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use Math::FFT;
  my $PI = 3.1415926539;
  my $N1 = 64;
  my ($series, $other_series);
  for (my $k=0; $k<$N1; $k++) {
   
     $series->[$k] = 2 * sin((2*$PI*$k)/8);        
  }

for ($i=0; $i<$N1; $i++)
  { 
     print "$i $series->[$i] ";
     print "\n";
  }

$f_cut=0.00005;  
$width=0.1;

@out_data1=lowpass_filter  ($f_cut, $width, $N1);
@out_data2=highpass_filter ($f_cut, $width, $N1);
@out_data3=bandpass_filter ($f_cut, $width, $N1);

for ($i=0; $i<$N1; $i++)
  { 
     print "$i $out_data1[$i] ";
     print "\n";
  }

sub lowpass_filter ($$$)
{
  
    my( $f_cut, $width, $N) = @_; 
    my $i;

my $fft = new Math::FFT($series);
  my $coeff = $fft->rdft();

for ($i=0; $i< $N; $i++)
  {

$f=$i/(2*$N);

if ( $f <= $f_cut)
    {
     
         $C_[$i]=1;
         $C_[$i+1]=1;
    }
    else
    {
       $C=($f-$f_cut)*($f-$f_cut)/($width*$width);
       $C_[$i]=exp(-$C);

$C_[$i+1]=$C_[$i];

}

$i=$i+1;
  }

for ($i=0; $i<$N; $i++)
  {

$$coeff[$i]=$$coeff[$i]*$C_[$i];

$$coeff[$i+1]=$$coeff[$i+1]*$C_[$i]; 
      $i=$i+1; 
  }

$$coeff[1]=(0.5-$f_cut)/$width;

my $original_data = $fft->invrdft($coeff);

$start_0=$$original_data[0];
  $slp=($$original_data[$N-1] - $$original_data[0])/($N-1);

for ($i=0; $i<$N; $i++)
  { 
   $out[$i]=$$original_data[$i]+ $start_0+$slp*$i;
    
  }

return @out;

}

sub highpass_filter ($$$)
{
  
    my( $f_cut, $width, $N) = @_; 
    my $i;

my $fft = new Math::FFT($series);
  my $coeff = $fft->rdft();

for ($i=0; $i< $N; $i++)
  {

$f=$i/(2*$N);

if ( $f >= $f_cut)
    {
     
         $C_[$i]=1;
         $C_[$i+1]=1;
    }
    else
    {
       $C=($f-$f_cut)*($f-$f_cut)/($width*$width);
       $C_[$i]=exp(-$C);

$C_[$i+1]=$C_[$i];

}

$i=$i+1;
  }

for ($i=0; $i<$N; $i++)
  {

$$coeff[$i]=$$coeff[$i]*$C_[$i];

$$coeff[$i+1]=$$coeff[$i+1]*$C_[$i]; 
      $i=$i+1; 
  }

$$coeff[1]=(0.5-$f_cut)/$width;

my $original_data = $fft->invrdft($coeff);

$start_0=$$original_data[0];
  $slp=($$original_data[$N-1] - $$original_data[0])/($N-1);

for ($i=0; $i<$N; $i++)
  { 
   $out[$i]=$$original_data[$i]+ $start_0+$slp*$i;
    
  }

return @out;

}

sub bandpass_filter ($$$)
{
  
    my( $f_cut, $width, $N) = @_; 
    my $i;

my $fft = new Math::FFT($series);
  my $coeff = $fft->rdft();

for ($i=0; $i< $N; $i++)
  {

$f=$i/(2*$N);

if ( $f = $f_cut)
    {
     
         $C_[$i]=1;
         $C_[$i+1]=1;
    }
    else
    {
       $C=($f-$f_cut)*($f-$f_cut)/($width*$width);
       $C_[$i]=exp(-$C);

$C_[$i+1]=$C_[$i];

}

$i=$i+1;
  }

for ($i=0; $i<$N; $i++)
  {

$$coeff[$i]=$$coeff[$i]*$C_[$i];

$$coeff[$i+1]=$$coeff[$i+1]*$C_[$i]; 
      $i=$i+1; 
  }

$$coeff[1]=(0.5-$f_cut)/$width;

my $original_data = $fft->invrdft($coeff);

$start_0=$$original_data[0];
  $slp=($$original_data[$N-1] - $$original_data[0])/($N-1);

for ($i=0; $i<$N; $i++)
  { 
   $out[$i]=$$original_data[$i]+ $start_0+$slp*$i;
    
  }

return @out;

}