| 1 | (*****************************************************************************
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| 2 |
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| 3 | DIGITAL SIGNAL PROCESSING TOOLS
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| 4 | Version 1.03, 2001/06/15
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| 5 | (c) 1999 - Laurent de Soras
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| 6 |
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| 7 | FFTReal.h
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| 8 | Fourier transformation of real number arrays.
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| 9 | Portable ISO C++
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| 10 |
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| 11 | ------------------------------------------------------------------------------
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| 12 |
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| 13 | LEGAL
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| 14 |
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| 15 | Source code may be freely used for any purpose, including commercial
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| 16 | applications. Programs must display in their "About" dialog-box (or
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| 17 | documentation) a text telling they use these routines by Laurent de Soras.
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| 18 | Modified source code can be distributed, but modifications must be clearly
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| 19 | indicated.
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| 20 |
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| 21 | CONTACT
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| 22 |
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| 23 | Laurent de Soras
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| 24 | 92 avenue Albert 1er
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| 25 | 92500 Rueil-Malmaison
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| 26 | France
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| 27 |
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| 28 | [email protected]
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| 29 |
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| 30 | ------------------------------------------------------------------------------
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| 31 |
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| 32 | Translation to ObjectPascal by :
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| 33 | Frederic Vanmol
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| 34 | [email protected]
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| 35 |
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| 36 | *****************************************************************************)
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| 37 |
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| 38 |
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| 39 | unit
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| 40 | FFTReal;
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| 41 |
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| 42 | interface
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| 43 |
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| 44 | uses
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| 45 | Windows;
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| 46 |
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| 47 | (* Change this typedef to use a different floating point type in your FFTs
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| 48 | (i.e. float, double or long double). *)
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| 49 | type
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| 50 | pflt_t = ^flt_t;
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| 51 | flt_t = single;
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| 52 |
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| 53 | pflt_array = ^flt_array;
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| 54 | flt_array = array[0..0] of flt_t;
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| 55 |
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| 56 | plongarray = ^longarray;
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| 57 | longarray = array[0..0] of longint;
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| 58 |
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| 59 | const
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| 60 | sizeof_flt : longint = SizeOf(flt_t);
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| 61 |
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| 62 |
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| 63 |
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| 64 | type
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| 65 | // Bit reversed look-up table nested class
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| 66 | TBitReversedLUT = class
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| 67 | private
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| 68 | _ptr : plongint;
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| 69 | public
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| 70 | constructor Create(const nbr_bits: integer);
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| 71 | destructor Destroy; override;
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| 72 | function get_ptr: plongint;
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| 73 | end;
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| 74 |
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| 75 | // Trigonometric look-up table nested class
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| 76 | TTrigoLUT = class
