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filter

Filter data with filter object

Synopsis

Fixed-Point Filter Syntaxesy = filter(hd,x)

y = filter(hd,x,dim)

Adaptive Filter Syntaxy = filter(ha,x,d)

[y,e] = filter(ha,x,d)

Multirate Filter Syntaxy = filter(hm,x)

y = filter(hm,x,dim)

Description

This reference page contains three sections that describe the syntaxes for the filter objects:

Fixed-Point Filter Syntaxes

Adaptive Filter Syntaxes

Multirate Filter Syntaxes

Fixed-Point Filter Syntaxes

y = filter(hd,x)filters a vector of real or complex input data xthrough a fixed-point filter hd,

producing filtered output data y. The vectors xand yhave the same length. filter stores the final

conditions for the filter in the Statesproperty of hd

hd.states.When you set the property PersistentMemoryto false(the default setting), the initial conditions

for the filter are set to zero before filtering starts. To use nonzero initial conditions for hd,

set PersistentMemoryto true. Then sethd.statesto a vector

ofnstates(hd)elements, one element for each state to set. If you specify a scalar

forhd.states, filterexpands the scalar to a vector of the proper length for the states. All

elements of the expanded vector have the value of the scalar.

If xis a matrix, y = filter(hd,x)filters along each column of xto produce a matrix yof

independent channels. Ifxis a multidimensional array, y = filter(hd,x)filters xalong the first

nonsingleton dimension of x.

To use nonzero initial conditions when you are filtering a matrix x, set the filter states to a matrix of initial

condition values. Set the initial conditions by setting the Statesproperty for the filter (hd.states) to

a matrix of nstates(hd)rows andsize(x,2)columns.y = filter(hd,x,dim)applies the filter hdto the input data located along the specific

dimension of xspecified by dim.

When you are filtering multichannel data, dimlets you specify which dimension of the input matrix to filter

along whether a row represents a channel or a column represents a channel. When you provide

the diminput argument, the filter operates along the dimension specified by dim. When your input

data xis a vector or matrix and dimis 1, each column of xis treated as a one input channel.

When dimis 2, the filter treats each row of the input xas a channel.

To filter multichannel data in a loop environment, you must use the diminput argument to set the proper

processing dimension.

You specify the initial conditions for each channel individually, when needed, by setting hm.statesto a

matrix ofnstates(hd)rows (one row containing the states for one channel of input data)

and size(x,2)columns (one column containing the filter states for each channel).

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Adaptive Filter Syntaxes

y = filter(ha,x,d)filters a vector of real or complex input data xthrough an adaptive filter

object ha, producing the estimated desired response data yfrom the process of adapting the filter. The

vectors xand yhave the same length. Use dfor the desired signal. Note that dand xmust be the same

length signal chains.

[y,e] = filter(ha,x,d)produces the estimated desired response data yand the prediction

error e(refer to previous syntax for more information).

Multirate Filter Syntaxes

y = filter(hm,x)filters a vector of real or complex input data xthrough a multirate filter hm,

producing filtered output data y. The length of vectors xand ydiffer by approximately the resampling

factor. filterstores the final conditions for the filter in the Statesproperty of hmhm.states.

y = filter(hm,x,dim)applies the filter hmto the input data located along the specific

dimension of xspecified by dim.

When you are filtering multichannel data, dimlets you specify which dimension of the input matrix to filter

along whether a row represents a channel or a column represents a channel. When you provide

the diminput argument, the filter operates along the dimension specified by dim. When your input

data xis a vector or matrix and dimis 1, each column of xis treated as a one input channel.

When dimis 2, the filter treats each row of the input xas a channel.To filter multichannel data in a loop environment, you must use the diminput argument to set the

processing dimension.

You specify the initial conditions for each channel individually, when needed, by setting hm.statesto a

matrix ofnstates(hm)rows (one row containing the states for one channel of input data)

and size(x,2)columns (one column containing the filter states for each channel).

