MATLAB Function Reference

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,

See Also

filter2

filtfilt, filtic in the Signal Processing Toolbox

References

[1]  Oppenheim, A. V. and R.W. Schafer. Discrete-Time Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1989, pp. 311-312.

fill3

filter2