And finally (cue human-interest story), the version using PDL::FFTW3; unfortunately for me I had to learn about power spectra and then convert Math::FFT's spctrm code into a small PDL function:

use strict;
use warnings;
use PDL;
use PDL::FFTW3;
use PDL::Graphics::Simple;
my $filePath = $ARGV[0] // "testData.txt";
my @data = do { open my $fh, $filePath or die "Can't open $filePath: $
+!"; local $/; split /\s+/, <$fh> };

sub spectrum {my ($d)=@_;
  my $hn=$d->dim(0)-1;
  my $a2=$d->abs2/(($hn*2)**2);
  $a2->slice([1,$hn-1])*=2;
  $a2;
}
my $spectrum = spectrum(rNfft1 pdl(\@data));
$spectrum = $spectrum->slice('1:-1'); # Remove DC signal component

line pdl($spectrum);
print "ret> "; <STDIN>;
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If you're into IRC, then next time you feel you might benefit from using PDL but don't feel 100% clear on where to start, do feel free to join #pdl on irc.perl.org and ask questions! A lightweight way to do so is on the MetaCPAN page for various PDL modules, with the "Chat with us" link.