Filter design specification object
Use the fdesign
function to create a filter design
specification object that contains the specifications for a filter, such as passband ripple,
stopband attenuation, and filter order. Then, use the design
function to design the filter from the filter design specifications
object. For an example, see Design of Lowpass Decimator.
Here is the workflow diagram that shows the simple procedure to design, analyze, and finally apply the filter on streaming data.
For more control options, see Filter Design Procedure. For a complete workflow, see Design a Filter in Fdesign — Process Overview.
returns a design specification object for the filter with a given
designSpecs
= fdesign.response
.response
specifies the variables to use that define your filter design. The filter design parameters
are applied to the filter design method you choose for your filter. The specification option
you choose determines which design methods apply to the designSpecs
= fdesign.response
(spec
)fdesign
object.
specifies the sample rate in Hz to use in the filter specifications. The sample rate scalar
must be the last input argument. If you specify a sample rate, all frequency specifications
are in Hz.designSpecs
= fdesign.response
(___,Fs
)
specifies the units for any magnitude specification you provide in the input
arguments.designSpecs
= fdesign.response
(___,magunits
)
Design a 100tap FIR lowpass decimator filter that reduces the sample rate of a signal from 60 kHz to 20 kHz. The passband of the filter extends up to 6 kHz. Specify a passband ripple of 0.01 dB and a stopband attenuation of 100 dB.
Fs = 60e3; N = 99; Fpass = 6e3; Apass = 0.01; Astop = 100; M = Fs/20e3;
Setup the filter design specifications object using the fdesign.decimator
function.
filtSpecs = fdesign.decimator(M,'lowpass','N,Fp,Ap,Ast',N,Fpass,Apass,Astop,Fs);
Design the FIR lowpass decimator using the design
function.
The resulting filter is a dsp.FIRDecimator
System object™. For details on how to apply this filter to streaming data, refer to dsp.FIRDecimator
.
decimFIR = design(filtSpecs,'SystemObject',true)
decimFIR = dsp.FIRDecimator with properties: DecimationFactor: 3 NumeratorSource: 'Property' Numerator: [1.5100e05 2.2164e05 9.6058e06 4.3636e05 ... ] Structure: 'Direct form' Show all properties
Use info
to display information about the filter.
info(decimFIR)
ans = 10x56 char array
'DiscreteTime FIR Multirate Filter (real) '
' '
'Filter Structure : DirectForm FIR Polyphase Decimator'
'Decimation Factor : 3 '
'Polyphase Length : 34 '
'Filter Length : 100 '
'Stable : Yes '
'Linear Phase : Yes (Type 2) '
' '
'Arithmetic : double '
Visualize the magnitude response of the filter using fvtool
.
fvtool(decimFIR,'Fs',Fs)
Design a lowpass filter to use on a signal sampled at 96 kHz. The passband of the filter extends up to 20 kHz. The stopband of the filter starts at 24 kHz. Specify a passband ripple of 0.01 dB and a stopband attenuation of 80 dB. Determine automatically the order required to meet the specifications.
Set up the filter design specifications object using the fdesign.lowpass
function.
Fs = 96e3; Fpass = 20e3; Fstop = 24e3; Apass = 0.01; Astop = 80; filtSpecs = fdesign.lowpass(Fpass,Fstop,Apass,Astop,Fs);
Determine the available design algorithms using the designmethods
function.
designmethods(filtSpecs,'SystemObject',true)
Design Methods that support System objects for class fdesign.lowpass (Fp,Fst,Ap,Ast): butter cheby1 cheby2 ellip equiripple ifir kaiserwin multistage
Using the design
function, design an equiripple FIR filter and an elliptic IIR filter that meet the specifications.
lpFIR = design(filtSpecs,'equiripple','SystemObject',true)
lpFIR = dsp.FIRFilter with properties: Structure: 'Direct form' NumeratorSource: 'Property' Numerator: [1.0908e04 2.1016e05 2.3369e04 2.8798e04 ... ] InitialConditions: 0 Show all properties
lpIIR = design(filtSpecs,'ellip','SystemObject',true)
lpIIR = dsp.BiquadFilter with properties: Structure: 'Direct form II' SOSMatrixSource: 'Property' SOSMatrix: [5x6 double] ScaleValues: [6x1 double] InitialConditions: 0 OptimizeUnityScaleValues: true Show all properties
You can also measure
the designs to verify that the filters satisfy the constraints.
