Filter Analyzer

View, analyze, and compare filters

Since R2024a. Replaces fvtool.

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Description

The Filter Analyzer app is an interactive tool for visualizing, analyzing, and comparing digital filters. Using the app, you can:

  • Import filter objects or filter coefficients. For more information, see Import Filter.

  • View, analyze, and compare responses of multiple digital filters. For more information, see Analysis.

  • View a list of filters in the Filters table and the details for each filter in the Filter Information table.

  • Plot a new filter analysis plot in a separate display window.

  • Specify filter sample rate and analysis sample rate separately.

  • Save the state of the current session, including filters, displays, and analysis options, for use in a future session of the app.

For more information, see Use Filter Analyzer App.

You can use the filterAnalyzer command-line interface to add, remove, and update filters, displays, and analysis options.

Filter Analyzer app

Open the Filter Analyzer App

  • MATLAB® Toolstrip: On the Apps tab, under Signal Processing and Audio, click the app icon.

  • MATLAB command prompt: Enter filterAnalyzer.

Examples

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Open Live Script

Design sixth-order Chebyshev Type 1 lowpass and highpass filters with a normalized passband edge frequency of 0.4π rad/sample and 12 dB of passband ripple. Express the designs as cascades of fourth-order transfer functions. Use Filter Analyzer to display the magnitude and phase responses of the filters.

[zl,pl,kl] = cheby1(6,12,0.4);
[bl,al] = zp2ctf(zl,pl,kl,SectionOrder=4);
[zh,ph,kh] = cheby1(6,12,0.4,"high");
[bh,ah] = zp2ctf(zh,ph,kh,SectionOrder=4);

filterAnalyzer(bl,al,bh,ah,OverlayAnalysis="phase")

Design a 30th-order FIR bandpass filter to filter signals sampled at 2 kHz. Specify a stopband ranging from 250 Hz to 400 Hz. Use Filter Analyzer to display the poles and zeros of the filter transfer function.

iirbp = designfilt("bandpassfir",FilterOrder=30, ...
    CutoffFrequency1=250,CutoffFrequency2=400, ...
    SampleRate=2000);

filterAnalyzer(iirbp,Analysis="polezero")

Open Live Script

Design a tenth-order elliptic bandpass filter with 5 dB of passband ripple and 60 dB of stopband attenuation. Specify passband edge frequencies of 0.2π rad/sample and 0.45π rad/sample. Express the design as a cascade of fourth-order transfer functions.

[z,p,k] = ellip(5,5,60,[0.2 0.45]);
[bb,aa] = zp2ctf(z,p,k,SectionOrder=4);

Design a finite impulse response bandpass filter with 5 dB of passband ripple and asymmetric stopbands for use with signals sampled at 2 kHz.

  • At lower frequencies, the stopband has 80 dB of attenuation and the transition region ranges from 500 Hz to 600 Hz.

  • At higher frequencies, the stopband has 40 dB of attenuation and the transition region ranges from 750 Hz to 900 Hz.

dfir = designfilt("bandpassfir", ...
    SampleRate=2e3,PassbandRipple=5, ...
    StopbandFrequency1=500,PassbandFrequency1=600, ...
    StopbandAttenuation1=80, ...
    PassbandFrequency2=750,StopbandFrequency2=900, ...
    StopbandAttenuation2=40);

Start a Filter Analyzer session to analyze the filters. Import the filters. On the Analyzer tab, click Import Filter.

  • To import the elliptic filter, select Filter Coefficients. Select bb as the Numerator and aa as the Denominator. Specify Ellip for the Filter Name, and leave the Sample Rate as Normalized. Click Import.

  • To import the FIR filter, select Filter Objects, select dfir, and click Import and Close.

Alternatively, open Filter Analyzer by using the command-line interface. By default, the app displays magnitude responses. Only one of the filters has a sample rate, so the app displays the responses using normalized frequencies.

fa = filterAnalyzer(bb,aa,dfir,FilterNames=["ellip" "dfir"]);

Add a display and use it to plot the magnitude responses and the phase responses of the filters.

