Filter Analyzer
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.
You can use the filterAnalyzer
commandline interface to add, remove, and update filters, displays, and analysis
options.
Open the Filter Analyzer App
MATLAB^{®} Toolstrip: On the Apps tab, under Signal Processing and Communications, click the app icon.
MATLAB command prompt: Enter
filterAnalyzer
.
Examples
Analyze Filters
Design sixthorder Chebyshev Type 1 lowpass and highpass filters with normalized passband edge frequency $0.4\pi $ rad/sample and 12 dB of passband ripple. Express the designs as cascades of fourthorder 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 30thorder FIR bandpass filter designed 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")
Analyze Elliptic and FIR Bandpass Filters
Design a tenthorder elliptic bandpass filter with 5 dB of passband ripple and 60 dB of stopband attenuation. Specify passband edge frequencies of $0.2\pi $ rad/sample and $0.45\pi $ rad/sample. Express the design as a cascade of fourthorder 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. Enter
bb
as the Numerator andaa
as the Denominator. ChooseEllip
for the Filter Name and leave the Sample Rate asNormalized
. Click Import.To import the FIR filter, select Filter Objects, select
dfir
, and click Import and Close.
Alternatively, open Filter Analyzer by using the commandline 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
, 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 commandline 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 deselectSpecification
.
Alternatively, use the commandline interface.
addDisplays(fa)
showFilters(fa,true,FilterNames="dfir")
Related Examples
Parameters
Filters
— View and edit filter information
table
Use the Filters table to edit information about the filters under analysis.
Name — Click this column to edit the name of the filter. You can also rightclick the filter in the Filters table and select Rename.
Line — Click this column to edit the color used to display the filter responses.
Eye — Click this column to add the filter to the current display or to remove it.
Cursor — Click this column to show or remove a data cursor for the filter.
Sample Rate — Click this column to edit the sample rate for the filter.
To duplicate a filter, rightclick it in the Filters table and select Duplicate.
To delete a filter from the app, rightclick it in the Filters table and select Delete.
Analyzer
— File, analysis, and analysis options
toolstrip tab
Import Filter
— Import filter from MATLAB workspace
toolstrip button
Click Import Filter to import the filter you want to analyze. Filter Analyzer supports these filter types.
Filter Coefficients
You can use Filter Analyzer to analyze filters specified as numerator and denominator coefficients. If you specify the coefficients as the Krow matrices
$$B=\left[\begin{array}{cccc}{b}_{11}& {b}_{12}& \cdots & {b}_{1,m+1}\\ {b}_{21}& {b}_{22}& \cdots & {b}_{2,m+1}\\ \vdots & \vdots & \ddots & \vdots \\ {b}_{K1}& {b}_{K2}& \cdots & {b}_{K,m+1}\end{array}\right],\text{\hspace{1em}}A=\left[\begin{array}{cccc}{a}_{11}& {a}_{12}& \cdots & {a}_{1,n+1}\\ {a}_{21}& {a}_{22}& \cdots & {a}_{2,n+1}\\ \vdots & \vdots & \ddots & \vdots \\ {a}_{K1}& {a}_{K2}& \cdots & {a}_{K,n+1}\end{array}\right],$$
Signal Analyzer assumes you have specified the filter as a sequence of K cascaded transfer functions (CTF) such that the full transfer function of the filter is
$$H\left(z\right)=\frac{{b}_{11}+{b}_{12}{z}^{1}+\cdots +{b}_{1,m+1}{z}^{m}}{{a}_{11}+{a}_{12}{z}^{1}+\cdots +{a}_{1,n+1}{z}^{n}}\times \frac{{b}_{21}+{b}_{22}{z}^{1}+\cdots +{b}_{2,m+1}{z}^{m}}{{a}_{21}+{a}_{22}{z}^{1}+\cdots +{a}_{2,n+1}{z}^{n}}\times \cdots \times \frac{{b}_{K1}+{b}_{K2}{z}^{1}+\cdots +{b}_{K,m+1}{z}^{m}}{{a}_{K1}+{a}_{K2}{z}^{1}+\cdots +{a}_{K,n+1}{z}^{n}},$$
where m ≥ 0 is the numerator order of the filter and n ≥ 0 is the denominator order.
If K = 1, then B and A are row vectors that specify the transfer function of an IIR filter.
If you specify both B and A as column vectors, Filter Analyzer assumes they represent the transfer function of an IIR filter.
If B is a scalar, Filter Analyzer assumes you specified the filter as a cascade of allpole IIR filters with each section having a scaling gain equal to B.
If A is a scalar, Filter Analyzer assumes you specified the filter as a cascade of FIR filters with each section having a scaling gain equal to 1/A.
Note
Coefficients and Gain
If you have a scaling gain separate from the coefficient values, you can
enter it in Filter Analyzer using the Import
Filter dialog box. At the command line, you can specify the
coefficients and gain as a cell array of the form {B,A,g}
, where B and A are as
previously defined.
The gain can be a scalar overall gain or a vector of section gains.
If the gain is a scalar, Filter Analyzer applies the value uniformly to all the cascade filter sections.
If the gain is a vector, it must have one more element than the number of filter sections in the cascade. Filter Analyzer applies a scale value to each of the filter sections and applies the last value uniformly to all the filter sections.
If you specify the coefficient matrices and gain vector as
$$B=\left[\begin{array}{cccc}{b}_{11}& {b}_{12}& \cdots & {b}_{1,m+1}\\ {b}_{21}& {b}_{22}& \cdots & {b}_{2,m+1}\\ \vdots & \vdots & \ddots & \vdots \\ {b}_{K1}& {b}_{K2}& \cdots & {b}_{K,m+1}\end{array}\right],\text{\hspace{1em}}A=\left[\begin{array}{cccc}{a}_{11}& {a}_{12}& \cdots & {a}_{1,n+1}\\ {a}_{21}& {a}_{22}& \cdots & {a}_{2,n+1}\\ \vdots & \vdots & \ddots & \vdots \\ {a}_{K1}& {a}_{K2}& \cdots & {a}_{K,n+1}\end{array}\right],\text{\hspace{1em}}g=\left[\begin{array}{ccccc}{g}_{1}& {g}_{2}& \cdots & {g}_{K}& {g}_{0}\end{array}\right],$$
Signal Analyzer uses the transfer function
$$H\left(z\right)={g}_{0}\left({g}_{1}\frac{{b}_{11}+{b}_{12}{z}^{1}+\cdots +{b}_{1,m+1}{z}^{m}}{{a}_{11}+{a}_{12}{z}^{1}+\cdots +{a}_{1,n+1}{z}^{n}}\times {g}_{2}\frac{{b}_{21}+{b}_{22}{z}^{1}+\cdots +{b}_{2,m+1}{z}^{m}}{{a}_{21}+{a}_{22}{z}^{1}+\cdots +{a}_{2,n+1}{z}^{n}}\times \cdots \times {g}_{K}\frac{{b}_{K1}+{b}_{K2}{z}^{1}+\cdots +{b}_{K,m+1}{z}^{m}}{{a}_{K1}+{a}_{K2}{z}^{1}+\cdots +{a}_{K,n+1}{z}^{n}}\right).$$
digitalFilter
Objects
You can use Filter Analyzer to analyze digitalFilter
objects. Use
designfilt
to generate or edit digital
filters based on frequencyresponse specifications.
Filter System Objects
If you have DSP System Toolbox™, you can use Filter Analyzer to analyze these filter System objects.
System object™ 

