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kotlin fft
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@nicolas-f
nicolas-f committed Nov 14, 2023
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204 changes: 204 additions & 0 deletions NoiseCapture/src/commonMain/kotlin/org/noise_planet/noisecapture/signal/FFT.kt
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package org.noise_planet.noisecapture.signal

import kotlin.math.*

class FFT {
fun fft(length: Int, riArray: DoubleArray) {
val n = (2.0.pow(length) + 0.5).toInt()
var wCos: Double
var wSin: Double
var uCos: Double
var uSin: Double
val n2 = n shr 1
var l1 = n
var l2: Int

for (l in 0 until length) {
l2 = l1 shr 1
wCos = 1.0
wSin = 0.0
uCos = cos(PI / l2)
uSin = -sin(PI / l2)

for (j in 0 until l2) {
for (i in j until n step l1) {
val ir = 2 * i
val ii = ir + 1
val l22 = 2 * l2
val sumRe = riArray[ir] + riArray[ir + l22]
val sumIm = riArray[ii] + riArray[ii + l22]
val diffRe = riArray[ir] - riArray[ir + l22]
val diffIm = riArray[ii] - riArray[ii + l22]
riArray[ir + l22] = diffRe * wCos - diffIm * wSin
riArray[ii + l22] = diffRe * wSin + diffIm * wCos
riArray[ir] = sumRe
riArray[ii] = sumIm
}
val w = wCos * uCos - wSin * uSin
wSin = wCos * uSin + wSin * uCos
wCos = w
}
l1 = l1 shr 1
}

var k: Int
var j = 0
val n1 = n - 1

for (i in 0 until n1) {
if (i < j) {
val jr = 2 * j
val ji = jr + 1
val ir = 2 * i
val ii = ir + 1
val tre = riArray[jr]
val tim = riArray[ji]
riArray[jr] = riArray[ir]
riArray[ji] = riArray[ii]
riArray[ir] = tre
riArray[ii] = tim
}
k = n2
while (k <= j) {
j -= k
k = k shr 1
}
j += k
}
}

fun iFFT(length: Int, riArray: DoubleArray) {
val n = (2.0.pow(length) + 0.5).toInt()
var wCos: Double
var wSin: Double
var uCos: Double
var uSin: Double
val n2 = n shr 1
var l1 = n
var l2: Int

for (l in 0 until length) {
l2 = l1 shr 1
wCos = 1.0
wSin = 0.0
uCos = cos(PI / l2)
uSin = sin(PI / l2)

for (j in 0 until l2) {
for (i in j until n step l1) {
val ir = 2 * i
val ii = ir + 1
val l22 = 2 * l2
val sumRe = 0.5 * (riArray[ir] + riArray[ir + l22])
val sumIm = 0.5 * (riArray[ii] + riArray[ii + l22])
val diffRe = 0.5 * (riArray[ir] - riArray[ir + l22])
val diffIm = 0.5 * (riArray[ii] - riArray[ii + l22])
riArray[ir + l22] = diffRe * wCos - diffIm * wSin
riArray[ii + l22] = diffRe * wSin + diffIm * wCos
riArray[ir] = sumRe
riArray[ii] = sumIm
}
val w = wCos * uCos - wSin * uSin
wSin = wCos * uSin + wSin * uCos
wCos = w
}
l1 = l1 shr 1
}

var k: Int
var j = 0
val n1 = n - 1

for (i in 0 until n1) {
if (i < j) {
val jr = 2 * j
val ji = jr + 1
val ir = 2 * i
val ii = ir + 1
val tre = riArray[jr]
val tim = riArray[ji]
riArray[jr] = riArray[ir]
riArray[ji] = riArray[ii]
riArray[ir] = tre
riArray[ii] = tim
}
k = n2
while (k <= j) {
j -= k
k = k shr 1
}
j += k
}
}

fun realFFT(length: Int, realArray: DoubleArray) {
fft(length - 1, realArray)
val n = (2.0.pow(length) + 0.5).toInt()
val a = DoubleArray(n)
val b = DoubleArray(n)

for (i in 0 until n / 2) {
a[2 * i] = 0.5 * (1 - sin(2 * PI / n * i))
a[2 * i + 1] = -0.5 * cos(2 * PI / n * i)
b[2 * i] = 0.5 * (1 + sin(2 * PI / n * i))
b[2 * i + 1] = 0.5 * cos(2 * PI / n * i)
}

for (k in 1 until n / 4 + 1) {
val k2 = 2 * k
val xr =
realArray[k2] * a[k2] - realArray[k2 + 1] * a[k2 + 1] + realArray[n - k2] * b[k2] + realArray[n - k2 + 1] * b[k2 + 1]
val xi =
realArray[k2] * a[k2 + 1] + realArray[k2 + 1] * a[k2] + realArray[n - k2] * b[k2 + 1] - realArray[n - k2 + 1] * b[k2]
val xrN =
realArray[n - k2] * a[n - k2] - realArray[n - k2 + 1] * a[n - k2 + 1] + realArray[k2] * b[n - k2] + realArray[k2 + 1] * b[n - k2 + 1]
val xiN =
realArray[n - k2] * a[n - k2 + 1] + realArray[n - k2 + 1] * a[n - k2] + realArray[k2] * b[n - k2 + 1] - realArray[k2 + 1] * b[n - k2]
realArray[k2] = xr
realArray[k2 + 1] = xi
realArray[n - k2] = xrN
realArray[n - k2 + 1] = xiN
}

val temp = realArray[0]
realArray[0] = realArray[0] + realArray[1]
realArray[n] = temp - realArray[1]
realArray[1] = 0.0
realArray[n + 1] = 0.0
}

fun realIFFT(length: Int, realArray: DoubleArray) {
val n = (2.0.pow(length) + 0.5).toInt()
val a = DoubleArray(n)
val b = DoubleArray(n)

for (i in 0 until n / 2) {
a[2 * i] = 0.5 * (1 - sin(2 * PI / n * i))
a[2 * i + 1] = -0.5 * cos(2 * PI / n * i)
b[2 * i] = 0.5 * (1 + sin(2 * PI / n * i))
b[2 * i + 1] = 0.5 * cos(2 * PI / n * i)
}

for (k in 1 until n / 4 + 1) {
val k2 = 2 * k
val xr =
realArray[k2] * a[k2] + realArray[k2 + 1] * a[k2 + 1] + realArray[n - k2] * b[k2] - realArray[n - k2 + 1] * b[k2 + 1]
val xi =
-realArray[k2] * a[k2 + 1] + realArray[k2 + 1] * a[k2] - realArray[n - k2] * b[k2 + 1] - realArray[n - k2 + 1] * b[k2]
val xrN =
realArray[n - k2] * a[n - k2] + realArray[n - k2 + 1] * a[n - k2 + 1] + realArray[k2] * b[n - k2] - realArray[k2 + 1] * b[n - k2 + 1]
val xiN =
-realArray[n - k2] * a[n - k2 + 1] + realArray[n - k2 + 1] * a[n - k2] - realArray[k2] * b[n - k2 + 1] - realArray[k2 + 1] * b[n - k2]
realArray[k2] = xr
realArray[k2 + 1] = xi
realArray[n - k2] = xrN
realArray[n - k2 + 1] = xiN
}

val temp = realArray[0]
realArray[0] = 0.5 * realArray[0] + 0.5 * realArray[n]
realArray[1] = 0.5 * temp - 0.5 * realArray[n]
iFFT(length - 1, realArray)
}

}

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