

or `Spectrum and spectrogram`

.

See PlotMaxHoldTrace.

`Min hold trace`

— Minimum hold trace viewoff (default) | on

Select this check box to enable Spectrum Analyzer to plot the minimum spectral values of all the estimates obtained.

This parameter applies only when View is
`Spectrum`

or `Spectrum and spectrogram`

.

See PlotMinHoldTrace.

`Two-sided spectrum`

— Enable two-sided spectrum viewoff (default) | on

Select this check box to enable a two-sided spectrum view. In this view, both negative and positive frequencies are shown. If you clear this check box, Spectrum Analyzer shows a one-sided spectrum with only positive frequencies. Spectrum Analyzer requires that this parameter is selected when the input signal is complex-valued.

The **Configuration Properties** dialog box controls visual aspects of the Spectrum Analyzer.
To open the Configuration Properties, in the Spectrum Analyzer menu, select **View** > **Configuration Properties** or select the button in the toolbar dropdown.

`Title`

— Display titlecharacter vector | string

Specify the display title. Enter `%<SignalLabel>`

to use the signal labels in
the Simulink model as the axes titles.

**Tunable: **Yes

See Title.

`Show legend`

— Display signal legendoff (default) | on

Show signal legend. The names listed in the legend are the signal names from the model. For signals with multiple channels, a channel index is appended after the signal name. Continuous signals have straight lines before their names and discrete signals have step-shaped lines.

From the legend, you can control which signals are visible. This control is equivalent to changing
the visibility in the **Style** parameters. In the scope legend, click a signal name
to hide the signal in the scope. To show the signal, click the signal name again. To show only one
signal, right-click the signal name, which hides all other signals. To show all signals, press
**ESC**.

To enable this parameter, set View to
`Spectrum`

or `Spectrum and spectrogram`

.

See ShowLegend.

`Show grid`

— Show internal grid linesoff (default) | on

`Y-limits (minimum)`

— Y-axis minimum`-80`

(default) | scalar`Y-limits (maximum)`

— Y-axis maximum`20`

(default) | scalar`Y-label`

— Y-axis labelcharacter vector | string

To display signal units, add `(%<SignalUnits>)`

to the label. At the
beginning of a simulation, Simulink replaces `(%SignalUnits)`

with the units associated with the signals.
For example, if you have a signal for velocity with units of m/s
enter

Velocity (%<SignalUnits>)

See YLabel.

`Color map`

— Spectrogram colormap`jet(256)`

(default) | `hot(256)`

| `bone(256)`

| `cool(256)`

| `copper(256)`

| `gray(256)`

| `parula(256)`

| 3-column matrix`Color-limits (minimum)`

— Spectrogram minimum`-80`

(default) | scalarSpecify the signal power for the minimum color value of the spectrogram.

**Tunable: **Yes

To use this parameter, set View to
`Spectrogram`

or ```
Spectrum and
spectrogram
```

.

See ColorLimits.

`Color-limits (maximum)`

— Spectrogram maximum20 (default) | scalar

Specify the signal power for the maximum color value of the spectrogram.

**Tunable: **Yes

To use this parameter, set View to
`Spectrogram`

or ```
Spectrum and
spectrogram
```

.

See ColorLimits.

The **Style** dialog box controls how to Spectrum Analyzer appears. To open the Style
properties, in the Spectrum Analyzer menu, select **View** > **Style** or select the button in the toolbar dropdown.

`Figure color`

— Window backgroundgray (default) | color picker

Specify the color that you want to apply to the background of the scope figure.

`Plot type`

— Plot type`Line`

(default) | `Stem`

`Axes colors`

— Axes background colorblack (default) | color picker

Specify the color that you want to apply to the background of the axes.

`Properties for line`

— Channel for visual property settingschannel names

Specify the channel for which you want to modify the visibility, line properties, and marker properties.

`Visible`

— Channel visibilityon (default) | off

Specify whether the selected channel is visible. If you clear this check box, the line disappears. You can also change signal visibility using the scope legend.

`Line`

— Line styleline, 0.5, yellow (default)

Specify the line style, line width, and line color for the selected channel.

`Marker`

— Data point markers`none`

(default)Specify marks for the selected channel to show at its data points. This parameter is similar to the 'Marker' property for plots. You can choose any of the marker symbols from the dropdown.

The **Axes Scaling** dialog box controls the axes limits of the Spectrum Analyzer. To open the
Axes Scaling properties, in the Spectrum Analyzer menu, select **Tools** > **Axes Scaling** > **Axes Scaling Properties**.