dsp.AllpassFilter 
dsp.AllpoleFilter 
dsp.BiquadFilter 
dsp.CICCompensationDecimator 
dsp.CICCompensationInterpolator 
dsp.CICDecimator 
dsp.CICInterpolator 
dsp.CoupledAllpassFilter 
dsp.Delay 
dsp.Differentiator 
dsp.DigitalDownConverter 
dsp.DigitalUpConverter 
dsp.FIRDecimator 
dsp.FIRFilter 
dsp.FIRHalfbandDecimator 
dsp.FIRHalfbandInterpolator 
dsp.FIRInterpolator 
dsp.FIRRateConverter 
dsp.FarrowRateConverter 
dsp.FilterCascade 
dsp.FourthOrderSectionFilter — Filter Analyzer
does not support fixedpoint arithmetic for this object 
dsp.HighpassFilter 
dsp.IIRFilter 
dsp.IIRHalfbandDecimator 
dsp.IIRHalfbandInterpolator 
dsp.LowpassFilter 
dsp.NotchPeakFilter —
Filter Analyzer does not support fixedpoint arithmetic
for this System object 
dsp.ParallelFilter 
dsp.SOSFilter 
dsp.VariableBandwidthFIRFilter 
dsp.VariableBandwidthIIRFilter 
Analysis
— Display filter analysis
gallery
Filter Analyzer supports these analysis types. To access the
options available for each analysis, use the Analysis
Options button in the Analysis
Options
toolstrip section.
FrequencyDomain Analyses
Analysis  Icon  Options  Description 

Magnitude response 
 Magnitude Mode: Select
Normalize Magnitude: Toggle on or off 

