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# filter

Filter data with filter object

## Synopsis

### Fixed-Point Filter Syntaxes

```y = filter(hd,x)
y = filter(hd,x,dim)```

### Adaptive Filter Syntax

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

### Multirate Filter Syntax

```y = 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

y = filter(hd,x) filters a vector of real or complex input data x through a fixed-point filter hd, producing filtered output data y. The vectors x and y have the same length. filter stores the final conditions for the filter in the States property of hdhd.states.

When you set the property PersistentMemory to 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 PersistentMemory to true. Then set hd.states to a vector of nstates(hd) elements, one element for each state to set. If you specify a scalar for hd.states, filter expands 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 x is a matrix, y = filter(hd,x) filters along each column of x to produce a matrix y of independent channels. If x is a multidimensional array, y = filter(hd,x) filters x along 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 States property for the filter (hd.states) to a matrix of nstates(hd) rows and size(x,2) columns.

y = filter(hd,x,dim) applies the filter hd to the input data located along the specific dimension of x specified by dim.

When you are filtering multichannel data, dim lets 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 dim input argument, the filter operates along the dimension specified by dim. When your input data x is a vector or matrix and dim is 1, each column of x is treated as a one input channel. When dim is 2, the filter treats each row of the input x as a channel.

To filter multichannel data in a loop environment, you must use the dim input argument to set the proper processing dimension.

You specify the initial conditions for each channel individually, when needed, by setting hm.states to a matrix of nstates(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).

### Adaptive Filter Syntaxes

y = filter(ha,x,d) filters a vector of real or complex input data x through an adaptive filter object ha, producing the estimated desired response data y from the process of adapting the filter. The vectors x and y have the same length. Use d for the desired signal. Note that d and x must be the same length signal chains.

[y,e] = filter(ha,x,d) produces the estimated desired response data y and 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 x through a multirate filter hm, producing filtered output data y. The length of vectors x and y differ by approximately the resampling factor. filter stores the final conditions for the filter in the States property of hmhm.states.

y = filter(hm,x,dim) applies the filter hm to the input data located along the specific dimension of x specified by dim.

When you are filtering multichannel data, dim lets 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 dim input argument, the filter operates along the dimension specified by dim. When your input data x is a vector or matrix and dim is 1, each column of x is treated as a one input channel. When dim is 2, the filter treats each row of the input x as a channel.

To filter multichannel data in a loop environment, you must use the dim input argument to set the processing dimension.

You specify the initial conditions for each channel individually, when needed, by setting hm.states to a matrix of nstates(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 x does not need to be a multiple of the rate change factor r for the object. When the rate change factor is not an even divisor of the number of input samples x, filter processes 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 r number of input samples.

## 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 filter with 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]);
for i=1:5,
yloop(:,i) = filter(hd,xblock(:,i));
end```

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.```

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]);
for i=1:5,
yloop(:,i) = filter(hm,xblock(:,i));
end
stem([y3 yloop(:)]);```

## More About

expand all

### Quantized Filters

The filter command implements fixed- or floating-point arithmetic on the quantized filter structure you specify.

The algorithm applied by filter when 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 filter reference page.

 Note   dfilt/filter does not normalize the filter coefficients automatically. Function filter supplied by MATLAB does normalize the coefficients.

### Adaptive Filters

The algorithm used by filter when 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.algorithm reference page.

### Multirate Filters

The algorithm applied by filter when 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.

## See Also

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