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| 77 | private
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| 78 | _ptr : pflt_t;
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| 79 | public
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| 80 | constructor Create(const nbr_bits: integer);
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| 81 | destructor Destroy; override;
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| 82 | function get_ptr(const level: integer): pflt_t;
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| 83 | end;
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| 84 |
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| 85 | TFFTReal = class
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| 86 | private
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| 87 | _bit_rev_lut : TBitReversedLUT;
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| 88 | _trigo_lut : TTrigoLUT;
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| 89 | _sqrt2_2 : flt_t;
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| 90 | _length : longint;
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| 91 | _nbr_bits : integer;
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| 92 | _buffer_ptr : pflt_t;
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| 93 | public
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| 94 | constructor Create(const length: longint);
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| 95 | destructor Destroy; override;
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| 96 |
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| 97 | procedure do_fft(f: pflt_array; const x: pflt_array);
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| 98 | procedure do_ifft(const f: pflt_array; x: pflt_array);
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| 99 | procedure rescale(x: pflt_array);
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| 100 | end;
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| 101 |
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| 102 |
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| 103 |
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| 104 |
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| 105 |
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| 106 |
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| 107 |
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| 108 | implementation
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| 109 |
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| 110 | uses
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| 111 | Math;
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| 112 |
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| 113 | { TBitReversedLUT }
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| 114 |
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| 115 | constructor TBitReversedLUT.Create(const nbr_bits: integer);
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| 116 | var
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| 117 | length : longint;
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| 118 | cnt : longint;
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| 119 | br_index : longint;
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| 120 | bit : longint;
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| 121 | begin
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| 122 | inherited Create;
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| 123 |
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| 124 | length := 1 shl nbr_bits;
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| 125 | GetMem(_ptr, length*SizeOf(longint));
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| 126 |
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| 127 | br_index := 0;
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| 128 | plongarray(_ptr)^[0] := 0;
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| 129 | for cnt := 1 to length-1 do
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| 130 | begin
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| 131 | // ++br_index (bit reversed)
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| 132 | bit := length shr 1;
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| 133 | br_index := br_index xor bit;
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| 134 | while br_index and bit = 0 do
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| 135 | begin
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| 136 | bit := bit shr 1;
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| 137 | br_index := br_index xor bit;
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| 138 | end;
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| 139 |
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| 140 | plongarray(_ptr)^[cnt] := br_index;
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| 141 | end;
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| 142 | end;
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| 143 |
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| 144 | destructor TBitReversedLUT.Destroy;
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| 145 | begin
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| 146 | FreeMem(_ptr);
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| 147 | _ptr := nil;
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| 148 | inherited;
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| 149 | end;
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| 150 |
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| 151 | function TBitReversedLUT.get_ptr: plongint;
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| 152 | begin
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| 153 | Result := _ptr;
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| 154 | end;
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| 155 |
