aboutsummaryrefslogblamecommitdiffstats
path: root/us_maker_edition/src/lib/fft/UFFT.pas
blob: 5a056a8c9c615de588e20dcf446717f48d17c1d2 (plain) (tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602

























































































































































































































































































































































































































































































































































































































                                                                                                                                                                       
{**********************************************************************

  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}
  {$H+} // Use long strings
{$ENDIF}

interface
type
  TSingleArray = array[0 .. (MaxInt div SizeOf(Single))-1] of Single;
  PSingleArray = ^TSingleArray;

  TFFTWindowFunc = (
    fwfRectangular,
    fwfBartlett,
    fwfHamming,
    fwfHanning,
    fwfBlackman,
    fwfBlackman_Harris,
    fwfWelch,
    fwfGaussian2_5,
    fwfGaussian3_5,
    fwfGaussian4_5
  );
  
const
  FFTWindowName: array[TFFTWindowFunc] of string = (
     'Rectangular',
     'Bartlett',
     'Hamming',
     'Hanning',
     'Blackman',
     'Blackman-Harris',
     'Welch',
     'Gaussian(a=2.5)',
     'Gaussian(a=3.5)',
     'Gaussian(a=4.5)'
  );

(*
 * This is the function you will use the most often.
 * Given an array of floats, this will compute the power
 * spectrum by doing a Real FFT and then computing the
 * sum of the squares of the real and imaginary parts.
 * Note that the output array is half the length of the
 * input array, and that NumSamples must be a power of two.
 *)
procedure PowerSpectrum(NumSamples: Integer; In_, Out_: PSingleArray);

(*
 * Computes an FFT when the input data is real but you still
 * want complex data as output.  The output arrays are half
 * the length of the input, and NumSamples must be a power of
 * two.
 *)
procedure RealFFT(NumSamples: integer;
                  RealIn, RealOut, ImagOut: PSingleArray);

(*
 * Computes a FFT of complex input and returns complex output.
 * Currently this is the only function here that supports the
 * inverse transform as well.
 *)
procedure FFT(NumSamples: Integer;
              InverseTransform: boolean;
              RealIn, ImagIn, RealOut, ImagOut: PSingleArray);

(*
 * Applies a windowing function to the data in place
 *
 * 0: Rectangular (no window)
 * 1: Bartlett    (triangular)
 * 2: Hamming
 * 3: Hanning
 * 4: Blackman
 * 5: Blackman-Harris
 * 6: Welch
 * 7: Gaussian(a=2.5)
 * 8: Gaussian(a=3.5)
 * 9: Gaussian(a=4.5)
 *)
procedure WindowFunc(whichFunction: TFFTWindowFunc; NumSamples: Integer; in_: PSingleArray);

(*
 * Returns the name of the windowing function (for UI display)
 *)
function WindowFuncName(whichFunction: TFFTWindowFunc): string;

(*
 * Returns the number of windowing functions supported
 *)
function NumWindowFuncs(): integer;


implementation

uses
  SysUtils;

type TIntArray = array[0 .. (MaxInt div SizeOf(Integer))-1] of Integer;
type PIntArray = ^TIntArray;
type TIntIntArray = array[0 .. (MaxInt div SizeOf(PIntArray))-1] of PIntArray;
type PIntIntArray = ^TIntIntArray;
var gFFTBitTable: PIntIntArray;
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; {$IFDEF HasInline}inline;{$ENDIF}
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;

(*
 * Real Fast Fourier Transform
 *
 * This function was based on the code in Numerical Recipes in C.
 * In Num. Rec., the inner loop is based on a single 1-based array
 * of interleaved real and imaginary numbers.  Because we have two
 * separate zero-based arrays, our indices are quite different.
 * Here is the correspondence between Num. Rec. indices and our indices:
 *
 * i1  <->  real[i]
 * i2  <->  imag[i]
 * i3  <->  real[n/2-i]
 * i4  <->  imag[n/2-i]
 *)
procedure RealFFT(NumSamples: integer; RealIn, RealOut, ImagOut: PSingleArray);
var
  Half: Integer;
  i: Integer;
  theta: Single;
  tmpReal, tmpImag: PSingleArray;
  wtemp: Single;
  wpr, wpi, wr, wi: Single;
  i3: Integer;
  h1r, h1i, h2r, h2i: Single;
begin
   Half := NumSamples div 2;

   theta := Pi / Half;

