FFT Library
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FFT Library

mikroPascal PRO for dsPIC30/33 and PIC24 includes a library for FFT calculation. All routines work with fractional Q15 format.

Library Dependency Tree

FFT Library Dependency Tree

Library Routines

FFT

Prototype

procedure FFT(log2N: word; TwiddleFactorsAddress: longint; var Samples: array[1024] of word);
Description

Function applies FFT transformation to input samples, input samples must be in Y data space.

  • f(n): array of complex input samples
  • WN: TwiddleFactors
  • N = 2m, m Î Z
The amplitude of current FFT sample is calculated as:
Parameters
  • log2N: buffer length (must be the power of 2).
  • TwiddleFactorsAddress: address of constant array which contains complex twiddle factors. The array is expected to be in program memory. See Twiddle Factors for adequate array values.
  • Samples: array of input samples. Upon completion, complex array of FFT samples is placed in the Samples: parameter.
Returns

Nothing.
Requires

Nothing.
Example 
var InputSamples: array[512] of word; ydata;
...
// Perform FFT (DFT), 7 stages, 128 samples of complex pairs
FFT(8, TwiddleCoeff_256, InputSamples);
Notes

Complex array of FFT samples is placed in Samples parameter. Input Samples are arranged in manner Re,Im,Re,Im... (where Im is always zero). Output samples are arranged in the same manner but Im parts are different from zero. Output samples are symmetrical (First half of output samples (index from 0 to N/2) is identical as second half of output samples(index from N/2 to N).

Input data is a complex vector such that the magnitude of the real and imaginary parts of each of its elements is less than 0.5. If greater or equal to this value the results could produce saturation. Note that the output values are scaled by a factor of 1/N, with N the length of the FFT. input is expected in natural ordering, while output is produced in bit reverse ordering.

Twiddle Factors :


TwiddleCoeff_64

const TwiddleCoeff_64: array[64] of word = (
  0x7FFF, 0x0000, 0x7F62, 0xF374, 0x7D8A, 0xE707, 0x7A7D, 0xDAD8,
  0x7642, 0xCF04, 0x70E3, 0xC3A9, 0x6A6E, 0xB8E3, 0x62F2, 0xAECC,
  0x5A82, 0xA57E, 0x5134, 0x9D0E, 0x471D, 0x9592, 0x3C57, 0x8F1D,
  0x30FC, 0x89BE, 0x2528, 0x8583, 0x18F9, 0x8276, 0x0C8C, 0x809E,
  0x0000, 0x8000, 0xF374, 0x809E, 0xE707, 0x8276, 0xDAD8, 0x8583,
  0xCF04, 0x89BE, 0xC3A9, 0x8F1D, 0xB8E3, 0x9592, 0xAECC, 0x9D0E,
  0xA57E, 0xA57E, 0x9D0E, 0xAECC, 0x9592, 0xB8E3, 0x8F1D, 0xC3A9,
  0x89BE, 0xCF04, 0x8583, 0xDAD8, 0x8276, 0xE707, 0x809E, 0xF374);

