Files
Terrarum/src/net/torvald/terrarum/audio/FFT.kt
2023-11-25 21:46:49 +09:00

304 lines
11 KiB
Kotlin

package net.torvald.terrarum.audio
import org.apache.commons.math3.exception.MathIllegalStateException
import org.apache.commons.math3.transform.DftNormalization
import org.apache.commons.math3.transform.TransformType
import org.apache.commons.math3.util.FastMath
data class FComplex(var real: Float = 0f, var imaginary: Float = 0f) {
operator fun times(other: FComplex) = FComplex(
this.real * other.real - this.imaginary * other.imaginary,
this.real * other.imaginary + this.imaginary * other.real
)
}
/**
* Modification of the code form JDSP and Apache Commons Math
*
* Created by minjaesong on 2023-11-25.
*/
object FFT {
// org.apache.commons.math3.transform.FastFouriesTransformer.java:370
fun fft(signal: FloatArray): Array<FComplex> {
val dataRI = arrayOf(signal.copyOf(), FloatArray(signal.size))
transformInPlace(dataRI, DftNormalization.STANDARD, TransformType.FORWARD)
val output = dataRI.toComplexArray()
return getComplex(output, false)
}
// org.apache.commons.math3.transform.FastFouriesTransformer.java:404
fun ifftAndGetReal(y: Array<FComplex>): FloatArray {
val dataRI = Array<FloatArray>(2) { FloatArray(y.size) }
for (i in y.indices) {
dataRI[0][i] = y[i].real
dataRI[1][i] = y[i].imaginary
}
transformInPlace(dataRI, DftNormalization.STANDARD, TransformType.INVERSE)
return dataRI[0]
}
private fun Array<FloatArray>.toComplexArray(): Array<FComplex> {
return Array(this[0].size) {
FComplex(this[0][it], this[1][it])
}
}
// com.github.psambit9791.jdsp.transform.FastFourier.java:190
/**
* Returns the complex value of the fast fourier transformed sequence
* @param onlyPositive Set to True if non-mirrored output is required
* @throws java.lang.ExceptionInInitializerError if called before executing transform() method
* @return Complex[] The complex FFT output
*/
@Throws(ExceptionInInitializerError::class)
fun getComplex(output: Array<FComplex>, onlyPositive: Boolean): Array<FComplex> {
val dftout: Array<FComplex> = if (onlyPositive) {
val numBins: Int = output.size / 2 + 1
Array<FComplex>(numBins) { FComplex() }
}
else {
Array<FComplex>(output.size) { FComplex() }
}
System.arraycopy(output, 0, dftout, 0, dftout.size)
return dftout
}
// org.apache.commons.math3.transform.FastFouriesTransformer.java:214
/**
* Computes the standard transform of the specified complex data. The
* computation is done in place. The input data is laid out as follows
* <ul>
* <li>{@code dataRI[0][i]} is the real part of the {@code i}-th data point,</li>
* <li>{@code dataRI[1][i]} is the imaginary part of the {@code i}-th data point.</li>
* </ul>
*
* @param dataRI the two dimensional array of real and imaginary parts of the data
* @param normalization the normalization to be applied to the transformed data
* @param type the type of transform (forward, inverse) to be performed
* @throws DimensionMismatchException if the number of rows of the specified
* array is not two, or the array is not rectangular
* @throws MathIllegalArgumentException if the number of data points is not
* a power of two
*/
private fun transformInPlace(dataRI: Array<FloatArray>, normalization: DftNormalization, type: TransformType) {
val dataR = dataRI[0]
val dataI = dataRI[1]
val n = dataR.size
if (n == 1) {
return
}
else if (n == 2) {
val srcR0 = dataR[0]
val srcI0 = dataI[0]
val srcR1 = dataR[1]
val srcI1 = dataI[1]
// X_0 = x_0 + x_1
dataR[0] = srcR0 + srcR1
dataI[0] = srcI0 + srcI1
// X_1 = x_0 - x_1
dataR[1] = srcR0 - srcR1
dataI[1] = srcI0 - srcI1
normalizeTransformedData(dataRI, normalization, type)
return
}
bitReversalShuffle2(dataR, dataI)
// Do 4-term DFT.
// Do 4-term DFT.