  • On the Analyzer tab, click New Display.

  • Expand the Analysis gallery so the Overlay Analysis section is visible, and click Phase.

  • Add the filters by clicking the eye icons on the Filters table.

Alternatively, use the filterAnalysisOptions object and the addDisplays and showFilters functions.

opts = filterAnalysisOptions(OverlayAnalysis="phase");
addDisplays(fa,AnalysisOptions=opts)
showFilters(fa,true,FilterNames=["ellip" "dfir"])

Add another display and show the cumulative magnitude responses of the cascaded transfer functions that specify the elliptic filter.

  • Click New Display to add the display and click the eye icon for the elliptic filter.

  • On the Display Options tab, click CTF View ▼ and select Cumulative.

Alternatively, use the command-line interface.

addDisplays(fa,CTFAnalysisMode="cumulative")
showFilters(fa,true,FilterNames="ellip")

Add one more display and show the filter specification mask for the FIR filter.

  • On the Analyzer tab, click New Display and click the eye icon for the FIR filter. The app displays the frequencies in units of Hz.

  • For a digitalFilter object, the app shows the specification mask by default. To remove the mask, on the Display Options tab, click Mask ▼ and clear Specification.

Alternatively, use the command-line interface.

addDisplays(fa)
showFilters(fa,true,FilterNames="dfir")

Related Examples

Parameters

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Main Pane

Filters Table

Select a filter in the Filters table to edit its parameters or see its filter information. Interact with the table to change the visualization of each filter.

Filters table showing name, line color, eye, cursor, and sample rate columns

  • Name — Double-click an entry in this column to edit the name of the filter. You can also right-click the filter in the Filters table and select Rename.

  • Line — Click an entry in this column to edit the color used to display that filter response.

  • Eye — Click an entry in this column to add the corresponding filter to the current display or to remove it. You can also (since R2024b) drag filters from the Filters table onto any display for visualization.

  • Cursor — Click an entry in this column to show or remove data cursors for the corresponding filter. Point to an entry in this column to select between showing one cursor and showing two.

  • Sample Rate — Click an entry in this column to edit the sample rate for the corresponding filter. Edit the sample rate and units:

    • Sample Rate, specified as Normalized (rad/sample) or as a positive scalar that represents cyclical frequencies.

    • Sample Rate Units, specified as Hz, kHz, MHz, or GHz.

To duplicate, rename, or delete a filter from the app, right-click in the selected filter and select one of these options:

  • Duplicate — The app names the duplicated filter using the same name as the original one and appends it with the string _Copy.

  • Rename — Type the new filter name and press Enter. Alternatively, double-click the filter name, type a new filter name, and press Enter.

  • Delete — Confirm the deletion in the dialog box that appears.

Filter Information Table

After selecting a filter in the Filters table, you can see its filter information.

  • Display filter information including design specifications and design options.

  • If you have a DSP System Toolbox™ license, Filter Analyzer also displays filter measurements.

Analyzer Tab

Create a new app session, open an existing session, or save session to file.

Click New Session to clear all the data from the current session and start a new session.

Click Open Session to open a Filter Design session file. The app accepts session files created with previous versions.

Click Save Session or Save Session As to save the state of the current session—including filters, displays, and analysis options—as a MAT file for use in a future session of the app.

Click Import Filter to import the filter you want to analyze.

Filter Analyzer supports these filter types.

  • digitalFilter Objects — You can use Filter Analyzer to design and modify digitalFilter objects. To generate or edit digital filters based on frequency-response specifications at the command line, use designfilt.

  • Filter System objects — If you have DSP System Toolbox, then Filter Analyzer supports filter System objects. For more information, see Supported Filter System Objects.