FIRmeas = measure(lpFIR)
FIRmeas = Sample Rate : 96 kHz Passband Edge : 20 kHz 3dB Point : 21.4297 kHz 6dB Point : 21.8447 kHz Stopband Edge : 24 kHz Passband Ripple : 0.0092309 dB Stopband Atten. : 80.6014 dB Transition Width : 4 kHz
IIRmeas = measure(lpIIR)
IIRmeas = Sample Rate : 96 kHz Passband Edge : 20 kHz 3dB Point : 20.5524 kHz 6dB Point : 20.7138 kHz Stopband Edge : 24 kHz Passband Ripple : 0.01 dB Stopband Atten. : 80 dB Transition Width : 4 kHz
Estimate and display the computational cost
of each filter. The equiripple FIR filter requires many more coefficients than the elliptic IIR filter.
FIRcost = cost(lpFIR)
FIRcost = struct with fields:
NumCoefficients: 101
NumStates: 100
MultiplicationsPerInputSample: 101
AdditionsPerInputSample: 100
IIRcost = cost(lpIIR)
IIRcost = struct with fields:
NumCoefficients: 20
NumStates: 10
MultiplicationsPerInputSample: 20
AdditionsPerInputSample: 20
Use fvtool
function to visualize the resulting designs and compare their properties.
fvtool(lpFIR,lpIIR,'Fs',Fs); legend('FIR Equiripple','Elliptic IIR')
Design a lowpass Butterworth filter that has a passband edge frequency of $$0.4\pi $$ rad/sample, a stopband frequency of $$0.5\pi $$ rad/sample, a passband ripple of 1 dB, and a stopband attenuation of 80 dB.
Create a lowpass
filter design specification object using the fdesign.lowpass
function. Specify the design parameters.
lowpassSpecs = fdesign.lowpass(0.4,0.5,1,80);
To view a list of design methods available for the specification object, use the designmethods
function. If multiple methods are available, pick one that best meets the design criteria. For this example, pick 'butter'
.
designmethods(lowpassSpecs,'SystemObject',true)
Design Methods that support System objects for class fdesign.lowpass (Fp,Fst,Ap,Ast): butter cheby1 cheby2 ellip equiripple ifir kaiserwin multistage
Furthermore, you can specify the design options used in designing the filter. To see a list of available options, run the designoptions
function on lowpassSpecs
. The design options are dependent on the design method you pick. The design method, in this case, 'butter'
, must be specified as an argument to the designoptions
function.
designoptions(lowpassSpecs,'butter','Systemobject',true)
ans = struct with fields:
FilterStructure: {1x6 cell}
SOSScaleNorm: 'ustring'
SOSScaleOpts: 'fdopts.sosscaling'
MatchExactly: {'passband' 'stopband'}
DefaultFilterStructure: 'df2sos'
DefaultMatchExactly: 'stopband'
DefaultSOSScaleNorm: ''
DefaultSOSScaleOpts: [1x1 fdopts.sosscaling]
The filter order necessary to meet a set of design constraints must also be rounded up to an integer value. This loosens some of the constraints, and as a consequence, some design specifications are met while others are exceeded. The 'MatchExactly'
option allows you to match the passband or stopband exactly while exceeding the specification for the other band. Design the filter so that it matches the passband exactly.
The resulting filter is a dsp.BiquadFiter
System object™. For details on how to apply this filter on streaming data, refer to dsp.BiquadFilter
.
IIRbutter = design(lowpassSpecs,'butter','MatchExactly','passband', ... 'SystemObject',true)
IIRbutter = dsp.BiquadFilter with properties: Structure: 'Direct form II' SOSMatrixSource: 'Property' SOSMatrix: [16x6 double] ScaleValues: [17x1 double] InitialConditions: 0 OptimizeUnityScaleValues: true Show all properties
Use fvtool
to visualize the magnitude response of the filter.
fvtool(IIRbutter)
response
— Desired filter responseThe table specifies the possible filter responses.
fdesign Response Method  Description 



















































Use the doc fdesign.
response
syntax at
the MATLAB prompt to get help on a specific structure. For example, this command
provides more information about the lowpass specification object:
doc fdesign.lowpass
Each response
has a Specification
property
that defines the specifications to use to design your filter. You can use defaults or
specify the Specification
property when you construct the
specifications object.