The number of data samples in your input data set xdoes not need to be a multiple of the rate change

factor rfor the object. When the rate change factor is not an even divisor of the number of input

samples x, filterprocesses the samples as shown in the following figure, where the rate change

factor is 3 and the number of input samples is 23. Decimators always take the first input sample to

generate the first output sample. After that, the next output sample comes after each rnumber of input

samples.

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Examples

Filter a signal using a filter with various initial conditions (IC) or no initial conditions.

x = randn(100,1); % Original signal.

b = fir1(50,.4); % 50th-order linear-phase FIR filter.

hd = dfilt.dffir(b); % Direct-form FIR implementation.% Do not set specific initial conditions.y1 = filter(hd,x); % 'PersistentMemory'='false'(default).

zf = hd.states; % Final conditions.

Now use nonzero initial conditions by setting ICs after before you filter.

hd.persistentmemory = true;

hd.states = 1; % Uses scalar expansion.

y2 = filter(hd,x);

stem([y1 y2]) % Different sequences at beginning.

Looking at the stem plot shows that the sequences are different at the beginning of the filter process.

Here is one way to use filterwith streaming data.

reset(hd); % Clear filter history.

y3 = filter(hd,x); % Filter entire signal in one block.

As an experiment, repeat the process, filtering the data as sections, rather than in streaming form.

reset(hd); % Clear filter history.

yloop = zeros(20,5); % Preallocate output array.

xblock = reshape(x,[20 5]);

fori=1:5,

yloop(:,i) = filter(hd,xblock(:,i));end

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Use a stem plot to see the comparison between streaming and block-by-block filtering.

stem([y3 yloop(:)]);

Filtering the signal section-by-section is equivalent to filtering the entire signal at once.

To show the similarity between filtering with discrete-time and with multirate filters, this example

demonstrates multirate filtering.

Fs = 44.1e3; % Original sampling frequency: 44.1kHz.

n = [0:10239].'; % 10240 samples, 0.232 second long signal.

x = sin(2*pi*1e3/Fs*n); % Original signal, sinusoid at 1kHz.

m = 2; % Decimation factor.

hm = mfilt.firdecim(m); % Use the default filter.

First, filter without setting initial conditions.

y1 = filter(hm,x); % PersistentMemory is false (default).

zf = hm.states; % Final conditions.

This time, set nonzero initial conditions before filtering the data.

hm.persistentmemory = true;

hm.states = 1; % Uses scalar expansion to set ICs.

y2 = filter(hm,x);

stem([y1(1:60) y2(1:60)]) % Show the filtering results.

Note the different sequences at the start of filtering.

Finally, try filtering streaming data.

reset(hm); % Clear the filter history.y3 = filter(hm,x); % Filter entire signal in one block.

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As with the discrete-time filter, filtering the signal section by section is equivalent to filtering the entire

signal at once.

reset(hm); % Clear filter history again.

yloop = zeros(1024,5); % Preallocate output array.

xblock = reshape(x,[2048 5]);

fori=1:5,yloop(:,i) = filter(hm,xblock(:,i));

endstem([y3 yloop(:)]);

More About

collapse all

Algorithms

Quantized Filters

The filtercommand implements fixed- or floating-point arithmetic on the quantized filter structure you

specify.

The algorithm applied by filterwhen you use a discrete-time filter object on an input signal depends

on the response you chose for the filter, such as lowpass or Nyquist or bandstop. To learn more about

each filter algorithm, refer to the literature reference provided on the appropriate discrete-time fi lter

reference page.

Note dfilt/filterdoes not normalize the filter coefficients automatically. Function filtersupplied by

MATLAB does normalize the coefficients.

Adaptive Filters

The algorithm used by filterwhen you apply an adaptive filter object to a signal depends on the

algorithm you chose for your adaptive filter. To learn more about each adaptive filter algorithm, refer to the

literature reference provided on the appropriate adaptfilt.algorithmreference page.Multirate Filters

The algorithm applied by filterwhen you apply a multirate filter objects to signals depends on the

algorithm you chose for the filter the form of the multirate filter, such as decimator or interpolator. To

learn more about each filter algorithm, refer to the literature reference provided on the appropriate

multirate filter reference page.

References

[1] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1989.