Spectrum Analyzer

Display frequency spectrum

• Library:

• Simscape / Utilities

• 

Description

Note

The Spectrum Analyzer block in the Simscape™ product contains a subset of functionality of the DSP System Toolbox™ block with the same name. This page describes the block configuration and functionality available with a Simscape license. If you also have a DSP System Toolbox license, then the Spectrum Analyzer block in the Simscape > Utilities library is identical to the block in the DSP System Toolbox > Sinks library. For more information, see Spectrum Analyzer (DSP System Toolbox) in the DSP System Toolbox documentation.

The Spectrum Analyzer block accepts input signals with discrete sample times and displays frequency spectra of these signals.

To use a Spectrum Analyzer block, instead of a regular scope, in a Simscape model:

1. Add a Spectrum Analyzer block to your block diagram.

2. If your model uses a variable-step solver, also add a Rate Transition block and connect it to the input of the Spectrum Analyzer, setting the Output port sample time to the sample time you wish the Spectrum Analyzer to use.

   If your model uses a local solver, then it produces output physical signals with discrete sample times and you do not need to add a Rate Transition block. However, if you need to down-sample from the solver fixed step size, you can also use a Rate Transition block. For more information on using local solvers, see Making Optimal Solver Choices for Physical Simulation.

3. Use a PS-Simulink Converter block to connect the output physical signal of interest to the input of the Spectrum Analyzer block (or to the input of the Rate Transition block, if using one). For more information, see Connecting Simscape Diagrams to Simulink Sources and Scopes. You can also use additional signal processing blocks between the PS-Simulink Converter and the Spectrum Analyzer to enhance signal quality.

4. Run the simulation. The Spectrum Analyzer, referred to here as the scope, opens and displays the frequency spectrum of the signal.

Note

To prevent the scope from opening when you run your model, right-click the scope icon and select Comment Out. If the scope is already open, and you comment it out in the model, the scope displays, "No data can be shown because this scope is commented out." Select Uncomment to turn the scope back on.

Reduce Plot Rate to Improve Performance

By default, Spectrum Analyzer updates the display at fixed intervals of time at a rate not exceeding 20 hertz. If you want Spectrum Analyzer to plot a spectrum on every simulation time step, you can disable the Reduce Plot Rate to Improve Performance option. In the Spectrum Analyzer menu, select Simulation > Reduce Plot Rate to Improve Performance to clear the check box. Tunable.

Note

When this check box is selected, Spectrum Analyzer may display a misleading spectrum in some situations. For example, if the input signal is wide-band with non-stationary behavior, such as a chirp signal, Spectrum Analyzer might display a stationary spectrum. The reason for this behavior is that Spectrum Analyzer buffers the input signal data and only updates the display periodically at approximately 20 times per second. Therefore, Spectrum Analyzer does not render changes to the spectrum that occur and elapse between updates, which gives the impression of an incorrect spectrum. To ensure that spectral estimates are as accurate as possible, clear the Reduce Plot Rate to Improve Performance check box. When you clear this box, Spectrum Analyzer calculates spectra whenever there is enough data, rendering results correctly.

Limitations

This reference page describes the Spectrum Analyzer block available with Simscape or RF Blockset™. If you have DSP System Toolbox, more parameters and measurements are available. For information about the full Spectrum Analyzer, see Spectrum Analyzer (DSP System Toolbox).

Ports

Input

Port_1 — Signals to visualize

scalar | 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.

• Dimension — One dimensional (vector), two dimensional (matrix), or multidimensional (array). Input must have fixed number of channels. See Signal Dimensions and Determine Signal Dimensions.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point
Complex Number Support: Yes

Parameters

This section lists the parameters available in the Spectrum Analyzer when you do not have DSP System Toolbox. For the full parameter list, see Spectrum Analyzer (DSP System Toolbox).

Spectrum Settings

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.

Main

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

Programmatic Use

See SpectrumType.

Sample rate — Sample rate of the input signal in hertz

Inherited (default) | positive scalar

Sample rate of the input signal in hertz, specified as either

• Inherited to use the same sample rate as the input signal.

• Positive scalar. The specified sample rate must be at least twice the input signal sample rate. Otherwise, you might see unexpected behavior in your signal visualization due to aliasing.

Programmatic Use

See SampleRate (DSP System Toolbox).