Using the Specification
property, you can provide filter
constraints such as the filter order or the passband attenuation to use when you
construct your filter from the specification object.
spec
— Filter design specificationsFilter design specifications, specified as a character vector. The set of available
specification options depends on the
fdesign.
function. For more
information, refer to the individual
response
fdesign.
pages.response
The filter design is based on the specifications provided by the
fdesign.
object. For
example, when you create a default lowpass filter design specification object,
response
fdesign.lowpass
, the specification expression is set to
'Fp,Fst,Ap,Ast'
. The filter design parameters —
Fp
(passband frequency), Fst
(stopband
frequency), Ap
(passband ripple), and Ast
(stopband attenuation) — are set to default values. The design
function designs the filter based on these parameters.
Specifications that do not contain the filter order result in minimumorder designs
when you invoke the design
function:
d = fdesign.lowpass; % Specification is 'Fp,Fst,Ap,Ast' FIReq = design(d,'equiripple','SystemObject',true); length(FIReq.Numerator) % Returns 43. The filter order is 42
The specification option you choose determines which design methods are applicable.
You can use the setspecs
function to set all of the
specifications simultaneously.
You can set filter specification values by passing them after the
Specification
argument, or by passing the values without the
Specification
.
Filter object constructors take the input arguments in the same order as setspecs
and Specification
.
When the first input to
fdesign.
is not a valid
response
Specification
option, fdesign
assumes that
the input argument is a filter specification and applies it using the default
Specification
option. For example,
'Fp,Fst,Ap,Ast'
is the default for a lowpass object.
Fs
— Sample rateSample rate to use in filter specifications, specified in Hz. The sample rate scalar must be the last input argument. If you specify a sample rate, all frequency specifications are in Hz.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
magunits
— Units for magnitude specification'dB'
(default)  'linear'
 'squared'
Units for magnitude specification, specified as:
'dB'
–– decibels
'linear'
–– linear units
'squared'
–– power units
When you omit the magunits
argument, fdesign
assumes that all magnitudes are in dB. Note that fdesign
stores all
magnitude specifications in dB. If you set magunits
to an option
other than 'dB'
, the function converts the unit to
'dB'
.
designSpecs
— Filter design specification objectfdesign.response
objectfdesign
returns a filter design specification object. Every
filter design specification object has these properties:
Property Name  Default Value  Description 

 Depends on the chosen type  Defines the type of filter to design, such as an interpolator or bandpass filter. This is a readonly value. 
 Depends on the chosen type  Defines the filter characteristics used to define the desired filter
performance, such as the cutoff frequency 
 Depends on the filter type you choose  Contains descriptions of the filter specifications used to define the object, and the filter specifications you use when you create a filter from the object. This is a readonly value. 
 Logical  Determines whether the filter calculation uses a normalized frequency
from 0 to 1, or the frequency band from 0 to F_{s}/2, the sampling frequency. Accepts either

In addition to these properties, filter design specification objects may have other properties as well, depending on whether they design singlerate filters or multirate filters.
Added Properties for Multirate Filters  Description 

 Specifies the amount to decrease the sampling rate. Always a positive integer. 
 Specifies the amount to increase the sampling rate. Always a positive integer. 
 Polyphase length is the length of each polyphase subfilter that
composes the decimator or interpolator or ratechange factor filters. Total
filter length is the product of 
Here is the workflow diagram of the overall procedure for designing and analyzing the filter.
Here are the steps in detail:
Create an fdesign.
specification object to specify the design parameters.response
Use designmethods
to determine the filter
design methods that work for your new filter specification object. If you choose to
use the default design method, then this step is optional.
If you prefer to change the design options and would like to see a list of
available options, run the designoptions
function on the specification object. The output also
shows the design options the filter uses by default.
Use design
to design the filter from the
filter specification object. Specify the design method (determined from step 2) as an
input. If the design options must change from the default values, specify them as
namevalue pairs following the design method.
If you call the design
function without any output arguments,
FVTool is launched and shows the magnitude response of the designed filter.
Alternatively, use the fvtool
function.
Further analysis, such as viewing the frequency response of the filter, computing the cost of implementing the filter, and measuring the filter response characteristics, can be done using one of the supported Analysis Methods for Filter System Objects.
Once you analyze the filter and determine that the filter satisfies the design constraints, you can apply the filter object to streaming input data. For details on how to pass data to the filter object, refer to the corresponding filter System object™ reference pages.
For a detailed example on the design and analysis, see Lowpass Butterworth Filter Specification and Design.
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