filter

Filter data with an infinite impulse response (IIR) or finite impulse response (FIR) filter

Syntax

• y = filter(b,a,X)
  [y,zf] = filter(b,a,X)
  [y,zf] = filter(b,a,X,zi)
  y = filter(b,a,X,zi,dim)
  [...] = filter(b,a,X,[],dim)
  

Description

The filter function filters a data sequence using a digital filter which works for both real and complex inputs. The filter is a direct form II transposed implementation of the standard difference equation (see "Algorithm").

y = filter(b,a,X) filters the data in vector X with the filter described by numerator coefficient vector b and denominator coefficient vector a. If a(1) is not equal to 1, filter normalizes the filter coefficients by a(1). If a(1) equals 0, filter returns an error.

If X is a matrix, filter operates on the columns of X. If X is a multidimensional array, filter operates on the first nonsingleton dimension.

[y,zf] = filter(b,a,X) returns the final conditions, zf, of the filter delays. If X is a row or column vector, output zf is a column vector of max(length(a),length(b))-1. If X is a matrix, zf is an array of such vectors, one for each column of X, and similarly for multidimensional arrays.

[y,zf] = filter(b,a,X,zi) accepts initial conditions, zi, and returns the final conditions, zf, of the filter delays. Input zi is a vector of length max(length(a),length(b))-1, or an array with the leading dimension of size max(length(a),length(b))-1 and with remaining dimensions matching those of X.

y = filter(b,a,X,zi,dim) and [...] = filter(b,a,X,[],dim) operate across the dimension dim.

Example

You can use filter to find a running average without using a for loop. This example finds the running average of a 16-element vector, using a window size of 5.

• data = [1:0.2:4]';
  windowSize = 5;
  filter(ones(1,windowSize)/windowSize,1,data)
  
  ans =
      0.2000
      0.4400
      0.7200
      1.0400
      1.4000
      1.6000
      1.8000
      2.0000
      2.2000
      2.4000
      2.6000
      2.8000
      3.0000
      3.2000
      3.4000
      3.6000
  

Algorithm

The filter function is implemented as a direct form II transposed structure,

or

• y(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb)
                   - a(2)*y(n-1) - ... - a(na+1)*y(n-na)
  

where n-1 is the filter order, and which handles both FIR and IIR filters [1].

The operation of filter at sample is given by the time domain difference equations

• 

The input-output description of this filtering operation in the -transform domain is a rational transfer function,

• 

filter2

Two-dimensional digital filtering

Syntax

• Y = filter2(h,X)
  Y = filter2(h,X,shape)
  

Description

Y = filter2(h,X) filters the data in X with the two-dimensional FIR filter in the matrix h. It computes the result, Y, using two-dimensional correlation, and returns the central part of the correlation that is the same size as X.

Y = filter2(h,X,shape) returns the part of Y specified by the shape parameter. shape is a string with one of these values:

'full'	Returns the full two-dimensional correlation. In this case, Y is larger than X.
'same'	(default) Returns the central part of the correlation. In this case, Y is the same size as X.
'valid'	Returns only those parts of the correlation that are computed without zero-padded edges. In this case, Y is smaller than X.

Remarks

Two-dimensional correlation is equivalent to two-dimensional convolution with the filter matrix rotated 180 degrees. See the Algorithm section for more information about how filter2 performs linear filtering.

Algorithm

Given a matrix X and a two-dimensional FIR filter h, filter2 rotates your filter matrix 180 degrees to create a convolution kernel. It then calls conv2, the two-dimensional convolution function, to implement the filtering operation.

filter2 uses conv2 to compute the full two-dimensional convolution of the FIR filter with the input matrix. By default, filter2 then extracts the central part of the convolution that is the same size as the input matrix, and returns this as the result. If the shape parameter specifies an altternate part of the convolution for the result, filter2 returns the appropriate part.