dfilt - Discrete-time filter

Syntax

hd = dfilt.structure(input1,...) hd = [dfilt.structure(input1,...), dfilt.structure(input1,...),...] hd = design(d,'designmethod')

Description

hd = dfilt.structure(input1,...) returns a discrete-time filter, hd, of type structure. Each structure takes one or more inputs. When you specify a dfilt.structure with no inputs, a default filter is created.

Note You must use a structure with dfilt.

hd = [dfilt.structure(input1,...), dfilt.structure(input1,...),...] returns a vector containing dfilt filters.

Structures

Structures for dfilt.structure specify the type of filter structure. Available types of structures for dfilt are shown below.

dfilt.structure	Description	Coefficient Mapping Support in realizemdl
`dfilt.allpass`	Allpass filter	Supported
`dfilt.cascadeallpass`	Cascade of allpass filter sections	Supported
`dfilt.cascadewdfallpass`	Cascade of allpass wave digital filters	Supported
`dfilt.delay`	Delay	Not supported
`dfilt.df1`	Direct-form I	Supported
`dfilt.df1sos`	Direct-form I, second-order sections	Supported.
`dfilt.df1t`	Direct-form I transposed	Supported
`dfilt.df1tsos`	Direct-form I transposed, second-order sections	Supported.
`dfilt.df2`	Direct-form II	Supported
`dfilt.df2sos`	Direct-form II, second-order sections	Supported.
`dfilt.df2t`	Direct-form II transposed	Supported
`dfilt.df2tsos`	Direct-form II transposed, second-order sections	Supported.
`dfilt.dffir`	Direct-form FIR	Supported
`dfilt.dffirt`	Direct-form FIR transposed	Supported
`dfilt.dfsymfir`	Direct-form symmetric FIR	Supported
`dfilt.dfasymfir`	Direct-form antisymmetric FIR	Supported
`dfilt.farrowfd`	Generic fractional delay Farrow filter	Supported.
`dfilt.farrowlinearfd`	Linear fractional delay Farrow filter	Not supported
`dfilt.fftfir`	Overlap-add FIR	Not supported
`dfilt.latticeallpass`	Lattice allpass	Supported
`dfilt.latticear`	Lattice autoregressive (AR)	Supported
`dfilt.latticearma`	Lattice autoregressive moving- average (ARMA)	Supported
`dfilt.latticemamax`	Lattice moving-average (MA) for maximum phase	Supported
`dfilt.latticemamin`	Lattice moving-average (MA) for minimum phase	Supported
`dfilt.calattice`	Coupled, allpass lattice	Supported
`dfilt.calatticepc`	Coupled, allpass lattice with power complementary output	Supported
`dfilt.statespace`	State-space	Supported.
`dfilt.scalar`	Scalar gain object	Supported
`dfilt.wdfallpass`	Allpass wave digital filter object	Supported
`dfilt.cascade`	Filters arranged in series	Supported
`dfilt.parallel`	Filters arranged in parallel	Supported

For more information on each structure, refer to its reference page.

hd = design(d,'designmethod') returns the dfilt object hd resulting from the filter specification object d and the design method you specify in designmethod. When you omit the designmethod argument, design uses the default design method to construct a filter from the object d.

With this syntax, you design filters by

Specifying the filter specifications, such as the response shape (perhaps highpass) and details (passband edges and attenuation).
Selecting a method (such as equiripple) to design the filter.
Applying the method to the specifications object with design(d,'designmethod).

Using the specification-based technique can be more effective than the coefficient-based filter design techniques.

Design Methods for Design Syntax

When you use the hd = design(d,'designmethod') syntax, you have a range of design methods available depending on d, the filter specification object. The table below lists all of the design methods in the toolbox.

