use strict;
use warnings;
use Data::Dumper;

my $str = '"$a $a $a" ab bc "c$d e$f$" c$d "$a $a $a"';

my @uniq =
    keys %{{map {$_ => 1}($str=~m/("[^"]*\$[^"]*")/g)}};

print Dumper(\@uniq);