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| 156 | { TTrigLUT }
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| 157 |
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| 158 | constructor TTrigoLUT.Create(const nbr_bits: integer);
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| 159 | var
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| 160 | total_len : longint;
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| 161 | PI : double;
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| 162 | level : integer;
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| 163 | level_len : longint;
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| 164 | level_ptr : pflt_array;
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| 165 | mul : double;
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| 166 | i : longint;
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| 167 | begin
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| 168 | inherited Create;
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| 169 |
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| 170 | _ptr := nil;
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| 171 |
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| 172 | if (nbr_bits > 3) then
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| 173 | begin
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| 174 | total_len := (1 shl (nbr_bits - 1)) - 4;
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| 175 | GetMem(_ptr, total_len * sizeof_flt);
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| 176 |
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| 177 | PI := ArcTan(1) * 4;
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| 178 | for level := 3 to nbr_bits-1 do
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| 179 | begin
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| 180 | level_len := 1 shl (level - 1);
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| 181 | level_ptr := pointer(get_ptr(level));
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| 182 | mul := PI / (level_len shl 1);
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| 183 |
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| 184 | for i := 0 to level_len-1 do
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| 185 | level_ptr^[i] := cos(i * mul);
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| 186 | end;
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| 187 | end;
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| 188 | end;
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| 189 |
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| 190 | destructor TTrigoLUT.Destroy;
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| 191 | begin
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| 192 | FreeMem(_ptr);
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| 193 | _ptr := nil;
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| 194 | inherited;
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| 195 | end;
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| 196 |
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| 197 | function TTrigoLUT.get_ptr(const level: integer): pflt_t;
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| 198 | var
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| 199 | tempp : pflt_t;
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| 200 | begin
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| 201 | tempp := _ptr;
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| 202 | inc(tempp, (1 shl (level-1)) - 4);
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| 203 | Result := tempp;
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| 204 | end;
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| 205 |
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| 206 | { TFFTReal }
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| 207 |
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| 208 | constructor TFFTReal.Create(const length: longint);
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| 209 | begin
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| 210 | inherited Create;
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| 211 |
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| 212 | _length := length;
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| 213 | _nbr_bits := Floor(Ln(length) / Ln(2) + 0.5);
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| 214 | _bit_rev_lut := TBitReversedLUT.Create(Floor(Ln(length) / Ln(2) + 0.5));
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| 215 | _trigo_lut := TTrigoLUT.Create(Floor(Ln(length) / Ln(2) + 0.05));
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| 216 | _sqrt2_2 := Sqrt(2) * 0.5;
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| 217 |
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| 218 | _buffer_ptr := nil;
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| 219 | if _nbr_bits > 2 then
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| 220 | GetMem(_buffer_ptr, _length * sizeof_flt);
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| 221 | end;
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| 222 |
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| 223 | destructor TFFTReal.Destroy;
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| 224 | begin
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| 225 | if _buffer_ptr <> nil then
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| 226 | begin
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| 227 | FreeMem(_buffer_ptr);
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| 228 | _buffer_ptr := nil;
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| 229 | end;
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| 230 |
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| 231 | _bit_rev_lut.Free;
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| 232 | _bit_rev_lut := nil;