Design Method String	Filter Design Result
`butter`	Butterworth IIR
`cheby1`	Chebyshev Type I IIR
`cheby2`	Chebyshev Type II IIR
`ellip`	Elliptic IIR
`equiripple`	Equiripple with the same ripple in the pass and stopbands
`firls`	Least-squares FIR
`freqsamp`	Frequency-Sampled FIR
`ifir`	Interpolated FIR
`iirlpnorm`	Least Pth norm IIR
`iirls`	Least-Squares IIR
`kaiserwin`	Kaiser-windowed FIR
`lagrange`	Fractional delay filter
`multistage`	Multistage FIR
`window`	Windowed FIR

As the specifications object d changes, the available methods for designing filters from d also change. For instance, if d is a lowpass filter with the default specification 'Fp,Fst,Ap,Ast', the applicable methods are:

% Create an object to design a lowpass filter.
d=fdesign.lowpass; 
designmethods(d) % What design methods apply to object d?

Design Methods for class fdesign.lowpass (Fp,Fst,Ap,Ast):

butter
cheby1
cheby2
ellip
equiripple
ifir
kaiserwin
multistage

If you change the specification string to 'N,F3dB', the available design methods change:

d=fdesign.lowpass('N,F3dB');
designmethods(d)
Design Methods for class fdesign.lowpass (N,F3dB):

butter
maxflat

Analysis Methods

Methods provide ways of performing functions directly on your dfilt object without having to specify the filter parameters again. You can apply these methods directly on the variable you assigned to your dfilt object.

For example, if you create a dfilt object, hd, you can check whether it has linear phase with islinphase(hd), view its frequency response plot with fvtool(hd), or obtain its frequency response values with h = freqz(hd). You can use all of the methods described here in this way.

Note If your variable hd is a 1-D array of dfilt filters, the method is applied to each object in the array. Only freqz, grpdelay, impz, is*, order, and stepz methods can be applied to arrays. The zplane method can be applied to an array only if zplane is used without outputs.

Some of the methods listed here have the same name as functions in Signal Processing Toolbox or Filter Design Toolbox™ software. They behave similarly.