`Axes scaling/Color scaling`

— Automatic axes scaling`Auto`

(default) | `Manual`

| `After N Updates`

Specify
when the scope automatically scales the y-axis. If the spectrogram is displayed, specify when the
scope automatically scales the color axis. By default, this parameter is set to
`Auto`

, and the scope does not shrink the y-axis limits when scaling the axes
or color. You can select one of the following options:

`Auto`

— The scope scales the axes or color as needed, both during and after simulation. Selecting this option shows the**Do not allow Y-axis limits to shrink**or**Do not allow color limits to shrink**.`Manual`

— When you select this option, the scope does not automatically scale the axes or color. You can manually scale the axes or color in any of the following ways:Select

**Tools**>**Scaling Properties**.Press one of the

**Scale Axis Limits**toolbar buttons.When the scope figure is the active window, press

**Ctrl+A**.

`After N Updates`

— Selecting this option causes the scope to scale the axes or color after a specified number of updates. This option is useful, and most efficient, when your frequency signal values quickly reach steady-state after a short period. Selecting this option shows the**Number of updates**edit box where you can modify the number of updates to wait before scaling.

**Tunable: **Yes

See AxesScaling.

`Do not allow Y-axis/color limits to shrink`

— Axes scaling limitson (default) | off

When you select this parameter, the y-axis is allowed to grow during axes scaling operations. If the spectrogram is displayed, selecting this parameter allows the color limits to grow during axis scaling. If you clear this check box, the y-axis or color limits can shrink during axes scaling operations.

This parameter appears only when you select `Auto`

for the
**Axis scaling** or **Color scaling** parameter. When you set
the **Axes scaling** or **Color scaling** parameter to
`Manual`

or `After N Updates`

, the
*y*-axis or color limits can shrink.

`Number of updates`

— Number of updates before scaling`10`

(default) | positive numberThe number of updates after which the axes scale, specified as a positive integer. If the spectrogram is displayed, this parameter specifies the number of updates after which the color axes scales.

