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package breeze.signal
import breeze.linalg._
import breeze.linalg.{sum, DenseMatrix, DenseVector}
import breeze.generic.UFunc
import breeze.math.Complex
import breeze.signal.support.JTransformsSupport._
import breeze.macros.expand
import breeze.numerics.{sin, cos}
/**
* Returns the discrete fourier transform of a DenseVector or DenseMatrix. Currently,
* DenseVector/DenseMatrix types of Double and Complex are supported. Scaling
* follows the common signal processing convention, i.e. no scaling on forward DFT,
* and 1/n scaling for the inverse DFT. Of note, fft(x: DenseMatrix[Double]) will
* perform the 2D fft in both row and column dimensions, as opposed to the MatLab
* toolbox syntax, which performs column-wise 1D fft.
* Implementation is via the implicit trait fft.Impl[ InputType, OutputType ],
* which is found in breeze.signal.support.fft.Impl.scala.
*
* @return
* @author ktakagaki, dlwh
*/
object fourierTr extends UFunc {
implicit val dvDouble1DFFT : fourierTr.Impl[DenseVector[Double], DenseVector[Complex]] = {
new fourierTr.Impl[DenseVector[Double], DenseVector[Complex]] {
def apply(v: DenseVector[Double]) = {
//reformat for input: note difference in format for input to complex fft
val tempArr = denseVectorDToTemp(v)
//actual action
val fft_instance = getD1DInstance(v.length)
fft_instance.realForwardFull( tempArr ) //does operation in place
//reformat for output
tempToDenseVector(tempArr)
}
}
}
implicit def dvDT1DFFT_Float: Impl[DenseVector[Float], DenseVector[Complex]] = {
new Impl[DenseVector[Float], DenseVector[Complex]] {
def apply(v: DenseVector[Float]) = fourierTr( v.map( _.toDouble) )
}
}
implicit def dvDT1DFFT_Int: Impl[DenseVector[Int], DenseVector[Complex]] = {
new Impl[DenseVector[Int], DenseVector[Complex]] {
def apply(v: DenseVector[Int]) = fourierTr( v.map( _.toDouble) )
}
}
implicit def dvDT1DFFT_Long: Impl[DenseVector[Long], DenseVector[Complex]] = {
new Impl[DenseVector[Long], DenseVector[Complex]] {
def apply(v: DenseVector[Long]) = fourierTr( v.map( _.toDouble) )
}
}
implicit val dvComplex1DFFT : fourierTr.Impl[DenseVector[Complex], DenseVector[Complex]] = {
new fourierTr.Impl[DenseVector[Complex], DenseVector[Complex]] {
def apply(v: DenseVector[Complex]) = {
//reformat for input: note difference in format for input to real fft
val tempArr = denseVectorCToTemp(v)
//actual action
val fft_instance = getD1DInstance(v.length)
fft_instance.complexForward( tempArr ) //does operation in place
//reformat for output
tempToDenseVector(tempArr)
}
}
}
implicit val dmComplex2DFFT : fourierTr.Impl[DenseMatrix[Complex], DenseMatrix[Complex]] = {
new fourierTr.Impl[DenseMatrix[Complex], DenseMatrix[Complex]] {
def apply(v: DenseMatrix[Complex]) = {
//reformat for input: note difference in format for input to real fft
val tempMat = denseMatrixCToTemp(v)
//actual action
val fft_instance = getD2DInstance(v.rows, v.cols)
fft_instance.complexForward( tempMat ) //does operation in place
//reformat for output
tempToDenseMatrix(tempMat, v.rows, v.cols)
}
}
}
implicit val dmDouble2DFFT : fourierTr.Impl[DenseMatrix[Double], DenseMatrix[Complex]] = {
new fourierTr.Impl[DenseMatrix[Double], DenseMatrix[Complex]] {
def apply(v: DenseMatrix[Double]) = {
//reformat for input
val tempMat = denseMatrixDToTemp(v)
//actual action
val fft_instance = getD2DInstance(v.rows, v.cols)
fft_instance.complexForward( tempMat ) //does operation in place
//ToDo this could be optimized to use realFullForward for speed, but only if the indexes are powers of two
//reformat for output
tempToDenseMatrix(tempMat, v.rows, v.cols)
}
}
}
implicit val dvDouble1DFourierRange: Impl2[DenseVector[Double], Range, DenseVector[Complex]] = {
new Impl2[DenseVector[Double], Range, DenseVector[Complex]] {
def apply(v: DenseVector[Double], rangeNegative: Range ): DenseVector[Complex] = {
val range = rangeNegative.getRangeWithoutNegativeIndexes( v.length )
//ToDo check lengths and throw errors
val tempret =
for( k <- range ) yield {
val pk2_N = scala.math.Pi * k * 2d / v.length
sum(DenseVector.tabulate[Complex](v.length)( (n: Int) => {
val nd = n.toDouble
Complex(cos(pk2_N * nd), sin(pk2_N * nd))
} ))
}
new DenseVector[Complex]( tempret.toArray[Complex] )
}
}
}
}