   GetMem(tmpReal, Half * sizeof(Single));
   GetMem(tmpImag, Half * sizeof(Single));

   for i := 0 to Half-1 do
   begin
      tmpReal[i] := RealIn[2 * i];
      tmpImag[i] := RealIn[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]);

      RealOut[i] := h1r + wr * h2r - wi * h2i;
      ImagOut[i] := h1i + wr * h2i + wi * h2r;
      RealOut[i3] := h1r - wr * h2r + wi * h2i;
      ImagOut[i3] := -h1i + wr * h2i + wi * h2r;

      wtemp := wr;
      wr := wtemp * wpr - wi * wpi + wr;
      wi := wi * wpr + wtemp * wpi + wi;
   end;

   h1r := RealOut[0];
   RealOut[0] := h1r + ImagOut[0];
   ImagOut[0] := h1r - ImagOut[0];

   FreeMem(tmpReal);
   FreeMem(tmpImag);
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;

(*
 * Windowing Functions
 *)
function NumWindowFuncs(): integer;
begin
  Result := Length(FFTWindowName);
end;

function WindowFuncName(whichFunction: TFFTWindowFunc): string;
begin
  Result := FFTWindowName[whichFunction];
end;

procedure WindowFunc(whichFunction: TFFTWindowFunc; NumSamples: Integer; in_: PSingleArray);
var
  i: Integer;
  A: Single;
begin
  case whichFunction of
    fwfBartlett:
    begin
      // Bartlett (triangular) window
      for i := 0 to (NumSamples div 2)-1 do
      begin
        in_[i] := in_[i] * (i / (NumSamples / 2));
        in_[i + (NumSamples div 2)] :=
            in_[i + (NumSamples div 2)] *
            (1.0 - (i / (NumSamples / 2)));
      end;
    end;
    fwfHamming:
    begin
      // Hamming
      for i := 0 to NumSamples-1 do
      begin
        in_[i] := in_[i] * (0.54 - 0.46 * cos(2 * Pi * i / (NumSamples - 1)));
      end;
    end;
    fwfHanning:
    begin
      // Hanning
      for i := 0 to NumSamples-1 do
      begin
        in_[i] := in_[i] * (0.50 - 0.50 * cos(2 * Pi * i / (NumSamples - 1)));
      end;
    end;
    fwfBlackman:
    begin
      // Blackman
      for i := 0 to NumSamples-1 do
      begin
        in_[i] := in_[i] * (0.42 - 0.5 * cos (2 * Pi * i / (NumSamples - 1)) + 0.08 * cos (4 * Pi * i / (NumSamples - 1)));
      end;
    end;
    fwfBlackman_Harris:
    begin
      // Blackman-Harris
      for i := 0 to NumSamples-1 do
      begin
        in_[i] := in_[i] * (0.35875 - 0.48829 * cos(2 * Pi * i /(NumSamples-1)) + 0.14128 * cos(4 * Pi * i/(NumSamples-1)) - 0.01168 * cos(6 * Pi * i/(NumSamples-1)));
      end;
    end;
    fwfWelch:
    begin
      // Welch
      for i := 0 to NumSamples-1 do
      begin
        in_[i] := in_[i] * 4*i/NumSamples*(1-(i/NumSamples));
      end;
    end;
    fwfGaussian2_5:
    begin
      // Gaussian (a=2.5)
      // Precalculate some values, and simplify the fmla to try and reduce overhead
      A := -2*2.5*2.5;

      for i := 0 to NumSamples-1 do
      begin
        // full
        // in_[i] := in_[i] * exp(-0.5*(A*((i-NumSamples/2)/NumSamples/2))*(A*((i-NumSamples/2)/NumSamples/2)));
        // reduced
        //in_[i] := in_[i] * exp(A*(0.25 + ((i/NumSamples)*(i/NumSamples)) - (i/NumSamples)));
      end;
    end;
    fwfGaussian3_5:
    begin
      // Gaussian (a=3.5)
      A := -2*3.5*3.5;

      for i := 0 to NumSamples-1 do
      begin
        // reduced
        in_[i] := in_[i] * exp(A*(0.25 + ((i/NumSamples)*(i/NumSamples)) - (i/NumSamples)));
      end;
    end;
    fwfGaussian4_5:
    begin
      // Gaussian (a=4.5)
      A := -2*4.5*4.5;

      for i := 0 to NumSamples-1 do
      begin
        // reduced
        in_[i] := in_[i] * exp(A*(0.25 + ((i/NumSamples)*(i/NumSamples)) - (i/NumSamples)));
      end;
    end;
  end;
end;

end.