John Lapeyre

NAME

PDL::DSP::Fir - Finite impulse response filter kernels.

SYNOPSIS

  use PDL;
  use PDL::DSP::Fir qw( firwin );

  # return a 10 sample lowpass filter kernel 
  # with a cutoff at 90% of the Nyquist frequency.
  $kernel = firwin( N => 10, fc => 0.9 );

  # Equivalent way of calling.
  $kernel = firwin( { N => 10, fc => 0.9 } );

DESCRIPTION

This module provides routines to create one-dimensional finite impulse response (FIR) filter kernels. This distribution inlcudes a simple interface for filtering in PDL::DSP::Fir::Simple.

The routine "firwin" returns a filter kernel constructed from windowed sinc functions. Available filters are lowpass, highpass, bandpass, and bandreject. The window functions are in the module PDL::DSP::Windows.

Below, the word order refers to the number of elements in the filter kernel.

No functions are exported be default.

FUNCTIONS

firwin

Usage

 $kern = firwin({OPTIONS});
 $kern = firwin(OPTIONS);

Returns a filter kernel (a finite impulse response function) to be convolved with data.

The kernel is built from windowed sinc functions. With the option type => 'window' no sinc is used, rather the kernel is just the window. The options may be passed as a list of key-value pairs, or as an anonymous hash.

OPTIONS

N

order of filter. This is the number of elements in the returned kernel pdl.

type

Filter type. One of lowpass, highpass, bandpass, bandstop, window. Aliases for bandstop are bandreject and notch. Default is lowpass. For bandpass and bandstop the number of samples "N" must be odd. If type is window, then the kernel returned is just the window function.

fc

Cutoff frequency for low- and highpass filters as a fraction of the Nyquist frequency. Must be a number between 0 and 1. No default value.

fclo, fchi

Lower and upper cutoff frequencies for bandpass and bandstop filters. No default values.

All other options to "firwin" are passed to the function "window" in PDL::DSP::Windows.

The following three functions are called by the firwin, but may also be useful by themselves, for instance, to construct more complicated filters.

ir_sinc

  $sinc = ir_sinc($f_cut, $N);

Return an $N point sinc function representing a lowpass filter with cutoff frequency $f_cut.

$f_cut must be between 0 and 1, with 1 being Nyquist freq. The output pdl is the function sin( $f_cut * $x ) / $x where $x is pdl of $N uniformly spaced values ranging from - PI * ($N-1)/2 through PI * ($N-1)/2. For what it's worth, a bit of efficiency is gained by computing the index at which $x is zero, rather than searching for it.

spectral_inverse

  $fir_inv = spectral_inverse($fir);

Return output kernel whose spectrum is the inverse of the spectrum of the input kernel.

The number of samples in the input kernel must be odd. Input $fir and output $fir_inv are real-space fir filter kernels. The spectrum of the output kernel is the additive inverse with respect to 1 of the spectrum of the input kernel.

spectral_reverse

  $fir_rev = spectral_reverse($fir);

Return output kernel whose spectrum is the reverse of the spectrum of the input kernel.

That is, the spectrum is mirrored about the center frequency.

AUTHOR

John Lapeyre, <jlapeyre at cpan.org>

ACKNOWLEDGEMENTS

LICENSE AND COPYRIGHT

Copyright 2012 John Lapeyre.

This program is free software; you can redistribute it and/or modify it under the terms of either: the GNU General Public License as published by the Free Software Foundation; or the Artistic License.

See http://dev.perl.org/licenses/ for more information.