Phase response 
 Phase Units: Select
Phase
Display: Select  
Group delay response 
 Group Delay Units: Select
Samples or
Time  
Phase delay response 
 Phase Units: Select
Radians or
Degrees 

Magnitude estimate 
 Magnitude Mode: Select
Normalize Magnitude: Toggle on or off Number of Trials: Specify a number 

Roundoff noise power spectrum 
 Number of Trials: Specify a number 

TimeDomain Analyses
Analysis  Icon  Options  Description 

Impulse response 
 Specify Length: Select
Auto or
Userdefined  
Step response 
 Specify Length: Select
Auto or
Userdefined 
Other Analyses
Analysis  Icon  Options  Description 

Polezero plot 
 N/A  
Filter coefficients 
 Coefficients Format: Select
Decimal ,
Hexadecimal , or
Binary 

Filter information 
 N/A 

Analysis Options
— Frequency display and sample rates
tab section
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, on the Analysis Options section of the Analyzer tab, click Frequency Normalization.
Auto
— If some filters do not have a sample rate, analyze filter responses using normalized frequencies measured in rad/sample. If all filters have a sample rate, analyze filter responses using cyclical frequencies measured in Hz.Normalized
— Analyze filter responses using normalized frequencies measured in rad/sample.Unnormalized
— Analyze filter responses using cyclical frequencies measured in Hz.
Analysis Sample Rate
You can choose a reference sample rate to compare the filters plotted in a
display by entering a value in the Analysis Options section
of the Analyzer tab. 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
These options are available for all frequencydomain analyses:
Frequency Scale — To display responses in linear frequency scale, select
Linear
. To use a logarithmic frequency scale, selectLog
.Frequency Range — To display responses over positive frequencies only, select
One Sided
. To display responses over the whole frequency range, selectTwo Sided
. To display responses over the whole frequency range centered at zero, selectCentered
. To display responses over a custom range of frequencies, selectUserdefined
.Number of Points — Select the number of discrete Fourier transform points you want to use to display frequencydomain responses.
For a list of options available with each analysis type, see Analysis
.
Display Options
— Annotations and advanced settings
toolstrip tab
View
— Legend, grid, cursors, masks
tab section
Filter Analyzer supports these display options:
Legend — Click the button to show or hide legends in the active display or in all displays.
Grid — Click the button to show or hide the grid in the active display or in all displays.
Hide Cursors — Click the button to hide the cursors in the active display or in all displays. To show the cursor corresponding to a given filter, click in the cursor column of a signal in the Filters table.
Mask — Click the button 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.
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.
Note
Standard specification masks are available only for filters with design metadata. To include metadata in your design, use a
digitalFilter
object or a filter System object.
CTF View
— Visualize cascaded transfer functions
tab section
If you specify a filter as a cascade of transfer functions, you can choose the way that Filter Analyzer displays sectionbysection responses. This option applies only for displays with one filter. In the Display Options 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.Userdefined
— Show filter responses of selected sections or combinations of sections. To specify your selection, click User Settings and use a cell array.For example,
{[1 2 3],[4 5 6]}
directs the app to display responses for a cascade of sections 1, 2, and 3 and a cascade of sections 4, 5, and 6.
Programmatic Use
filterAnalyzer(filt
1,...,filt
n)
filt
1,...,filt
n)filterAnalyzer(
plots the responses of the specified filters in the Filter Analyzer app.filt
1,...,filt
n)
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(filt
1,...,filt
n,Name=Value
)
filt
1,...,filt
n,Name=Value
)filterAnalyzer(
specifies nondefault options using one or more namevalue arguments.filt
1,...,filt
n,Name=Value
)
filterAnalyzer(filename
)
filename
)filterAnalyzer(
opens a Filter
Analyzer session stored in the MATfile called filename
)filename
. If
Filter Analyzer is already open, this syntax replaces the current app session
with the new session.
filterAnalyzer(filename
,"append")
filename
,"append")filterAnalyzer(
appends the
filters stored in the MATfile called filename
,"append")filename
to the current
Filter Analyzer session. If Filter Analyzer is not open, this syntax
is equivalent to the previous syntax.
[fa
,dispnums
] = filterAnalyzer(___)
fa
,dispnums
] = filterAnalyzer(___)[
returns a handle object for the Filter Analyzer and the numbers corresponding to
the newly added displays. You can also obtain the handle fa
,dispnums
] = filterAnalyzer(___)fa
by typing
fa = getFilterAnalyzerHandle
at the command line.
Version History
Introduced in R2024a
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