NAME

PDL::DSP::Iir -- Infinite impulse response and recursive filters

DESCRIPTION

This module provides recursive filters. Currently, only moving average filters are implemented. The moving average is actually a FIR, but it is implemented recursively as are IIR filters, so it is included here.

SYNOPSIS

 use PDL::LiteF;
 use PDL::DSP::Iir( 'moving_average' );

 # apply three passes of a moving average with window size 2*5+1 = 11.
 $filtered_data = moving_average($data,5,3);

 # apply one pass of a moving average with window size 2*3+1 = 7.
 $filtered_data = moving_average($data,3);

 # call as method with window size 2 * $hw + 1
  $y = $x->moving_average($hw);

FUNCTIONS

The function moving_average calls one of the lower level functions mov_avg or multi_pass_mov_avg, but they can be used directly as well.

moving_average

 moving_average($data, $half_width [, $n_passes ]);

Other terms for this kind of filter are: smoothing, sliding average, box smoothing, boxcar smoothing, boxcar filter, etc.

This function applies a moving average of $data with window of size w = 2*$half_width+1. That is, the output value of point i is the (uniformly weighted) average of the input points from i - half_width through i + half_width. The filter is repeated $n_passes times if $n_passes is supplied. This effectively applies a filter with a response that decreases with the distance from the point i. The recursive algorithm is used, which can be much faster than the equivalent direct convolution with a rectangular window. The boundary at data[0] is treated by using a window of size 1 at data[0], then of size 3 at data[1], and so on until the size reaches w. The boundary at datap[n-1] is treated in the same way. In this way, the response around each point is symmetric.

The accumulator for all fixed point types is of type int, and for both floating point types is double.

mov_avg

  Signature: (x(n); double [o]y(n); int half_width)

Moving average with a single pass.

mov_avg ignores the bad-value flag of the input piddles. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

multi_pass_mov_avg

  Signature: (x(n); double [o]y(n); double [t]ytemp(n); int half_width; int n_passes)

This is the same as mov_avg, except that smoothing is repeated n_passes times. Note that storage ytemp is created.

multi_pass_mov_avg ignores the bad-value flag of the input piddles. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.