TwiddleCoeff_128

const TwiddleCoeff_128: array[128] of word = (
  0x7FFF, 0x0000, 0x7FD9, 0xF9B8, 0x7F62, 0xF374, 0x7E9D, 0xED38,
  0x7D8A, 0xE707, 0x7C2A, 0xE0E6, 0x7A7D, 0xDAD8, 0x7885, 0xD4E1,
  0x7642, 0xCF04, 0x73B6, 0xC946, 0x70E3, 0xC3A9, 0x6DCA, 0xBE32,
  0x6A6E, 0xB8E3, 0x66D0, 0xB3C0, 0x62F2, 0xAECC, 0x5ED7, 0xAA0A,
  0x5A82, 0xA57E, 0x55F6, 0xA129, 0x5134, 0x9D0E, 0x4C40, 0x9930,
  0x471D, 0x9592, 0x41CE, 0x9236, 0x3C57, 0x8F1D, 0x36BA, 0x8C4A,
  0x30FC, 0x89BE, 0x2B1F, 0x877B, 0x2528, 0x8583, 0x1F1A, 0x83D6,
  0x18F9, 0x8276, 0x12C8, 0x8163, 0x0C8C, 0x809E, 0x0648, 0x8027,
  0x0000, 0x8000, 0xF9B8, 0x8027, 0xF374, 0x809E, 0xED38, 0x8163,
  0xE707, 0x8276, 0xE0E6, 0x83D6, 0xDAD8, 0x8583, 0xD4E1, 0x877B,
  0xCF04, 0x89BE, 0xC946, 0x8C4A, 0xC3A9, 0x8F1D, 0xBE32, 0x9236,
  0xB8E3, 0x9592, 0xB3C0, 0x9930, 0xAECC, 0x9D0E, 0xAA0A, 0xA129,
  0xA57E, 0xA57E, 0xA129, 0xAA0A, 0x9D0E, 0xAECC, 0x9930, 0xB3C0,
  0x9592, 0xB8E3, 0x9236, 0xBE32, 0x8F1D, 0xC3A9, 0x8C4A, 0xC946,
  0x89BE, 0xCF04, 0x877B, 0xD4E1, 0x8583, 0xDAD8, 0x83D6, 0xE0E6,
  0x8276, 0xE707, 0x8163, 0xED38, 0x809E, 0xF374, 0x8027, 0xF9B8);

TwiddleCoeff_256

const TwiddleCoeff_256: array[256] of word = (
  0x7FFF, 0x0000, 0x7FF6, 0xFCDC, 0x7FD9, 0xF9B8, 0x7FA7, 0xF695,
  0x7F62, 0xF374, 0x7F0A, 0xF055, 0x7E9D, 0xED38, 0x7E1E, 0xEA1E,
  0x7D8A, 0xE707, 0x7CE4, 0xE3F4, 0x7C2A, 0xE0E6, 0x7B5D, 0xDDDC,
  0x7A7D, 0xDAD8, 0x798A, 0xD7D9, 0x7885, 0xD4E1, 0x776C, 0xD1EF,
  0x7642, 0xCF04, 0x7505, 0xCC21, 0x73B6, 0xC946, 0x7255, 0xC673,
  0x70E3, 0xC3A9, 0x6F5F, 0xC0E9, 0x6DCA, 0xBE32, 0x6C24, 0xBB85,
  0x6A6E, 0xB8E3, 0x68A7, 0xB64C, 0x66D0, 0xB3C0, 0x64E9, 0xB140,