    If you select a filter System object™, specify the Arithmetic option to set the coefficient quantization arithmetic of the filter as double-precision, single-precision, or fixed-point.

    Note

    To use fixed-point arithmetic, you must have a DSP System Toolbox license and a Fixed-Point Designer™ license.

  • Filter coefficients — You can use Filter Analyzer to import and display filter coefficients specified in cascaded transfer functions (CTF) format. In particular, you can import designs expressed as numerator and denominator coefficients. For more information, see Import Filter Coefficients.

Example: d = digitalFilter([2 4 2;3 2 0],[1 0 0;1 1 0],[1.4;1.4;5]) specifies a digitalFilter object.

Example: sysObj = dsp.HighpassFilter(FilterType="iir",PassbandRipple=0.2) specifies a DSP System object.

Example: [B,A] = zp2ctf([-1 -1 -1 -1], [0.2i -0.2i 0.66i -0.66i],9) and g=[1.4 1.4 5]' specify a digital filter with CTF numerator and denominator coefficients B and A, respectively. The scalar g represents the scaling gain of the filter.

Expand this gallery to choose a base and optional secondary analysis for the active display. Choose options using the thumbnail view or the details view of the gallery.

  • Analysis — Choose the base analysis type.

  • Overlay Analysis — Optionally, choose the secondary analysis that overlays the base analysis.

To access the options available for each analysis, use the Analysis Options button in the Analysis Options toolstrip section.

Filter Analyzer supports these analysis types.

Frequency-Domain Analyses

AnalysisIconOptionsDescription
Magnitude response

Magnitude Mode: Select dB, Linear, Squared, or Zero Phase

Normalize Magnitude: Toggle on or off

  • The frequency response is the filter transfer function evaluated at the unit circle, H(z) = H(ejω).

  • The frequency response is generally complex-valued. You can choose to plot the magnitude of the frequency response, either in linear units or in decibels, or its magnitude squared.

  • The zero-phase response Hr(ω) is related to the frequency response by H(ejω) = Hr(ω)ejϕ(ω), where ϕ(ω) is the continuous phase.

  • For more information, see freqz and zerophase.

  • If you import a filter System object, see freqz and zerophase.

Tip

If you select this analysis, you can zoom in the response to the passband or stopband. Hover on the top-right corner of he display and click the or icons.

Phase response

Phase Units: Select Radians or Degrees

Phase Display: Select Phase or Continuous

  • The phase response is the frequency-dependent phase angle ϕ(ω) of the filter transfer function.

  • For more information, see phasez, angle, and unwrap.

  • If you import a filter System object, see phasez.

Group delay response

Group Delay Units: Select Samples or Time

  • The group delay is the derivative of the phase response with respect to frequency.

  • The group delay is the average delay of the filter as a function of frequency.

  • For more information, see grpdelay.

  • If you import a filter System object, see grpdelay.

Phase delay response

Phase Units: Select Radians or Degrees

  • The phase delay is the phase response divided by the frequency.

  • The phase delay is the time delay the filter imposes on each frequency component of the input signal.

  • For more information, see phasedelay.

  • If you import a filter System object, see phasedelay.

Magnitude estimate

Magnitude Mode: Select dB, Linear, or Squared

Normalize Magnitude: Toggle on or off

Number of Trials: Specify a numeric scalar

  • Filter Analyzer estimates the magnitude response by filtering sinusoids with uniformly distributed random frequencies and computing the ratio of output to input.

  • For more information, see freqrespest and freqrespopts.

Round-off noise power spectrum

Number of Trials: Specify a numeric scalar

  • Filter Analyzer can compute the power spectral density due to the round-off noise produced by quantization errors within the filter. The result is an average over the specified number of trials.

  • For more information, see noisepsd and noisepsdopts.

Time-Domain Analyses

AnalysisIconOptionsDescription
Impulse response

Specify Length: Select Auto or User-defined

  • The impulse response is the response of the filter to a unit impulse.