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| 233 | _trigo_lut.Free;
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| 234 | _trigo_lut := nil;
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| 235 |
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| 236 | inherited;
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| 237 | end;
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| 238 |
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| 239 | (*==========================================================================*/
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| 240 | /* Name: do_fft */
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| 241 | /* Description: Compute the FFT of the array. */
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| 242 | /* Input parameters: */
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| 243 | /* - x: pointer on the source array (time). */
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| 244 | /* Output parameters: */
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| 245 | /* - f: pointer on the destination array (frequencies). */
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| 246 | /* f [0...length(x)/2] = real values, */
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| 247 | /* f [length(x)/2+1...length(x)-1] = imaginary values of */
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| 248 | /* coefficents 1...length(x)/2-1. */
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| 249 | /*==========================================================================*)
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| 250 | procedure TFFTReal.do_fft(f: pflt_array; const x: pflt_array);
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| 251 | var
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| 252 | sf, df : pflt_array;
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| 253 | pass : integer;
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| 254 | nbr_coef : longint;
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| 255 | h_nbr_coef : longint;
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| 256 | d_nbr_coef : longint;
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| 257 | coef_index : longint;
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| 258 | bit_rev_lut_ptr : plongarray;
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| 259 | rev_index_0 : longint;
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| 260 | rev_index_1 : longint;
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| 261 | rev_index_2 : longint;
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| 262 | rev_index_3 : longint;
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| 263 | df2 : pflt_array;
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| 264 | n1, n2, n3 : integer;
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| 265 | sf_0, sf_2 : flt_t;
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| 266 | sqrt2_2 : flt_t;
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| 267 | v : flt_t;
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| 268 | cos_ptr : pflt_array;
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| 269 | i : longint;
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| 270 | sf1r, sf2r : pflt_array;
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| 271 | dfr, dfi : pflt_array;
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| 272 | sf1i, sf2i : pflt_array;
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| 273 | c, s : flt_t;
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| 274 | temp_ptr : pflt_array;
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| 275 | b_0, b_2 : flt_t;
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| 276 | begin
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| 277 | n1 := 1;
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| 278 | n2 := 2;
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| 279 | n3 := 3;
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| 280 |
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| 281 | (*______________________________________________
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| 282 | *
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| 283 | * General case
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| 284 | *______________________________________________
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| 285 | *)
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| 286 |
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| 287 | if _nbr_bits > 2 then
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| 288 | begin
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| 289 | if _nbr_bits and 1 <> 0 then
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| 290 | begin
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| 291 | df := pointer(_buffer_ptr);
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| 292 | sf := f;
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| 293 | end
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| 294 | else
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| 295 | begin
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| 296 | df := f;
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| 297 | sf := pointer(_buffer_ptr);
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| 298 | end;
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| 299 |
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| 300 | //
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| 301 | // Do the transformation in several passes
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| 302 | //
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| 303 |
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| 304 | // First and second pass at once
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| 305 | bit_rev_lut_ptr := pointer(_bit_rev_lut.get_ptr);
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| 306 | coef_index := 0;
