Low-pass filter with Windows PowerShell

lowpass_filter.ps1

# create lowpass filter
function create_lowpass_filter(
    [double]$samplerate,
    [double]$cutoff_freq,
    [double]$resonance)
{
    #        a0 + a1*z^-1 + a2*z^-2
    # H(z) = ------------------------
    #         1 + b1*z^-1 + b2*z^-2
    $s = [Math]::Tan($cutoff_freq*3.14159265/$samplerate)
    $t = $s/$resonance
    $u = $s*$s + $t + 1.0
    $a0 = $s*$s/$u
    $a1 = 2.0*$s*$s/$u
    $a2 = $s*$s/$u
    $b1 = 2.0*($s*$s - 1.0)/$u
    $b2 = ($s*$s - $t + 1.0)/$u
    return @{
        a0 = $a0; a1 = $a1; a2 = $a2; b1 = $b1; b2 = $b2;
        in_z = 0.0; in_zz = 0.0; out_z = 0.0; out_zz = 0.0}
}

# filter execute
function filter_execute($f, [double]$in)
{
    $denormal_canceler = 1.0e-100
    $out = $f.a0*$in + $f.a1*$f.in_z + $f.a2*$f.in_zz - $f.b1*$f.out_z - $f.b2*$f.out_zz
    $f.in_zz = $f.in_z + $denormal_canceler
    $f.in_z = $in + $denormal_canceler
    $f.out_zz = $f.out_z + $denormal_canceler
    $f.out_z = $out + $denormal_canceler
    return $out
}

# SoX .dat format example
#
#; Sample Rate 48000
#; Channels 2
#               0      -0.45745626      -0.45745626
#   2.0833333e-05       -0.3917995       -0.3917995
#   4.1666667e-05     -0.067243849      -0.06724384
#        6.25e-05       0.32710202       0.32710202
#             ...              ...              ...

# parameter
$cutoff_freq = 1000.0
$resonance   = 0.70710678118

# read header
$reader = [System.IO.File]::ReadLines("in.dat")
$header = $reader | select -First 2
$samplerate, $channels = $header | foreach { (-split $_)[-1] }
if($channels -ne 2){ return }

# create filter
$f1 = create_lowpass_filter $samplerate $cutoff_freq $resonance
$f2 = create_lowpass_filter $samplerate $cutoff_freq $resonance

# start
$writer = [System.IO.File]::CreateText("out.dat")
$header | foreach { $writer.WriteLine($_) }
$reader `
    | foreach { ,(-split $_) } `
    | foreach { $_[0] + " " + (filter_execute $f1 $_[1]) + " " + (filter_execute $f2 $_[2]) } `
    | foreach { $writer.WriteLine($_) }
$writer.Close()