Method	Description
`addstage`	Adds a stage to a `cascade` or `parallel` object, where a stage is a separate, modular filter. Refer to `dfilt.cascade` and `dfilt.parallel`.
`block`	(Available only with Signal Processing Blockset) `block(hd)` creates a Signal Processing Blockset block of the `dfilt` object. The `block` method can specify these properties/values: `'Destination'` indicates where to place the block. `'Current'` places the block in the current Simulink model. `'New'` creates a new model. Default value is `'Current'`. `'Blockname'` assigns the entered string to the block name. Default name is `'Filter'`. `'OverwriteBlock'`indicates whether to overwrite the block generated by the block method (`'on'`) and defined by `Blockame`. Default is `'off'`. `'MapStates`' specifies initial conditions in the block (`'on'`). Default is `'off'`. Refer to "Using Filter States" in Signal Processing Toolbox documentation.
`cascade`	Returns the series combination of two `dfilt` objects. Refer to `dfilt.cascade`.
`coeffs`	Returns the filter coefficients in a structure containing fields that use the same property names as those in the original `dfilt`.
`convert`	Converts a `dfilt` object from one filter structure, to another filter structure
`fcfwrite`	Writes a filter coefficient ASCII file. The file can contain a single filter or a vector of objects. If Filter Design Toolbox software is installed, the file can contain multirate filters (mfilt) or adaptive filters (adaptfilt). Default filename is `untitled.fcf`. `fcfwrite(hd,filename)` writes to a disk file named `filename` in the current working directory. The `.fcf` extension is added automatically. `fcfwrite(...,fmt)` writes the coefficients in the format `fmt`, where valid `fmt` strings are: `'hex'` for hexadecimal `'dec'` for decimal `'bin'` for binary representation.
`fftcoeffs`	Returns the frequency-domain coefficients used when filtering with a `dfilt.fftfir`
`filter`	Performs filtering using the `dfilt` object
`firtype`	Returns the type (1-4) of a linear phase FIR filter
`freqz`	Plots the frequency response in `fvtool`. Note that unlike the `freqz` function, this `dfilt` `freqz` method has a default length of 8192.
`grpdelay`	Plots the group delay in `fvtool`
`impz`	Plots the impulse response in `fvtool`
`impzlength`	Returns the length of the impulse response
`info`	Displays `dfilt` information, such as filter structure, length, stability, linear phase, and, when appropriate, lattice and ladder length.
`isallpass`	Returns a logical `1` (i.e., true) if the `dfilt` object in an allpass filter or a logical `0` (i.e., false) if it is not
`iscascade`	Returns a logical `1` if the `dfilt` object is cascaded or a logical `0` if it is not
`isfir`	Returns a logical `1` if the `dfilt` object has finite impulse response (FIR) or a logical `0` if it does not
`islinphase`	Returns a logical `1` if the `dfilt` object is linear phase or a logical `0` if it is not
`ismaxphase`	Returns a logical `1` if the `dfilt` object is maximum-phase or a logical `0` if it is not
`isminphase`	Returns a logical `1` if the `dfilt` object is minimum-phase or a logical `0` if it is not
`isparallel`	Returns a logical `1` if the `dfilt` object has parallel stages or a logical `0` if it does not
`isreal`	Returns a logical `1` if the `dfilt` object has real-valued coefficients or a logical 0 if it does not
`isscalar`	Returns a logical `1` if the `dfilt` object is a scalar or a logical `0` if it is not scalar
`issos`	Returns a logical `1` if the `dfilt` object has second-order sections or a logical `0` if it does not
`isstable`	Returns a logical `1` if the `dfilt` object is stable or a logical `0` if it are not
`nsections`	Returns the number of sections in a second-order sections filter. If a multistage filter contains stages with multiple sections, using `nsections` returns the total number of sections in all the stages (a stage with a single section returns 1).
`nstages`	Returns the number of stages of the filter, where a stage is a separate, modular filter
`nstates`	Returns the number of states for an object
`order`	Returns the filter order. If `hd` is a single-stage filter, the order is given by the number of delays needed for a minimum realization of the filter. If `hd` has multiple stages, the order is given by the number of delays needed for a minimum realization of the overall filter.
`parallel`	Returns the parallel combination of two `dfilt` filters. Refer to `dfilt.parallel`.
`phasez`	Plots the phase response in `fvtool`
`realizemdl`	(Available only with Simulink ) `realizemdl(hd)` creates a Simulink model containing a subsystem block realization of your `dfilt`. `realizemdl(hd,p1,v1,p2,v2,...)` creates the block using the properties `p1`, `p2`,... and values `v1`, `v2`,... specified. The following properties are available: `'Blockname'` specifies the name of the block. The default value is `'Filter'`. `'Destination'` specifies whether to add the block to a current Simulink model or create a new model. Valid values are `'Current'` and `'New'`. `'OverwriteBlock'` specifies whether to overwrite an existing block that was created by `realizemdl` or create a new block. Valid values are `'on'` and `'off'`. Note that only blocks created by `realizemdl` are overwritten. The following properties optimize the block structure. Specifying `'on'` turns the optimization on and `'off'` creates the block without optimization. The default for each block is `'off'.` `'OptimizeZeros'` removes zero-gain blocks. `'OptimizeOnes'` replaces unity-gain blocks with a direct connection. `'OptimizeNegOnes'` replaces negative unity-gain blocks with a sign change at the nearest summation block. `'OptimizeDelayChains'` replaces cascaded chains of delay block with a single integer delay block set to the appropriate delay.
`removestage`	Removes a stage from a cascade or parallel `dfilt`. Refer to `dfilt.cascade` and `dfilt.parallel`.
`setstage`	Overwrites a stage of a cascade or parallel `dfilt`. Refer to `dfilt.cascade` and `dfilt.parallel`.
`sos`	Converts the `dfilt` to a second-order sections `dfilt`. If `hd` has a single section, the returned filter has the same class. `sos(hd,flag)` specifies the ordering of the second-order sections. If `flag='UP'`, the first row contains the poles closest to the origin, and the last row contains the poles closest to the unit circle. If `flag='down'`, the sections are ordered in the opposite direction. The zeros are always paired with the poles closest to them. `sos(hd,flag,scale)` specifies the scaling of the gain and the numerator coefficients of all second-order sections. `scale` can be `'none'`, `'inf'` (infinity-norm) or `'two'` (2-norm). Using infinity-norm scaling with `up` ordering minimizes the probability of overflow in the realization. Using 2-norm scaling with `down` ordering minimizes the peak roundoff noise.
`ss`	Converts the `dfilt` to state-space. To see the separate `A,B,C,D` matrices for the state-space model, use `[A,B,C,D]=ss(hd)`.
`stepz`	Plots the step response in `fvtool` `stepz(hd,n)` computes the first `n` samples of the step response. `stepz(hd,n,Fs)` separates the time samples by `T = 1/Fs`, where `Fs` is assumed to be in Hz.
`tf`	Converts the `dfilt` to a transfer function
`zerophase`	Plots the zero-phase response in `fvtool`
`zpk`	Converts the `dfilt` to zeros-pole-gain form
`zplane`	Plots a pole-zero plot in `fvtool`

