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Diffstat (limited to 'Game/Code/lib/fft/UFFT.pas')
-rw-r--r-- | Game/Code/lib/fft/UFFT.pas | 345 |
1 files changed, 345 insertions, 0 deletions
diff --git a/Game/Code/lib/fft/UFFT.pas b/Game/Code/lib/fft/UFFT.pas new file mode 100644 index 00000000..e97812f6 --- /dev/null +++ b/Game/Code/lib/fft/UFFT.pas @@ -0,0 +1,345 @@ +{********************************************************************** + + FFT.cpp + + Dominic Mazzoni + + September 2000 + +*********************************************************************** + +Fast Fourier Transform routines. + + This file contains a few FFT routines, including a real-FFT + routine that is almost twice as fast as a normal complex FFT, + and a power spectrum routine when you know you don't care + about phase information. + + Some of this code was based on a free implementation of an FFT + by Don Cross, available on the web at: + + http://www.intersrv.com/~dcross/fft.html + + The basic algorithm for his code was based on Numerican Recipes + in Fortran. I optimized his code further by reducing array + accesses, caching the bit reversal table, and eliminating + float-to-double conversions, and I added the routines to + calculate a real FFT and a real power spectrum. + +*********************************************************************** + + Salvo Ventura - November 2006 + Added more window functions: + * 4: Blackman + * 5: Blackman-Harris + * 6: Welch + * 7: Gaussian(a=2.5) + * 8: Gaussian(a=3.5) + * 9: Gaussian(a=4.5) + +*********************************************************************** + + This file is part of Audacity 1.3.4 beta (http://audacity.sourceforge.net/) + Ported to Pascal by the UltraStar Deluxe Team +} + +unit UFFT; + +{$ifdef fpc} + {$mode delphi}{$H+} +{$endif} + +interface +type + TSingleArray = array[0..0] of Single; + PSingleArray = ^TSingleArray; + +procedure PowerSpectrum(NumSamples: Integer; In_, Out_: PSingleArray); +procedure WindowFunc(NumSamples: Integer; in_: PSingleArray); inline; + +implementation + +uses + SysUtils; + +type TIntArray = array[0..0] of Integer; +type TIntIntArray = array[0..0] of ^TIntArray; +var gFFTBitTable: ^TIntIntArray; +const MaxFastBits: Integer = 16; + +function IsPowerOfTwo(x: Integer): Boolean; +begin + if (x < 2) then + result := false + else if ((x and (x - 1)) <> 0) then { Thanks to 'byang' for this cute trick! } + result := false + else + result := true; +end; + +function NumberOfBitsNeeded(PowerOfTwo: Integer): Integer; +var i: Integer; +begin + if (PowerOfTwo < 2) then begin + Writeln(ErrOutput, Format('Error: FFT called with size %d\n', [PowerOfTwo])); + Abort; + end; + + i := 0; + while(true) do begin + if (PowerOfTwo and (1 shl i) <> 0) then begin + result := i; + Exit; + end; + Inc(i); + end; +end; + +function ReverseBits(index, NumBits: Integer): Integer; +var + i, rev: Integer; +begin + rev := 0; + for i := 0 to NumBits-1 do begin + rev := (rev shl 1) or (index and 1); + index := index shr 1; + end; + + result := rev; +end; + +procedure InitFFT(); +var + len: Integer; + b, i: Integer; +begin + GetMem(gFFTBitTable, MaxFastBits * sizeof(PSingle)); + + len := 2; + for b := 1 to MaxFastBits do begin + GetMem(gFFTBitTable^[b - 1], len * sizeof(Single)); + for i := 0 to len-1 do + gFFTBitTable^[b - 1][i] := ReverseBits(i, b); + len := len shl 1; + end; +end; + +function FastReverseBits(i, NumBits: Integer): Integer; inline; +begin + if (NumBits <= MaxFastBits) then + result := gFFTBitTable[NumBits - 1][i] + else + result := ReverseBits(i, NumBits); +end; + +{* + * Complex Fast Fourier Transform + *} +procedure FFT(NumSamples: Integer; + InverseTransform: boolean; + RealIn, ImagIn, RealOut, ImagOut: PSingleArray); +var + NumBits: Integer; { Number of bits needed to store indices } + i, j, k, n: Integer; + BlockSize, BlockEnd: Integer; + delta_angle: Double; + angle_numerator: Double; + tr, ti: Double; { temp real, temp imaginary } + sm2, sm1, cm2, cm1: Double; + w: Double; + ar0, ar1, ar2, ai0, ai1, ai2: Double; + denom: Single; +begin + + angle_numerator := 2.0 * Pi; + + if (not IsPowerOfTwo(NumSamples)) then begin + Writeln(ErrOutput, Format('%d is not a power of two', [NumSamples])); + Abort; + end; + + if (gFFTBitTable = nil) then + InitFFT(); + + if (InverseTransform) then + angle_numerator := -angle_numerator; + + NumBits := NumberOfBitsNeeded(NumSamples); + + { + ** Do simultaneous data copy and bit-reversal ordering into outputs... + } + + for i := 0 to NumSamples-1 do begin + j := FastReverseBits(i, NumBits); + RealOut[j] := RealIn[i]; + if(ImagIn = nil) then + ImagOut[j] := 0.0 + else + ImagOut[j] := ImagIn[i]; + end; + + { + ** Do the FFT itself... + } + + BlockEnd := 1; + BlockSize := 2; + while(BlockSize <= NumSamples) do + begin + + delta_angle := angle_numerator / BlockSize; + + sm2 := sin(-2 * delta_angle); + sm1 := sin(-delta_angle); + cm2 := cos(-2 * delta_angle); + cm1 := cos(-delta_angle); + w := 2 * cm1; + + i := 0; + while(i < NumSamples) do + begin + ar2 := cm2; + ar1 := cm1; + + ai2 := sm2; + ai1 := sm1; + + j := i; + for n := 0 to BlockEnd-1 do + begin + ar0 := w * ar1 - ar2; + ar2 := ar1; + ar1 := ar0; + + ai0 := w * ai1 - ai2; + ai2 := ai1; + ai1 := ai0; + + k := j + BlockEnd; + tr := ar0 * RealOut[k] - ai0 * ImagOut[k]; + ti := ar0 * ImagOut[k] + ai0 * RealOut[k]; + + RealOut[k] := RealOut[j] - tr; + ImagOut[k] := ImagOut[j] - ti; + + RealOut[j] := RealOut[j] + tr; + ImagOut[j] := ImagOut[j] + ti; + + Inc(j); + end; + + Inc(i, BlockSize); + end; + + BlockEnd := BlockSize; + BlockSize := BlockSize shl 1; + end; + + { + ** Need to normalize if inverse transform... + } + + if (InverseTransform) then begin + denom := NumSamples; + + for i := 0 to NumSamples-1 do begin + RealOut[i] := RealOut[i] / denom; + ImagOut[i] := ImagOut[i] / denom; + end; + end; +end; + +{* + * PowerSpectrum + * + * This function computes the same as RealFFT, above, but + * adds the squares of the real and imaginary part of each + * coefficient, extracting the power and throwing away the + * phase. + * + * For speed, it does not call RealFFT, but duplicates some + * of its code. + *} +procedure PowerSpectrum(NumSamples: Integer; In_, Out_: PSingleArray); +var + Half: Integer; + i: Integer; + theta: Single; + tmpReal, tmpImag, RealOut, ImagOut: PSingleArray; + wtemp: Single; + wpr, wpi, wr, wi: Single; + i3: Integer; + h1r, h1i, h2r, h2i, rt, it: Single; +begin + Half := NumSamples div 2; + + theta := Pi / Half; + + GetMem(tmpReal, Half * sizeof(Single)); + GetMem(tmpImag, Half * sizeof(Single)); + GetMem(RealOut, Half * sizeof(Single)); + GetMem(ImagOut, Half * sizeof(Single)); + + for i := 0 to Half-1 do begin + tmpReal[i] := In_[2 * i]; + tmpImag[i] := In_[2 * i + 1]; + end; + + FFT(Half, false, tmpReal, tmpImag, RealOut, ImagOut); + + wtemp := sin(0.5 * theta); + + wpr := -2.0 * wtemp * wtemp; + wpi := sin(theta); + wr := 1.0 + wpr; + wi := wpi; + + for i := 1 to (Half div 2)-1 do + begin + i3 := Half - i; + + h1r := 0.5 * (RealOut[i] + RealOut[i3]); + h1i := 0.5 * (ImagOut[i] - ImagOut[i3]); + h2r := 0.5 * (ImagOut[i] + ImagOut[i3]); + h2i := -0.5 * (RealOut[i] - RealOut[i3]); + + rt := h1r + wr * h2r - wi * h2i; + it := h1i + wr * h2i + wi * h2r; + + Out_[i] := rt * rt + it * it; + + rt := h1r - wr * h2r + wi * h2i; + it := -h1i + wr * h2i + wi * h2r; + + Out_[i3] := rt * rt + it * it; + + wtemp := wr; + wr := wtemp * wpr - wi * wpi + wr; + wi := wi * wpr + wtemp * wpi + wi; + end; + + h1r := RealOut[0]; + rt := h1r + ImagOut[0]; + it := h1r - ImagOut[0]; + Out_[0] := rt * rt + it * it; + + rt := RealOut[Half div 2]; + it := ImagOut[Half div 2]; + Out_[Half div 2] := rt * rt + it * it; + + FreeMem(tmpReal); + FreeMem(tmpImag); + FreeMem(RealOut); + FreeMem(ImagOut); +end; + +procedure WindowFunc(NumSamples: Integer; in_: PSingleArray); inline; +var + i: Integer; +begin + for i := 0 to NumSamples-1 do + in_[i] := in_[i] * (0.50 - 0.50 * cos(2 * Pi * i / (NumSamples - 1))); +end; + +end. |