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| 307 |
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| 308 | repeat
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| 309 | rev_index_0 := bit_rev_lut_ptr^[coef_index];
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| 310 | rev_index_1 := bit_rev_lut_ptr^[coef_index + 1];
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| 311 | rev_index_2 := bit_rev_lut_ptr^[coef_index + 2];
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| 312 | rev_index_3 := bit_rev_lut_ptr^[coef_index + 3];
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| 313 |
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| 314 | df2 := pointer(longint(df) + (coef_index*sizeof_flt));
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| 315 | df2^[n1] := x^[rev_index_0] - x^[rev_index_1];
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| 316 | df2^[n3] := x^[rev_index_2] - x^[rev_index_3];
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| 317 |
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| 318 | sf_0 := x^[rev_index_0] + x^[rev_index_1];
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| 319 | sf_2 := x^[rev_index_2] + x^[rev_index_3];
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| 320 |
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| 321 | df2^[0] := sf_0 + sf_2;
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| 322 | df2^[n2] := sf_0 - sf_2;
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| 323 |
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| 324 | inc(coef_index, 4);
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| 325 | until (coef_index >= _length);
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| 326 |
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| 327 |
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| 328 | // Third pass
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| 329 | coef_index := 0;
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| 330 | sqrt2_2 := _sqrt2_2;
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| 331 |
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| 332 | repeat
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| 333 | sf^[coef_index] := df^[coef_index] + df^[coef_index + 4];
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| 334 | sf^[coef_index + 4] := df^[coef_index] - df^[coef_index + 4];
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| 335 | sf^[coef_index + 2] := df^[coef_index + 2];
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| 336 | sf^[coef_index + 6] := df^[coef_index + 6];
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| 337 |
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| 338 | v := (df [coef_index + 5] - df^[coef_index + 7]) * sqrt2_2;
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| 339 | sf^[coef_index + 1] := df^[coef_index + 1] + v;
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| 340 | sf^[coef_index + 3] := df^[coef_index + 1] - v;
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| 341 |
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| 342 | v := (df^[coef_index + 5] + df^[coef_index + 7]) * sqrt2_2;
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| 343 | sf [coef_index + 5] := v + df^[coef_index + 3];
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| 344 | sf [coef_index + 7] := v - df^[coef_index + 3];
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| 345 |
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| 346 | inc(coef_index, 8);
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| 347 | until (coef_index >= _length);
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| 348 |
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| 349 |
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| 350 | // Next pass
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| 351 | for pass := 3 to _nbr_bits-1 do
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| 352 | begin
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| 353 | coef_index := 0;
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| 354 | nbr_coef := 1 shl pass;
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| 355 | h_nbr_coef := nbr_coef shr 1;
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| 356 | d_nbr_coef := nbr_coef shl 1;
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| 357 |
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| 358 | cos_ptr := pointer(_trigo_lut.get_ptr(pass));
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| 359 | repeat
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| 360 | sf1r := pointer(longint(sf) + (coef_index * sizeof_flt));
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| 361 | sf2r := pointer(longint(sf1r) + (nbr_coef * sizeof_flt));
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| 362 | dfr := pointer(longint(df) + (coef_index * sizeof_flt));
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| 363 | dfi := pointer(longint(dfr) + (nbr_coef * sizeof_flt));
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| 364 |
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| 365 | // Extreme coefficients are always real
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| 366 | dfr^[0] := sf1r^[0] + sf2r^[0];
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| 367 | dfi^[0] := sf1r^[0] - sf2r^[0]; // dfr [nbr_coef] =
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| 368 | dfr^[h_nbr_coef] := sf1r^[h_nbr_coef];
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| 369 | dfi^[h_nbr_coef] := sf2r^[h_nbr_coef];
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| 370 |
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| 371 | // Others are conjugate complex numbers
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| 372 | sf1i := pointer(longint(sf1r) + (h_nbr_coef * sizeof_flt));
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| 373 | sf2i := pointer(longint(sf1i) + (nbr_coef * sizeof_flt));