**Tunable: **Yes

This parameter appears only when you set Axes scaling/Color scaling to ```
After N
Updates
```

.

`Scale limits at stop`

— Scale axes at stopoff (default) | on

Select this check box to
scale the axes when the simulation stops. If the spectrogram is displayed, select this check box to
scale the color when the simulation stops. The *y*-axis is always scaled. The
*x*-axis limits are only scaled if you also select the **Scale X-axis
limits** check box.

`Data range (%)`

— Percent of axes100 (default) | number in the range [1,100]

Set the percentage of the axis that the scope uses to display the data when scaling the axes. If the
spectrogram is displayed, set the percentage of the power values range within the colormap. Valid
values are from 1 through 100. For example, if you set this parameter to `100`

,
the scope scales the axis limits such that your data uses the entire axis range. If you then set this
parameter to `30`

, the scope increases the *y*-axis or color
range such that your data uses only 30% of the axis range.

**Tunable: **Yes

`Align`

— Alignment along axes`Center`

(default) | `Bottom`

| `Top`

| `Left`

| `Right`

Specify where the scope aligns your data along the axis when it scales the axes. If the spectrogram is displayed, specify where the scope aligns your data along the axis when it scales the color. If you are using CCDF Measurements, the x axis is also configurable.

**Tunable: **Yes

When you set the **Method** property to `Welch`

, the following algorithms
apply. The Spectrum Analyzer uses the `RBW`

or the `Window Length`

setting in the **Spectrum Settings** pane to determine the data window length. Then, it partitions
the input signal into a number of windowed data segments. Finally, Spectrum Analyzer uses the modified periodogram
method to compute spectral updates, averaging the windowed periodograms for each segment.

Spectrum Analyzer requires that a minimum number of samples to compute a spectral estimate. This number of input
samples required to compute one spectral update is shown as **Samples/update** in the **Main
options** pane. This value is directly related to resolution bandwidth, *RBW*, by the
following equation, or to the window length, by the equation shown in step 2.

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

The normalized effective noise bandwidth, *NENBW*, is a factor that depends on the windowing
method. Spectrum Analyzer shows the value of *NENBW* in the **Window Options** pane
of the **Spectrum Settings** pane. Overlap percentage, *O _{p}*,
is the value of the

When in

**RBW (Hz)**mode, the window length required to compute one spectral update,*N*, is directly related to the resolution bandwidth and normalized effective noise bandwidth:_{window}When in

**Window Length**mode, the window length is used as specified.The number of input samples required to compute one spectral update,

*N*, is directly related to the window length and the amount of overlap by the following equation._{samples}When you increase the overlap percentage, fewer new input samples are needed to compute a new spectral update. For example, if the window length is 100, then the number of input samples required to compute one spectral update is given as shown in the following table.

*O*_{p}*N*_{samples}0% 100 50% 50 80% 20 The normalized effective noise bandwidth,

*NENBW*, is a window parameter determined by the window length,*N*, and the type of window used. If_{window}*w*(*n*) denotes the vector of*N*window coefficients, then_{window}*NENBW*is given by the following equation.When in

**RBW (Hz)**mode, you can set the resolution bandwidth using the value of the**RBW (Hz)**parameter on the**Main options**pane of the**Spectrum Settings**pane. You must specify a value to ensure that there are at least two RBW intervals over the specified frequency span. The ratio of the overall span to RBW must be greater than two:$$\frac{span}{RBW}>2$$

By default, the

**RBW (Hz)**parameter on the**Main options**pane is set to`Auto`

. In this case, the Spectrum Analyzer determines the appropriate value to ensure that there are 1024 RBW intervals over the specified frequency span. When you set**RBW (Hz)**to`Auto`

,*RBW*is calculated as:$$RB{W}_{auto}=\frac{span}{1024}$$

When in

**Window Length**mode, you specify*N*and the resulting_{window}*RBW*is:

Sometimes, the number of input samples provided are not sufficient to achieve the resolution bandwidth that you specify. When this situation occurs, Spectrum Analyzer displays a message:

Spectrum Analyzer removes this message and displays a spectral estimate when enough data has been input.

The number of FFT points (*N _{fft}*) is independent of the window length
(

When you set the **Method** property to `Filter Bank`

, the following
algorithms apply. The Spectrum Analyzer uses the **RBW (Hz)** or the **Number of frequency
band** property in the **Spectrum Settings** pane to determine the input frame
length.

Spectrum Analyzer requires a minimum number of samples to compute a spectral estimate. This number of input samples
required to compute one spectral update is shown as **Samples/update** in the **Main
options** pane. This value is directly related to resolution bandwidth, *RBW*, by the
following equation.

$${N}_{samples}=\frac{{F}_{s}}{RBW}$$

*F _{s}* is the sample rate of the input signal. Spectrum Analyzer shows sample
rate in the

When in

**RBW (Hz)**mode, you can set the resolution bandwidth using the value of the**RBW (Hz)**parameter on the**Main options**pane of the**Spectrum Settings**pane. You must specify a value to ensure that there are at least two RBW intervals over the specified frequency span. The ratio of the overall span to RBW must be greater than two:$$\frac{span}{RBW}>2$$

By default, the

**RBW**parameter on the**Main options**pane is set to`Auto`

. In this case, the Spectrum Analyzer determines the appropriate value to ensure that there are 1024 RBW intervals over the specified frequency span. Thus, when you set**RBW**to`Auto`

, it is calculated by the following equation.$$RB{W}_{auto}=\frac{span}{1024}$$When in

**Number of frequency bands**mode, you specify the input frame size. When the number of frequency bands is`Auto`

, the resulting RBW is:$$RBW=\frac{{F}_{s}}{\text{InputFrameSize}}$$

When the number of frequency bands is manually specified, the resulting RBW is:

$$RBW=\frac{{F}_{s}}{FFTLength}$$

For more information about the filter bank algorithm, see Polyphase Implementation.

Sometimes, the number of input samples provided are not sufficient to achieve the resolution bandwidth that you specify. When this situation occurs, Spectrum Analyzer displays a message:

Spectrum Analyzer removes this message and displays a spectral estimate when enough data has been input.

When the PlotAsTwoSidedSpectrum property is
set to `true`

, the interval is $$\left[-\frac{SampleRate}{2},\frac{SampleRate}{2}\right]+FrequencyOffset$$ hertz.

When the `PlotAsTwoSidedSpectrum`

property is set to `false`

, the
interval is $$\left[0,\frac{SampleRate}{2}\right]+FrequencyOffset$$ hertz.

Spectrum Analyzer calculates and plots the power spectrum, power spectrum density, and RMS computed by the modified
*Periodogram* estimator. For more information about the Periodogram method, see `periodogram`

.

*Power Spectral Density* — The power spectral density (PSD) is given by the following
equation.

In this equation, *x*[*n*] is the discrete input signal. On every input signal
frame, Spectrum Analyzer generates as many overlapping windows as possible, with each window denoted as
*x ^{(p)}*[

*Power Spectrum* — The power spectrum is the product of the power spectral density and the
resolution bandwidth, as given by the following equation.

*Spectrogram* — You can plot any power as a spectrogram. Each line of
the spectrogram is one periodogram. The time resolution of each line is 1/*RBW*, which is the minimum
attainable resolution. Achieving the resolution you want may require combining several periodograms. You then use
interpolation to calculate noninteger values of 1/*RBW*. In the spectrogram display, time scrolls
from bottom to top, so the most recent data is shown at the bottom of the display. The offset shows the time value at
which the center of the most current spectrogram line occurred.

When set to `Auto`

, the frequency vector for frequency-domain input is calculated by the
software.

When the PlotAsTwoSidedSpectrum property is set to true, the frequency vector is:

When the PlotAsTwoSidedSpectrum property is set to false, the frequency vector is:

$$\left[0,\frac{SampleRate}{2}\right]$$

The *Occupied BW* is calculated as follows.

Calculate the total power in the measured frequency range.

Determine the lower frequency value. Starting at the lowest frequency in the range and moving upward, the power distributed in each frequency is summed until this result is

of the total power.Determine the upper frequency value. Starting at the highest frequency in the range and moving downward, the power distributed in each frequency is summed until the result reaches

of the total power.The bandwidth between the lower and upper power frequency values is the occupied bandwidth.

The frequency halfway between the lower and upper frequency values is the center frequency.

The *Distortion Measurements* are computed as follows.

Spectral content is estimated by finding peaks in the spectrum. When the algorithm detects a peak, it records the width of the peak and clears all monotonically decreasing values. That is, the algorithm treats all these values as if they belong to the peak. Using this method, all spectral content centered at DC (0 Hz) is removed from the spectrum and the amount of bandwidth cleared (

*W*) is recorded._{0}The fundamental power (

*P*) is determined from the remaining maximum value of the displayed spectrum. A local estimate (_{1}*Fe*) of the fundamental frequency is made by computing the central moment of the power near the peak. The bandwidth of the fundamental power content (_{1}*W*) is recorded. Then, the power from the fundamental is removed as in step 1._{1}The power and width of the higher-order harmonics (

*P*,_{2}*W*,_{2}*P*,_{3}*W*, etc.) are determined in succession by examining the frequencies closest to the appropriate multiple of the local estimate (_{3}*Fe*). Any spectral content that decreases monotonically about the harmonic frequency is removed from the spectrum first before proceeding to the next harmonic._{1}Once the DC, fundamental, and harmonic content is removed from the spectrum, the power of the remaining spectrum is examined for its sum (

*P*), peak value (_{remaining}*P*), and median value (_{maxspur}*P*)._{estnoise}The sum of all the removed bandwidth is computed as

*W*=_{sum}*W*+_{0}*W*+_{1}*W*+...+_{2}*W*._{n}The sum of powers of the second and higher-order harmonics are computed as

*P*=_{harmonic}*P*+_{2}*P*+_{3}*P*+...+_{4}*P*._{n}The sum of the noise power is estimated as:

$${P}_{noise}=({P}_{remaining}\cdot dF+{P}_{est.noise}\cdot {W}_{sum})/RBW$$

Where

*dF*is the absolute difference between frequency bins, and*RBW*is the resolution bandwidth of the window.The metrics for SNR, THD, SINAD, and SFDR are then computed from the estimates.

$$\begin{array}{l}THD=10\cdot {\mathrm{log}}_{10}\left(\frac{{P}_{harmonic}}{{P}_{1}}\right)\\ SINAD=10\cdot {\mathrm{log}}_{10}\left(\frac{{P}_{1}}{{P}_{harmonic}+{P}_{noise}}\right)\\ SNR=10\cdot {\mathrm{log}}_{10}\left(\frac{{P}_{1}}{{P}_{noise}}\right)\\ SFDR=10\cdot {\mathrm{log}}_{10}\left(\frac{{P}_{1}}{\mathrm{max}\left({P}_{maxspur},\mathrm{max}\left({P}_{2},{P}_{3},\mathrm{...},{P}_{n}\right)\right)}\right)\end{array}$$

The harmonic distortion measurements use the spectrum trace shown in the display as the input to the measurements. The default

`Hann`

window setting of the Spectrum Analyzer may exhibit leakage that can completely mask the noise floor of the measured signal.The harmonic measurements attempt to correct for leakage by ignoring all frequency content that decreases monotonically away from the maximum of harmonic peaks. If the window leakage covers more than 70% of the frequency bandwidth in your spectrum, you may see a blank reading (–) reported for

**SNR**and**SINAD**. If your application can tolerate the increased equivalent noise bandwidth (ENBW), consider using a Kaiser window with a high attenuation (up to 330 dB) to minimize spectral leakage.The DC component is ignored.

After windowing, the width of each harmonic component masks the noise power in the neighborhood of the fundamental frequency and harmonics. To estimate the noise power in each region, Spectrum Analyzer computes the median noise level in the nonharmonic areas of the spectrum. It then extrapolates that value into each region.

*N*th order intermodulation products occur at*A***F1*+*B***F2*,where

*F1*and*F2*are the sinusoid input frequencies and |*A*| + |*B*| =*N*.*A*and*B*are integer values.For intermodulation measurements, the third-order intercept (TOI) point is computed as follows, where

*P*is power in decibels of the measured power referenced to 1 milliwatt (dBm):*TOI*=_{lower}*P*+ (_{F1}*P*-_{F2}*P*)/2_{(2F1-F2)}*TOI*=_{upper}*P*+ (_{F2}*P*-_{F1}*P*)/2_{(2F2-F1)}*TOI*= + (*TOI*+_{lower}*TOI*)/2_{upper}

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