RBW (Hz) — Resolution bandwidth

Auto (default) | positive scalar

The 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 greater than two:

$$\frac{span}{RBW}>2$$

Tunable: Yes

Programmatic Use

See RBW (DSP System Toolbox).

Samples/update — Required number of input samples

positive 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 (DSP System Toolbox).

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

Window

Overlap (%) — Segment overlap percentage

0 (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

Programmatic Use

See OverlapPercent (DSP System Toolbox).

Window — Windowing method

Hann (default) | Rectangular

The 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

Programmatic Use

See Window (DSP System Toolbox).

NENBW — Normalized effective noise bandwidth

scalar

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.

Trace

Units — Spectrum units

dBm (default)

This property is read-only.

The units of the spectrum. To change units, you must have the DSP System Toolbox.

Tunable: Yes

Programmatic Use

See SpectrumUnits (DSP System Toolbox).

Averaging method — Smoothing method

Exponential (default) | Running

Specify the smoothing method as:

• Exponential — Weighted average of samples. Use the Forgetting factor property to specify the weighted forgetting factor.

• Running — Running average of the last n samples. Use the Averages property to specify n.

For more information about the averaging methods, see Averaging Method.

Programmatic Use

See AveragingMethod.

Averages — Number of spectral averages

1 (default) | positive integer

Specify 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.

Dependency

This parameter applies only when Averaging method is Running.

Programmatic Use

See SpectralAverages.

Forgetting factor — Weighting forgetting factor

0.9 (default) | scalar in the range (0,1]

Specify the exponential weighting as a scalar value greater than 0 and less than or equal to 1.

Dependency

This parameter applies only when the Averaging method is Exponential.

Programmatic Use

See ForgettingFactor.

Reference load — Reference load

1 (default) | positive real scalar

The reference load in ohms that the Spectrum Analyzer uses as a reference to compute power values.

Programmatic Use

See ReferenceLoad (DSP System Toolbox).

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.

Programmatic Use

See FrequencyScale (DSP System Toolbox).

Offset — Constant frequency offset

0 (default) | scalar

The 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 (DSP System Toolbox).

Dependency

To use this parameter, set Input domain (DSP System Toolbox) to Time.

Programmatic Use

See FrequencyOffset (DSP System Toolbox).

Two-sided spectrum — Enable two-sided spectrum view

off (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.

Programmatic Use

See PlotAsTwoSidedSpectrum (DSP System Toolbox).

Configuration Properties

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 title

character vector | string

Specify the display title. Enter %<SignalLabel> to use the signal labels in the Simulink model as the axes titles.

Tunable: Yes

Programmatic Use

See Title (DSP System Toolbox).

Show legend — Display signal legend

off (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.

Note

The legend only shows the first 20 signals. Any additional signals cannot be viewed or controlled from the legend.

Dependency

To enable this parameter, set View (DSP System Toolbox) to Spectrum or Spectrum and spectrogram.

Programmatic Use

See ShowLegend (DSP System Toolbox).

Show grid — Show internal grid lines

on (default) | off

Show internal grid lines on the Spectrum Analyzer

Programmatic Use

See ShowGrid (DSP System Toolbox).

Y-limits (minimum) — Y-axis minimum

-80 (default) | scalar

Specify the minimum value of the y-axis.

Programmatic Use

See YLimits (DSP System Toolbox).

Y-limits (maximum) — Y-axis maximum

20 (default) | scalar

Specify the maximum value of the y-axis.

Programmatic Use

See YLimits (DSP System Toolbox).

Y-label — Y-axis label

character 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>)

Programmatic Use

See YLabel (DSP System Toolbox).

Style

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 drop-down.

Figure color — Window background

gray (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

Specify whether to display a Line or Stem plot.

Programmatic Use

See PlotType (DSP System Toolbox).

Axes colors — Axes background color

black (default) | color picker

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

Properties for line — Channel for visual property settings

channel names

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

Visible — Channel visibility

on (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 style

line, 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 drop-down.

Axes Scaling

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 — Automatic axes scaling

Auto (default) | Manual | After N Updates

Specify when the scope automatically scales the y-axis. By default, this parameter is set to Auto, and the scope does not shrink the y-axis limits when scaling the axes. You can select one of the following options:

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

• Manual — When you select this option, the scope does not automatically scale the axes. You can manually scale the axes 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 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

Programmatic Use

See AxesScaling (DSP System Toolbox).