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| 374 |
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| 375 | for i := 1 to h_nbr_coef-1 do
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| 376 | begin
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| 377 | c := cos_ptr^[i]; // cos (i*PI/nbr_coef);
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| 378 | s := cos_ptr^[h_nbr_coef - i]; // sin (i*PI/nbr_coef);
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| 379 |
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| 380 | v := sf2r^[i] * c - sf2i^[i] * s;
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| 381 | dfr^[i] := sf1r^[i] + v;
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| 382 | dfi^[-i] := sf1r^[i] - v; // dfr [nbr_coef - i] =
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| 383 |
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| 384 | v := sf2r^[i] * s + sf2i^[i] * c;
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| 385 | dfi^[i] := v + sf1i^[i];
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| 386 | dfi^[nbr_coef - i] := v - sf1i^[i];
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| 387 | end;
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| 388 |
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| 389 | inc(coef_index, d_nbr_coef);
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| 390 | until (coef_index >= _length);
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| 391 |
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| 392 | // Prepare to the next pass
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| 393 | temp_ptr := df;
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| 394 | df := sf;
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| 395 | sf := temp_ptr;
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| 396 | end;
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| 397 | end
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| 398 |
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| 399 | (*______________________________________________
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| 400 | *
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| 401 | * Special cases
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| 402 | *______________________________________________
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| 403 | *)
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| 404 |
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| 405 | // 4-point FFT
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| 406 | else if _nbr_bits = 2 then
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| 407 | begin
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| 408 | f^[n1] := x^[0] - x^[n2];
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| 409 | f^[n3] := x^[n1] - x^[n3];
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| 410 |
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| 411 | b_0 := x^[0] + x^[n2];
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| 412 | b_2 := x^[n1] + x^[n3];
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| 413 |
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| 414 | f^[0] := b_0 + b_2;
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| 415 | f^[n2] := b_0 - b_2;
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| 416 | end
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| 417 |
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| 418 | // 2-point FFT
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| 419 | else if _nbr_bits = 1 then
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| 420 | begin
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| 421 | f^[0] := x^[0] + x^[n1];
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| 422 | f^[n1] := x^[0] - x^[n1];
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| 423 | end
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| 424 |
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| 425 | // 1-point FFT
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| 426 | else
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| 427 | f^[0] := x^[0];
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| 428 | end;
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| 429 |
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| 430 |
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| 431 | (*==========================================================================*/
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| 432 | /* Name: do_ifft */
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| 433 | /* Description: Compute the inverse FFT of the array. Notice that */
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| 434 | /* IFFT (FFT (x)) = x * length (x). Data must be */
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| 435 | /* post-scaled. */
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| 436 | /* Input parameters: */
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| 437 | /* - f: pointer on the source array (frequencies). */
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| 438 | /* f [0...length(x)/2] = real values, */
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| 439 | /* f [length(x)/2+1...length(x)-1] = imaginary values of */
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| 440 | /* coefficents 1...length(x)/2-1. */
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| 441 | /* Output parameters: */
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| 442 | /* - x: pointer on the destination array (time). */
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| 443 | /*==========================================================================*)
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| 444 | procedure TFFTReal.do_ifft(const f: pflt_array; x: pflt_array);
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| 445 | var
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| 446 | n1, n2, n3 : integer;