if (type == TransformType.INVERSE) {
var i0 = 0
while (i0 < n) {
val i1 = i0 + 1
val i2 = i0 + 2
val i3 = i0 + 3
val srcR0 = dataR[i0]
val srcI0 = dataI[i0]
val srcR1 = dataR[i2]
val srcI1 = dataI[i2]
val srcR2 = dataR[i1]
val srcI2 = dataI[i1]
val srcR3 = dataR[i3]
val srcI3 = dataI[i3]
// 4-term DFT
// X_0 = x_0 + x_1 + x_2 + x_3
dataR[i0] = srcR0 + srcR1 + srcR2 + srcR3
dataI[i0] = srcI0 + srcI1 + srcI2 + srcI3
// X_1 = x_0 - x_2 + j * (x_3 - x_1)
dataR[i1] = srcR0 - srcR2 + (srcI3 - srcI1)
dataI[i1] = srcI0 - srcI2 + (srcR1 - srcR3)
// X_2 = x_0 - x_1 + x_2 - x_3
dataR[i2] = srcR0 - srcR1 + srcR2 - srcR3
dataI[i2] = srcI0 - srcI1 + srcI2 - srcI3
// X_3 = x_0 - x_2 + j * (x_1 - x_3)
dataR[i3] = srcR0 - srcR2 + (srcI1 - srcI3)
dataI[i3] = srcI0 - srcI2 + (srcR3 - srcR1)
i0 += 4
}
}
else {
var i0 = 0
while (i0 < n) {
val i1 = i0 + 1
val i2 = i0 + 2
val i3 = i0 + 3
val srcR0 = dataR[i0]
val srcI0 = dataI[i0]
val srcR1 = dataR[i2]
val srcI1 = dataI[i2]
val srcR2 = dataR[i1]
val srcI2 = dataI[i1]
val srcR3 = dataR[i3]
val srcI3 = dataI[i3]
// 4-term DFT
// X_0 = x_0 + x_1 + x_2 + x_3
dataR[i0] = srcR0 + srcR1 + srcR2 + srcR3
dataI[i0] = srcI0 + srcI1 + srcI2 + srcI3
// X_1 = x_0 - x_2 + j * (x_3 - x_1)
dataR[i1] = srcR0 - srcR2 + (srcI1 - srcI3)
dataI[i1] = srcI0 - srcI2 + (srcR3 - srcR1)
// X_2 = x_0 - x_1 + x_2 - x_3
dataR[i2] = srcR0 - srcR1 + srcR2 - srcR3
dataI[i2] = srcI0 - srcI1 + srcI2 - srcI3
// X_3 = x_0 - x_2 + j * (x_1 - x_3)
dataR[i3] = srcR0 - srcR2 + (srcI3 - srcI1)
dataI[i3] = srcI0 - srcI2 + (srcR1 - srcR3)
i0 += 4
}
}
var lastN0 = 4
var lastLogN0 = 2
while (lastN0 < n) {
val n0 = lastN0 shl 1
val logN0 = lastLogN0 + 1
val wSubN0R = W_SUB_N_R[logN0]
var wSubN0I = W_SUB_N_I[logN0]
if (type == TransformType.INVERSE) {
wSubN0I = -wSubN0I
}
// Combine even/odd transforms of size lastN0 into a transform of size N0 (lastN0 * 2).
var destEvenStartIndex = 0
while (destEvenStartIndex < n) {
val destOddStartIndex = destEvenStartIndex + lastN0
var wSubN0ToRR = 1f
var wSubN0ToRI = 0f
for (r in 0 until lastN0) {
val grR = dataR[destEvenStartIndex + r]
val grI = dataI[destEvenStartIndex + r]
val hrR = dataR[destOddStartIndex + r]
val hrI = dataI[destOddStartIndex + r]
// dest[destEvenStartIndex + r] = Gr + WsubN0ToR * Hr
dataR[destEvenStartIndex + r] = grR + wSubN0ToRR * hrR - wSubN0ToRI * hrI
dataI[destEvenStartIndex + r] = grI + wSubN0ToRR * hrI + wSubN0ToRI * hrR
// dest[destOddStartIndex + r] = Gr - WsubN0ToR * Hr
dataR[destOddStartIndex + r] = grR - (wSubN0ToRR * hrR - wSubN0ToRI * hrI)
dataI[destOddStartIndex + r] = grI - (wSubN0ToRR * hrI + wSubN0ToRI * hrR)
// WsubN0ToR *= WsubN0R
val nextWsubN0ToRR = wSubN0ToRR * wSubN0R - wSubN0ToRI * wSubN0I
val nextWsubN0ToRI = wSubN0ToRR * wSubN0I + wSubN0ToRI * wSubN0R
wSubN0ToRR = nextWsubN0ToRR
wSubN0ToRI = nextWsubN0ToRI
}
destEvenStartIndex += n0
}
lastN0 = n0
lastLogN0 = logN0
}
normalizeTransformedData(dataRI, normalization, type)
}
/**
* Applies the proper normalization to the specified transformed data.
*
* @param dataRI the unscaled transformed data
* @param normalization the normalization to be applied
* @param type the type of transform (forward, inverse) which resulted in the specified data
*/
private fun normalizeTransformedData(
dataRI: Array<FloatArray>,
normalization: DftNormalization, type: TransformType
) {
val dataR = dataRI[0]
val dataI = dataRI[1]
val n = dataR.size
assert(dataI.size == n)
when (normalization) {
DftNormalization.STANDARD -> if (type == TransformType.INVERSE) {
val scaleFactor = 1f / n.toFloat()
var i = 0
while (i < n) {
dataR[i] *= scaleFactor
dataI[i] *= scaleFactor
i++
}
}
DftNormalization.UNITARY -> {
val scaleFactor = (1.0 / FastMath.sqrt(n.toDouble())).toFloat()
var i = 0
while (i < n) {
dataR[i] *= scaleFactor
dataI[i] *= scaleFactor
i++
}
}
else -> throw MathIllegalStateException()
}
}
/**
* Performs identical index bit reversal shuffles on two arrays of identical
* size. Each element in the array is swapped with another element based on
* the bit-reversal of the index. For example, in an array with length 16,
* item at binary index 0011 (decimal 3) would be swapped with the item at
* binary index 1100 (decimal 12).
*
* @param a the first array to be shuffled
* @param b the second array to be shuffled
*/
private fun bitReversalShuffle2(a: FloatArray, b: FloatArray) {
val n = a.size
assert(b.size == n)
val halfOfN = n shr 1
var j = 0
for (i in 0 until n) {
if (i < j) {
// swap indices i & j
var temp = a[i]
a[i] = a[j]
a[j] = temp
temp = b[i]
b[i] = b[j]
b[j] = temp
}
var k = halfOfN
while (k in 1..j) {
j -= k
k = k shr 1
}
j += k
}
}
private val W_SUB_N_R = FFTConsts.W_SUB_N_R.map { it.toFloat() }.toFloatArray()
private val W_SUB_N_I = FFTConsts.W_SUB_N_I.map { it.toFloat() }.toFloatArray()
}