Viewing Properties

As with any object, use get to view a dfilt properties. To see a specific property, use

 get(hd,'property')

To see all properties for an object, use

get(hd)

Note If you have Filter Design Toolbox software, dfilt objects include an arithmetic property. You can change the internal arithmetic of the filter from double- precision to single-precision using: hd.arithmetic = 'single'.

If you have both Filter Design Toolbox software and Fixed-Point Toolbox software, you can change the arithmetic property to fixed-point using: hd.arithmetic = 'fixed'

Changing Properties

To set specific properties, use

set(hd,'property1',value,'property2',value,...)

Note that you must use single quotation marks around the property name. Use single quotation marks around the value argument when the value is a string, such as specifyall or fixed.

Copying an Object

To create a copy of an object, use the copy method.

h2 = copy(hd)

Note Using the syntax H2 = hd copies only the object handle and does not create a new, independent object.

Converting Between Filter Structures

To change the filter structure of a dfilt object hd, use

hd2 = convert(hd,'structure_string');

where structure_string is any valid structure name in single quotation marks. If hd is a cascade or parallel structure, each stage is converted to the new structure.

Using Filter States

Two properties control the filter states:

states — stores the current states of the filter. Before the filter is applied, the states correspond to the initial conditions and after the filter is applied, the states correspond to the final conditions. For df1, df1t, df1sos and df1tsos structures, states returns a filtstates object.
PersistentMemory — controls whether filter states are saved. The default value is 'false', which causes the initial conditions to be reset to zero before filtering and turns off the display of states information. Setting PersistentMemory to 'true' allows the filter to use your initial conditions or to reuse the final conditions from a previous filtering operation as the initial conditions of the next filtering operation. The true setting also displays information about the filter states.

Note If you set the states and want to use them for filtering, you must set PersistentMemory to 'true' before you use the filter.

Examples

Create a direct-form I filter and use a method to see if it is stable.

[b,a] = butter(8,0.25);
hd = dfilt.df1(b,a)
 
hd = 
         FilterStructure: 'Direct-Form I'
               Numerator: [1x9 double]
             Denominator: [1x9 double]
        PersistentMemory: false
    
isstable(hd)
ans =
     1

If a dfilt's numerator values do not fit on a single line, a description of the vector is displayed. To see the specific numerator values for this example, use

get(hd,'numerator')

ans =
Columns 1 through 6 
    0.0001  0.0009  0.0030  0.0060  0.0076  0.0060
  Columns 7 through 9 
    0.0030  0.0009  0.0001

Create an array containing two dfilt objects, apply a method and verify that the method acts on both objects, and use a method to test whether the objects are FIR objects.

b = fir1(5,.5);
hd = dfilt.dffir(b);         % Create an FIR object
[b,a] = butter(5,.5);
hd(2) = dfilt.df2t(b,a);	   % Create DF2T object and place
                           % in the second column of hd.

[h,w] = freqz(hd);
size(h)								% Verify that resulting h is
ans =								% 2 columns.
        8192           2
size(w)								% Verify that resulting w is
ans =								% 1 column.
        8192           1

test_fir = isfir(hd)
test_fir =
     1     0								% hd(1) is FIR and hd(2) is not.

Refer to the reference pages for each structure for more examples.