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| 447 | n4, n5, n6, n7 : integer;
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| 448 | sf, df, df_temp : pflt_array;
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| 449 | pass : integer;
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| 450 | nbr_coef : longint;
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| 451 | h_nbr_coef : longint;
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| 452 | d_nbr_coef : longint;
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| 453 | coef_index : longint;
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| 454 | cos_ptr : pflt_array;
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| 455 | i : longint;
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| 456 | sfr, sfi : pflt_array;
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| 457 | df1r, df2r : pflt_array;
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| 458 | df1i, df2i : pflt_array;
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| 459 | c, s, vr, vi : flt_t;
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| 460 | temp_ptr : pflt_array;
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| 461 | sqrt2_2 : flt_t;
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| 462 | bit_rev_lut_ptr : plongarray;
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| 463 | sf2 : pflt_array;
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| 464 | b_0, b_1, b_2, b_3 : flt_t;
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| 465 | begin
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| 466 | n1 := 1;
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| 467 | n2 := 2;
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| 468 | n3 := 3;
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| 469 | n4 := 4;
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| 470 | n5 := 5;
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| 471 | n6 := 6;
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| 472 | n7 := 7;
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| 473 |
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| 474 | (*______________________________________________
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| 475 | *
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| 476 | * General case
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| 477 | *______________________________________________
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| 478 | *)
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| 479 |
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| 480 | if _nbr_bits > 2 then
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| 481 | begin
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| 482 | sf := f;
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| 483 |
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| 484 | if _nbr_bits and 1 <> 0 then
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| 485 | begin
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| 486 | df := pointer(_buffer_ptr);
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| 487 | df_temp := x;
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| 488 | end
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| 489 | else
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| 490 | begin
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| 491 | df := x;
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| 492 | df_temp := pointer(_buffer_ptr);
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| 493 | end;
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| 494 |
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| 495 | // Do the transformation in several pass
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| 496 |
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| 497 | // First pass
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| 498 | for pass := _nbr_bits-1 downto 3 do
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| 499 | begin
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| 500 | coef_index := 0;
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| 501 | nbr_coef := 1 shl pass;
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| 502 | h_nbr_coef := nbr_coef shr 1;
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| 503 | d_nbr_coef := nbr_coef shl 1;
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| 504 |
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| 505 | cos_ptr := pointer(_trigo_lut.get_ptr(pass));
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| 506 |
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| 507 | repeat
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| 508 | sfr := pointer(longint(sf) + (coef_index*sizeof_flt));
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| 509 | sfi := pointer(longint(sfr) + (nbr_coef*sizeof_flt));
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| 510 | df1r := pointer(longint(df) + (coef_index*sizeof_flt));
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| 511 | df2r := pointer(longint(df1r) + (nbr_coef*sizeof_flt));
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| 512 |
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| 513 | // Extreme coefficients are always real
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| 514 | df1r^[0] := sfr^[0] + sfi^[0]; // + sfr [nbr_coef]
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| 515 | df2r^[0] := sfr^[0] - sfi^[0]; // - sfr [nbr_coef]
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| 516 | df1r^[h_nbr_coef] := sfr^[h_nbr_coef] * 2;
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| 517 | df2r^[h_nbr_coef] := sfi^[h_nbr_coef] * 2;
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| 518 |
|
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| 519 | // Others are conjugate complex numbers
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| 520 | df1i := pointer(longint(df1r) + (h_nbr_coef*sizeof_flt));