Do not allow Y-axis limits to shrink — Axes scaling limits

on (default) | off

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

Dependency

This parameter appears only when you select Auto for the Axis scaling parameter. When you set the Axes scaling parameter to Manual or After N Updates, the y-axis limits can shrink.

Number of updates — Number of updates before scaling

10 (default) | positive number

The 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

Dependency

This parameter appears only when you set Axes scaling/Color scaling (DSP System Toolbox) to After N Updates.

Programmatic Use

See AxesScalingNumUpdates.

Scale limits at stop — Scale axes at stop

off (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 axes

100 (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 (DSP System Toolbox), the x axis is also configurable.

Tunable: Yes

Model Examples

Water Hammer Effect

Model shows how the Thermal Liquid foundation library can be used to model water hammer in a long pipe. After slowly establishing a steady flow within the pipe by opening a valve accordingly, the same valve is shut within a few milliseconds. This triggers a water hammer effect. The valve is modeled using a Variable Local Restriction (TL) block and the pipe is divided into four segments using the Pipe (TL) block. Breaking the pipe into more segments increases fidelity at the expense of simulation performance.

Algorithms

Spectrum Estimation — Welch's Method

When you choose the Welch method, the power spectrum estimate is averaged modified periodograms.

Given the signal input, x, the Spectrum Analyzer does the following:

1. Multiplies x by the given window and scales the result by the window power. The Spectrum Analyzer uses the RBW or the Window Length setting in the Spectrum Settings pane to determine the data window length.

2. Computes the FFT of the signal, Y, and takes the square magnitude using Z = Y.*conj(Y).

3. Computes the current power spectrum estimate by taking the moving average of the last N number of Z's, and scales the answer by the sample rate. For details on the moving average methods, see Averaging Method.

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 Overlap % parameter in the Window Options pane of the Spectrum Settings pane. F_s is the sample rate of the input signal. Spectrum Analyzer shows sample rate in the Main Options pane of the Spectrum Settings pane.

1. When in RBW (Hz) mode, the window length required to compute one spectral update, N_window, is directly related to the resolution bandwidth and normalized effective noise bandwidth:

   $$N_{window}=\frac{NENBW\times F_s}{RBW}$$

   When in Window Length mode, the window length is used as specified.

2. The number of input samples required to compute one spectral update, N_samples, is directly related to the window length and the amount of overlap by the following equation.

   $$N_{samples}=\left(1-\frac{O_p}{100}\right)N_{window}$$

   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.

   Op	Nsamples
   0%	100
   50%	50
   80%	20

3. The normalized effective noise bandwidth, NENBW, is a window parameter determined by the window length, N_window, and the type of window used. If w(n) denotes the vector of N_window window coefficients, then NENBW is given by the following equation.

   $$NENBW=N_{window}\times \frac{{\displaystyle \sum _{n=1}^{N_{window}}{w}^2(n)}}{{\left[{\displaystyle \sum _{n=1}^{N_{window}}w(n)}\right]}^2}$$

4. 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:

   $$RB{W}_{auto}=\frac{span}{1024}$$

5. When in Window Length mode, you specify N_window and the resulting RBW is:

   $$\frac{NENBW\times F_s}{N_{window}}$$

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.

Note

The number of FFT points (N_fft) is independent of the window length (N_window). You can set them to different values if N_fft is greater than or equal to N_window.

Nyquist frequency interval

When the PlotAsTwoSidedSpectrum (DSP System Toolbox) 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.

Periodogram and Spectrogram

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 (Signal Processing Toolbox).

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

$$\mathrm{PSD}\left(f\right)=\frac{1}{P}{\displaystyle \sum _{p=1}^P\frac{{\left|{\displaystyle \sum _{n=1}^{N_{FFT}}{x}^p\left[n\right]e^{-j2\pi f(n-1)T}}\right|}^2}{F_s\times {\displaystyle \sum _{n=1}^{N_{window}}{w}^2\left[n\right]}}}$$

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)[n], and computes their periodograms. Spectrum Analyzer displays a running average of the P most current periodograms.