  • The transfer function is the Fourier transform of the impulse response.

  • For more information, see impz.

  • If you import a filter System object, see impz.

Step response

Specify Length: Select Auto or User-defined

  • The step response is the response of the filter to a step input.

  • The step response is the cumulative sum of the impulse response.

  • For more information, see stepz.

  • If you import a filter System object, see stepz.

Other Analyses

AnalysisIconOptionsDescription
Pole-zero plot

N/A

  • The pole-zero plot shows the poles and zeros of the filter transfer function on the z-plane.

  • Filter Analyzer uses the symbol o to denote a zero and the symbol x to denote a pole.

  • For more information, see zplane.

  • If you import a filter System object, see zplane.

Filter coefficients

Coefficients Format: Select Decimal, Hexadecimal, or Binary

  • The coefficients depend on the filter structure (cascaded transfer functions, direct-form, or lattice).

  • For filters specified as cascaded transfer functions, Filter Analyzer displays the numerator coefficients, denominator coefficients, and gain of each section of the cascade separately.

  • You must have a Fixed-Point Designer license to use the Binary option.

Filter information

N/A

  • Display filter information including design specifications and design options.

  • If you have a DSP System Toolbox license, Filter Analyzer also displays filter measurements.

Frequency Normalization

In Filter Analyzer, you can display filter responses using normalized frequencies or in terms of a sample rate of your choice. To select how to display frequencies, in the Analysis Options section of the Analyzer tab, set Frequency Normalization to one of these values.

  • Auto — If some filters do not have a sample rate, the app analyzes filter responses using normalized frequencies measured in rad/sample. If all filters have a sample rate, the app analyzes filter responses using cyclical frequencies measured in Hz.

  • Normalized — The app analyzes filter responses using normalized frequencies measured in rad/sample.

  • Unnormalized — The app analyzes filter responses using cyclical frequencies measured in Hz.

Analysis Sample Rate

You can choose a reference sample rate, to use to compare the filters plotted in a display to each other, by entering a value for Analysis Sample Rate. You can also choose the highest sample rate among all the filters in the display by selecting Max. To edit the sample rate units, click the pencil icon.

Analysis Options

Select Analysis Options to open the Analysis Options pane, which contains these options for all frequency-domain analyses:

  • Frequency Scale — To display responses in linear frequency scale, select Linear. To use a logarithmic frequency scale, select Log.

  • Frequency Range — To display responses over positive frequencies only, select One Sided. To display responses over the whole frequency range, select Two Sided. To display responses over the whole frequency range centered at zero, select Centered. To display responses over a custom range of frequencies, select User-defined.

    By default, the app displays one-sided responses if all filters under analysis in a display have real-valued coefficients and centered responses if at least one filter has complex-valued coefficients.

  • Number of Points — Select the number of discrete Fourier transform points you want to use to display frequency-domain responses.

For a list of options available with each analysis type, see Analysis.

Click Default Layout to restore the display layout. When you click this button, Filter Analyzer arranges all displays into a single tile, while preserving the analysis plots and options within in each display.

Display Options Tab

Filter Analyzer supports these display options:

  • Legend — Toggle to show or hide legends in the active display. To show or hide the legend in all displays, click Legend▼ and select Show All Legends or Hide All Legends, respectively.

  • Grid — Toggle to show or hide the grid in the active display. To show or hide the grid in all displays, click Grid▼ and select Show All Grids or Hide All Grids, respectively.

  • Hide Cursors — Click to hide the cursors in the active display. To hide the data cursors in all displays, click Hide Cursors▼ and select Hide All Cursors.

    To show the cursor corresponding to a given filter, click the cursor column of a signal in the Filters table.

Click Mask to show or hide the spectral mask in the active display. You can use a standard filter specification mask or you can define your own.