  0x62F2, 0xAECC, 0x60EC, 0xAC65, 0x5ED7, 0xAA0A, 0x5CB4, 0xA7BD,
  0x5A82, 0xA57E, 0x5843, 0xA34C, 0x55F6, 0xA129, 0x539B, 0x9F14,
  0x5134, 0x9D0E, 0x4EC0, 0x9B17, 0x4C40, 0x9930, 0x49B4, 0x9759,
  0x471D, 0x9592, 0x447B, 0x93DC, 0x41CE, 0x9236, 0x3F17, 0x90A1,
  0x3C57, 0x8F1D, 0x398D, 0x8DAB, 0x36BA, 0x8C4A, 0x33DF, 0x8AFB,
  0x30FC, 0x89BE, 0x2E11, 0x8894, 0x2B1F, 0x877B, 0x2827, 0x8676,
  0x2528, 0x8583, 0x2224, 0x84A3, 0x1F1A, 0x83D6, 0x1C0C, 0x831C,
  0x18F9, 0x8276, 0x15E2, 0x81E2, 0x12C8, 0x8163, 0x0FAB, 0x80F6,
  0x0C8C, 0x809E, 0x096B, 0x8059, 0x0648, 0x8027, 0x0324, 0x800A,
  0x0000, 0x8000, 0xFCDC, 0x800A, 0xF9B8, 0x8027, 0xF695, 0x8059,
  0xF374, 0x809E, 0xF055, 0x80F6, 0xED38, 0x8163, 0xEA1E, 0x81E2,
  0xE707, 0x8276, 0xE3F4, 0x831C, 0xE0E6, 0x83D6, 0xDDDC, 0x84A3,
  0xDAD8, 0x8583, 0xD7D9, 0x8676, 0xD4E1, 0x877B, 0xD1EF, 0x8894,
  0xCF04, 0x89BE, 0xCC21, 0x8AFB, 0xC946, 0x8C4A, 0xC673, 0x8DAB,
  0xC3A9, 0x8F1D, 0xC0E9, 0x90A1, 0xBE32, 0x9236, 0xBB85, 0x93DC,
  0xB8E3, 0x9592, 0xB64C, 0x9759, 0xB3C0, 0x9930, 0xB140, 0x9B17,
  0xAECC, 0x9D0E, 0xAC65, 0x9F14, 0xAA0A, 0xA129, 0xA7BD, 0xA34C,
  0xA57E, 0xA57E, 0xA34C, 0xA7BD, 0xA129, 0xAA0A, 0x9F14, 0xAC65,
  0x9D0E, 0xAECC, 0x9B17, 0xB140, 0x9930, 0xB3C0, 0x9759, 0xB64C,
  0x9592, 0xB8E3, 0x93DC, 0xBB85, 0x9236, 0xBE32, 0x90A1, 0xC0E9,
  0x8F1D, 0xC3A9, 0x8DAB, 0xC673, 0x8C4A, 0xC946, 0x8AFB, 0xCC21,
  0x89BE, 0xCF04, 0x8894, 0xD1EF, 0x877B, 0xD4E1, 0x8676, 0xD7D9,
  0x8583, 0xDAD8, 0x84A3, 0xDDDC, 0x83D6, 0xE0E6, 0x831C, 0xE3F4,
  0x8276, 0xE707, 0x81E2, 0xEA1E, 0x8163, 0xED38, 0x80F6, 0xF055,
  0x809E, 0xF374, 0x8059, 0xF695, 0x8027, 0xF9B8, 0x800A, 0xFCDC);