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

$$P_{spectrum}\left(f\right)=\mathrm{PSD}\left(f\right)\times RBW=\mathrm{PSD}\left(f\right)\times \frac{F_s\times NENBW}{N_{window}}=\frac{1}{P}{\displaystyle \sum _{p=1}^P\frac{{\left|{\displaystyle \sum _{n=1}^{N_{FFT}}{x}^p\left[n\right]e^{-j2\pi f(n-1)T}}\right|}^2}{{\left[{\displaystyle \sum _{n=1}^{N_{window}}w\left[n\right]}\right]}^2}}$$

Frequency Vector

When set to Auto, the frequency vector for frequency-domain input is calculated by the software.

When the PlotAsTwoSidedSpectrum (DSP System Toolbox) property is set to true, the frequency vector is:

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

When the PlotAsTwoSidedSpectrum (DSP System Toolbox) property is set to false, the frequency vector is:

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

Occupied BW

The Occupied BW is calculated as follows.

1. Calculate the total power in the measured frequency range.

2. 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

   $$\frac{100-OccupiedBW\%}{2}$$

   of the total power.

3. 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

   $$\frac{100-OccupiedBW\%}{2}$$

   of the total power.

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

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

Distortion Measurements

The Distortion Measurements are computed as follows.

1. 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 (W₀) is recorded.

2. The fundamental power (P₁) is determined from the remaining maximum value of the displayed spectrum. A local estimate (Fe₁) of the fundamental frequency is made by computing the central moment of the power near the peak. The bandwidth of the fundamental power content (W₁) is recorded. Then, the power from the fundamental is removed as in step 1.

3. The power and width of the higher-order harmonics (P₂, W₂, P₃, W₃, etc.) are determined in succession by examining the frequencies closest to the appropriate multiple of the local estimate (Fe₁). Any spectral content that decreases monotonically about the harmonic frequency is removed from the spectrum first before proceeding to the next harmonic.

4. Once the DC, fundamental, and harmonic content is removed from the spectrum, the power of the remaining spectrum is examined for its sum (P_remaining), peak value (P_maxspur), and median value (P_estnoise).

5. The sum of all the removed bandwidth is computed as W_sum = W₀ + W₁ + W₂ +...+ W_n.

   The sum of powers of the second and higher-order harmonics are computed as P_harmonic = P₂ + P₃ + P₄ +...+ P_n.

6. 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.

7. The metrics for SNR, THD, SINAD, and SFDR are then computed from the estimates.

   $$\begin{array}{l}THD=10\cdot {\log }_{10}\left(\frac{P_{harmonic}}{P_1}\right)\\ SINAD=10\cdot {\log }_{10}\left(\frac{P_1}{P_{harmonic}+P_{noise}}\right)\\ SNR=10\cdot {\log }_{10}\left(\frac{P_1}{P_{noise}}\right)\\ SFDR=10\cdot {\log }_{10}\left(\frac{P_1}{\max \left(P_{maxspur},\max \left(P_2,P_3,\mathrm{...},P_n\right)\right)}\right)\end{array}$$

Harmonic Measurements

1. 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.

   

2. The DC component is ignored.

3. 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.

4. 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.

5. 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_(2F1-F2))/2

   • TOI_upper = P_F2 + (P_F1 - P_(2F2-F1))/2

   • TOI = + (TOI_lower + TOI_upper)/2

Averaging Method

The moving average is calculated using one of the two methods:

• Running — For each frame of input, average the last N-scaled Z vectors, which are computed by the algorithm. The variable N is the value you specify for the number of spectral averages. If the algorithm does not have enough Z vectors, the algorithm uses zeros to fill the empty elements.

  

• Exponential — The moving average algorithm using the exponential weighting method updates the weights and computes the moving average recursively for each Z vector that comes in by using the following recursive equations:

  $$\begin{array}{l}{w}_N=\lambda w_{N-1}+1\\ {\overline{z}}_N=\left(1-\frac{1}{w_N}\right){\overline{z}}_{N-1}+\left(\frac{1}{w_N}\right)z_N\end{array}$$

  • λ — Forgetting factor

  • $$w_N$$ — Weighting factor applied to the current Z vector

  • $$z_N$$ — Current Z vector

  • $${\overline{z}}_{N-1}$$ — Moving average until the previous Z vector

  • $$\left(1-\frac{1}{w_N}\right){\overline{z}}_{N-1}$$ — Effect of the previous Z vectors on the average

  • $${\overline{z}}_N$$ — Moving average including the current Z vector

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.