Fast Fourier transform: Difference between revisions

=={{header|Tcl}}==

{{tcllib|math::constants}}

{{tcllib|math::fourier}}

<lang tcl>package require math::constants

package require math::fourier

math::constants::constants pi

# Helper functions

proc wave {samples cycles} {

global pi

set wave {}

set factor [expr {2*$pi * $cycles / $samples}]

for {set i 0} {$i < $samples} {incr i} {

lappend wave [expr {sin($factor * $i)}]

}

return $wave

}

proc printwave {waveName {format "%7.3f"}} {

upvar 1 $waveName wave

set out [format "%-6s" ${waveName}:]

foreach value $wave {

append out [format $format $value]

}

puts $out

}

proc waveMagnitude {wave} {

set out {}

foreach value $wave {

lassign $value re im

lappend out [expr {hypot($re, $im)}]

}

return $out

}

set wave [wave 16 3]

printwave wave

# Uses FFT if input length is power of 2, and a less efficient algorithm otherwise

set fft [waveMagnitude [math::fourier::dft $wave]]

printwave fft</lang>

Output:

<pre>

wave: 0.000 0.924 0.707 -0.383 -1.000 -0.383 0.707 0.924 0.000 -0.924 -0.707 0.383 1.000 0.383 -0.707 -0.924

fft: 0.000 0.000 0.000 8.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 8.000 0.000 0.000

</pre>