In Filter Analyzer, a mask is a plot that outlines the passband ripples, stopband attenuation, and transition width of the filter. Showing a mask in the magnitude response serves as a visual reference that aids you to compare the expected magnitude and frequency specifications with the actual filter response, which can help you assess the filter design.

  • If the filter being plotted in the active display has design specifications, then the app can draw a specifications-based mask.

    Note

    To use standard specification masks, filters must have design metadata. To include metadata in your design, use a digitalFilter object or a filter System object.

  • If you define your own mask, then the app can draw a user-defined mask, based on the mask frequencies and magnitudes that you specify.

Specify a custom mask as a set of frequencies and a corresponding set of values. To specify your selection, click User Settings. You can use normalized frequencies or express frequencies in units of Hz, kHz, MHz, or GHz. You can specify values for the magnitude of interest, the square of the magnitude, or the magnitude expressed in dB. The frequencies and the values must be finite.

For IIR designs that result in filters with second-order cascaded sections, or for filters imported as cascaded transfer functions, you can choose the way that Filter Designer displays section-by-section responses. This option applies only for displays with one filter. In the Display Options toolstrip tab, click CTF View to toggle between displaying the overall response and displaying the responses section by section. Click CTF View ▼ to select one of these options:

  • Individual — Show filter responses of individual sections.

  • Cumulative — Show filter responses of cumulative sections.

  • User-defined — Show filter responses of selected sections or combinations of sections. To specify your selection, click User Settings and specify Sections a cell array.

    For example, assume a CTF of sections numbered from 1 through 7:

    • {1:7} or {[1 2 3 4 5 6 7]} directs the app to display the response for the entire CTF at once.

    • {1 2 6 7} directs the app to display responses for the CTF section 1, CTF section 2, CTF section 6, and CTF section 7.

    • {[1 2 3] [4 5 7]} directs the app to display responses for a first CTF that comprises the sections 1, 2, and 3, and a second CTF that comprises the sections 4, 5, and 7.

    • {1 [2:4] [6 7]} directs the app to display responses for CTF section 1, the CTF of sections 2 through 4, and the CTF of sections 6 and 7.

Click Reference Filters to show or hide double-precision reference responses for quantized filters in the active display.

When you enable Reference Filters, the app:

  • Displays the responses of all the selected filters using solid lines

  • Displays the reference responses using dotted lines

  • Appends the string Quantized or Reference to each legend entry

Click Polyphase View to show or hide polyphase decompositions of polyphase filters in the active display. For more information about polyphase decomposition of multirate filters, see polyphase.

When you enable Polyphase View, the app displays the response for each decomposed phase of the filters you select for visualization. If a filter has multiple polyphase sections, then Filter Analyzer appends the string Polyphase (p) to each legend entry, where p varies from 1 to the number of polyphase sections.

Programmatic Use

filterAnalyzer(filt1,...,filtn) plots the responses of the specified filters in the Filter Analyzer app.

  • If Filter Analyzer is not open, this syntax opens the app and plots the responses.

  • If Filter Analyzer is open, this syntax plots the responses in a new display in the app.

Specify input filters as coefficient matrices, cell arrays, digitalFilter objects, or System objects. For more information, see Import Filter.

filterAnalyzer(filt1,...,filtn,Name=Value) specifies nondefault options using one or more name-value arguments.

filterAnalyzer(filename) opens a Filter Analyzer session stored in the specified MAT file filename. If Filter Analyzer is already open, this syntax replaces the current app session with the new session.

filterAnalyzer(filename,"append") appends the filters stored in the specified MAT file filename to the current Filter Analyzer session. If Filter Analyzer is not open, this syntax is equivalent to the previous syntax.

[fa,dispnums] = filterAnalyzer(___) returns a handle object for the Filter Analyzer and the numbers corresponding to the newly added displays, using any combination of input arguments from previous syntaxes.. You can also obtain the handle fa by typing fa = getFilterAnalyzerHandle at the command line.

Version History

Introduced in R2024a

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See Also

Apps

Objects

Functions