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| 521 | df2i := pointer(longint(df1i) + (nbr_coef*sizeof_flt));
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| 522 |
|
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| 523 | for i := 1 to h_nbr_coef-1 do
|
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| 524 | begin
|
|---|
| 525 | df1r^[i] := sfr^[i] + sfi^[-i]; // + sfr [nbr_coef - i]
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|---|
| 526 | df1i^[i] := sfi^[i] - sfi^[nbr_coef - i];
|
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| 527 |
|
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| 528 | c := cos_ptr^[i]; // cos (i*PI/nbr_coef);
|
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| 529 | s := cos_ptr^[h_nbr_coef - i]; // sin (i*PI/nbr_coef);
|
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| 530 | vr := sfr^[i] - sfi^[-i]; // - sfr [nbr_coef - i]
|
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| 531 | vi := sfi^[i] + sfi^[nbr_coef - i];
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| 532 |
|
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| 533 | df2r^[i] := vr * c + vi * s;
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| 534 | df2i^[i] := vi * c - vr * s;
|
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| 535 | end;
|
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| 536 |
|
|---|
| 537 | inc(coef_index, d_nbr_coef);
|
|---|
| 538 | until (coef_index >= _length);
|
|---|
| 539 |
|
|---|
| 540 |
|
|---|
| 541 | // Prepare to the next pass
|
|---|
| 542 | if (pass < _nbr_bits - 1) then
|
|---|
| 543 | begin
|
|---|
| 544 | temp_ptr := df;
|
|---|
| 545 | df := sf;
|
|---|
| 546 | sf := temp_ptr;
|
|---|
| 547 | end
|
|---|
| 548 | else
|
|---|
| 549 | begin
|
|---|
| 550 | sf := df;
|
|---|
| 551 | df := df_temp;
|
|---|
| 552 | end
|
|---|
| 553 | end;
|
|---|
| 554 |
|
|---|
| 555 | // Antepenultimate pass
|
|---|
| 556 | sqrt2_2 := _sqrt2_2;
|
|---|
| 557 | coef_index := 0;
|
|---|
| 558 |
|
|---|
| 559 | repeat
|
|---|
| 560 | df^[coef_index] := sf^[coef_index] + sf^[coef_index + 4];
|
|---|
| 561 | df^[coef_index + 4] := sf^[coef_index] - sf^[coef_index + 4];
|
|---|
| 562 | df^[coef_index + 2] := sf^[coef_index + 2] * 2;
|
|---|
| 563 | df^[coef_index + 6] := sf^[coef_index + 6] * 2;
|
|---|
| 564 |
|
|---|
| 565 | df^[coef_index + 1] := sf^[coef_index + 1] + sf^[coef_index + 3];
|
|---|
| 566 | df^[coef_index + 3] := sf^[coef_index + 5] - sf^[coef_index + 7];
|
|---|
| 567 |
|
|---|
| 568 | vr := sf^[coef_index + 1] - sf^[coef_index + 3];
|
|---|
| 569 | vi := sf^[coef_index + 5] + sf^[coef_index + 7];
|
|---|
| 570 |
|
|---|
| 571 | df^[coef_index + 5] := (vr + vi) * sqrt2_2;
|
|---|
| 572 | df^[coef_index + 7] := (vi - vr) * sqrt2_2;
|
|---|
| 573 |
|
|---|
| 574 | inc(coef_index, 8);
|
|---|
| 575 | until (coef_index >= _length);
|
|---|
| 576 |
|
|---|
| 577 |
|
|---|
| 578 | // Penultimate and last pass at once
|
|---|
| 579 | coef_index := 0;
|
|---|
| 580 | bit_rev_lut_ptr := pointer(_bit_rev_lut.get_ptr);
|
|---|
| 581 | sf2 := df;
|
|---|
| 582 |
|
|---|
| 583 | repeat
|
|---|
| 584 | b_0 := sf2^[0] + sf2^[n2];
|
|---|
| 585 | b_2 := sf2^[0] - sf2^[n2];
|
|---|
| 586 | b_1 := sf2^[n1] * 2;
|
|---|
| 587 | b_3 := sf2^[n3] * 2;
|
|---|
| 588 |
|
|---|
| 589 | x^[bit_rev_lut_ptr^[0]] := b_0 + b_1;
|
|---|
| 590 | x^[bit_rev_lut_ptr^[n1]] := b_0 - b_1;
|
|---|
| 591 | x^[bit_rev_lut_ptr^[n2]] := b_2 + b_3;
|
|---|
| 592 | x^[bit_rev_lut_ptr^[n3]] := b_2 - b_3;
|
|---|
| 593 |
|
|---|
| 594 | b_0 := sf2^[n4] + sf2^[n6];
|
|---|
| 595 | b_2 := sf2^[n4] - sf2^[n6];
|
|---|
| 596 | b_1 := sf2^[n5] * 2;
|
|---|
| 597 | b_3 := sf2^[n7] * 2;
|
|---|
| 598 |
|
|---|
| 599 | x^[bit_rev_lut_ptr^[n4]] := b_0 + b_1;
|
|---|
| 600 | x^[bit_rev_lut_ptr^[n5]] := b_0 - b_1;
|
|---|
| 601 | x^[bit_rev_lut_ptr^[n6]] := b_2 + b_3;
|
|---|
| 602 | x^[bit_rev_lut_ptr^[n7]] := b_2 - b_3;
|
|---|
| 603 |
|
|---|
| 604 | inc(sf2, 8);
|
|---|
| 605 | inc(coef_index, 8);
|
|---|
| 606 | inc(bit_rev_lut_ptr, 8);
|
|---|
| 607 | until (coef_index >= _length);
|
|---|
| 608 | end
|
|---|
| 609 |
|
|---|
| 610 | (*______________________________________________
|
|---|
| 611 | *
|
|---|
| 612 | * Special cases
|
|---|
| 613 | *______________________________________________
|
|---|
| 614 | *)
|
|---|
| 615 |
|
|---|
| 616 | // 4-point IFFT
|
|---|
| 617 | else if _nbr_bits = 2 then
|
|---|
| 618 | begin
|
|---|
| 619 | b_0 := f^[0] + f [n2];
|
|---|
| 620 | b_2 := f^[0] - f [n2];
|
|---|
| 621 |
|
|---|
| 622 | x^[0] := b_0 + f [n1] * 2;
|
|---|
| 623 | x^[n2] := b_0 - f [n1] * 2;
|
|---|
| 624 | x^[n1] := b_2 + f [n3] * 2;
|
|---|
| 625 | x^[n3] := b_2 - f [n3] * 2;
|
|---|
| 626 | end
|
|---|
| 627 |
|
|---|
| 628 | // 2-point IFFT
|
|---|
| 629 | else if _nbr_bits = 1 then
|
|---|
| 630 | begin
|
|---|
| 631 | x^[0] := f^[0] + f^[n1];
|
|---|
| 632 | x^[n1] := f^[0] - f^[n1];
|
|---|
| 633 | end
|
|---|
| 634 |
|
|---|
| 635 | // 1-point IFFT
|
|---|
| 636 | else
|
|---|
| 637 | x^[0] := f^[0];
|
|---|
| 638 | end;
|
|---|
| 639 |
|
|---|
| 640 | (*==========================================================================*/
|
|---|
| 641 | /* Name: rescale */
|
|---|
| 642 | /* Description: Scale an array by divide each element by its length. */
|
|---|
| 643 | /* This function should be called after FFT + IFFT. */
|
|---|
| 644 | /* Input/Output parameters: */
|
|---|
| 645 | /* - x: pointer on array to rescale (time or frequency). */
|
|---|
| 646 | /*==========================================================================*)
|
|---|
| 647 | procedure TFFTReal.rescale(x: pflt_array);
|
|---|
| 648 | var
|
|---|
| 649 | mul : flt_t;
|
|---|
| 650 | i : longint;
|
|---|
| 651 | begin
|
|---|
| 652 | mul := 1.0 / _length;
|
|---|
| 653 | i := _length - 1;
|
|---|
| 654 |
|
|---|
| 655 | repeat
|
|---|
| 656 | x^[i] := x^[i] * mul;
|
|---|
| 657 | dec(i);
|
|---|
| 658 | until (i < 0);
|
|---|
| 659 | end;
|
|---|
| 660 |
|
|---|
| 661 | end.
|
|---|