TwiddleCoeff_512

const TwiddleCoeff_512: array[512] of word = (
  0x7FFF, 0x0000, 0x7FFE, 0xFE6E, 0x7FF6, 0xFCDC, 0x7FEA, 0xFB4A,
  0x7FD9, 0xF9B8, 0x7FC2, 0xF827, 0x7FA7, 0xF695, 0x7F87, 0xF505,
  0x7F62, 0xF374, 0x7F38, 0xF1E4, 0x7F0A, 0xF055, 0x7ED6, 0xEEC6,
  0x7E9D, 0xED38, 0x7E60, 0xEBAB, 0x7E1E, 0xEA1E, 0x7DD6, 0xE892,
  0x7D8A, 0xE707, 0x7D3A, 0xE57D, 0x7CE4, 0xE3F4, 0x7C89, 0xE26D,
  0x7C2A, 0xE0E6, 0x7BC6, 0xDF61, 0x7B5D, 0xDDDC, 0x7AEF, 0xDC59,
  0x7A7D, 0xDAD8, 0x7A06, 0xD958, 0x798A, 0xD7D9, 0x790A, 0xD65C,
  0x7885, 0xD4E1, 0x77FB, 0xD367, 0x776C, 0xD1EF, 0x76D9, 0xD079,
  0x7642, 0xCF04, 0x75A6, 0xCD92, 0x7505, 0xCC21, 0x7460, 0xCAB2,
  0x73B6, 0xC946, 0x7308, 0xC7DB, 0x7255, 0xC673, 0x719E, 0xC50D,
  0x70E3, 0xC3A9, 0x7023, 0xC248, 0x6F5F, 0xC0E9, 0x6E97, 0xBF8C,
  0x6DCA, 0xBE32, 0x6CF9, 0xBCDA, 0x6C24, 0xBB85, 0x6B4B, 0xBA33,
  0x6A6E, 0xB8E3, 0x698C, 0xB796, 0x68A7, 0xB64C, 0x67BD, 0xB505,
  0x66D0, 0xB3C0, 0x65DE, 0xB27F, 0x64E9, 0xB140, 0x63EF, 0xB005,
  0x62F2, 0xAECC, 0x61F1, 0xAD97, 0x60EC, 0xAC65, 0x5FE4, 0xAB36,
  0x5ED7, 0xAA0A, 0x5DC8, 0xA8E2, 0x5CB4, 0xA7BD, 0x5B9D, 0xA69C,
  0x5A82, 0xA57E, 0x5964, 0xA463, 0x5843, 0xA34C, 0x571E, 0xA238,
  0x55F6, 0xA129, 0x54CA, 0xA01C, 0x539B, 0x9F14, 0x5269, 0x9E0F,
  0x5134, 0x9D0E, 0x4FFB, 0x9C11, 0x4EC0, 0x9B17, 0x4D81, 0x9A22,
  0x4C40, 0x9930, 0x4AFB, 0x9843, 0x49B4, 0x9759, 0x486A, 0x9674,
  0x471D, 0x9592, 0x45CD, 0x94B5, 0x447B, 0x93DC, 0x4326, 0x9307,
  0x41CE, 0x9236, 0x4074, 0x9169, 0x3F17, 0x90A1, 0x3DB8, 0x8FDD,
  0x3C57, 0x8F1D, 0x3AF3, 0x8E62, 0x398D, 0x8DAB, 0x3825, 0x8CF8,
  0x36BA, 0x8C4A, 0x354E, 0x8BA0, 0x33DF, 0x8AFB, 0x326E, 0x8A5A,
  0x30FC, 0x89BE, 0x2F87, 0x8927, 0x2E11, 0x8894, 0x2C99, 0x8805,
  0x2B1F, 0x877B, 0x29A4, 0x86F6, 0x2827, 0x8676, 0x26A8, 0x85FA,
  0x2528, 0x8583, 0x23A7, 0x8511, 0x2224, 0x84A3, 0x209F, 0x843A,
  0x1F1A, 0x83D6, 0x1D93, 0x8377, 0x1C0C, 0x831C, 0x1A83, 0x82C6,
  0x18F9, 0x8276, 0x176E, 0x822A, 0x15E2, 0x81E2, 0x1455, 0x81A0,
  0x12C8, 0x8163, 0x113A, 0x812A, 0x0FAB, 0x80F6, 0x0E1C, 0x80C8,
  0x0C8C, 0x809E, 0x0AFB, 0x8079, 0x096B, 0x8059, 0x07D9, 0x803E,
  0x0648, 0x8027, 0x04B6, 0x8016, 0x0324, 0x800A, 0x0192, 0x8002,
  0x0000, 0x8000, 0xFE6E, 0x8002, 0xFCDC, 0x800A, 0xFB4A, 0x8016,
  0xF9B8, 0x8027, 0xF827, 0x803E, 0xF695, 0x8059, 0xF505, 0x8079,
  0xF374, 0x809E, 0xF1E4, 0x80C8, 0xF055, 0x80F6, 0xEEC6, 0x812A,
  0xED38, 0x8163, 0xEBAB, 0x81A0, 0xEA1E, 0x81E2, 0xE892, 0x822A,
  0xE707, 0x8276, 0xE57D, 0x82C6, 0xE3F4, 0x831C, 0xE26D, 0x8377,
  0xE0E6, 0x83D6, 0xDF61, 0x843A, 0xDDDC, 0x84A3, 0xDC59, 0x8511,
  0xDAD8, 0x8583, 0xD958, 0x85FA, 0xD7D9, 0x8676, 0xD65C, 0x86F6,
  0xD4E1, 0x877B, 0xD367, 0x8805, 0xD1EF, 0x8894, 0xD079, 0x8927,
  0xCF04, 0x89BE, 0xCD92, 0x8A5A, 0xCC21, 0x8AFB, 0xCAB2, 0x8BA0,
  0xC946, 0x8C4A, 0xC7DB, 0x8CF8, 0xC673, 0x8DAB, 0xC50D, 0x8E62,
  0xC3A9, 0x8F1D, 0xC248, 0x8FDD, 0xC0E9, 0x90A1, 0xBF8C, 0x9169,
  0xBE32, 0x9236, 0xBCDA, 0x9307, 0xBB85, 0x93DC, 0xBA33, 0x94B5,
  0xB8E3, 0x9592, 0xB796, 0x9674, 0xB64C, 0x9759, 0xB505, 0x9843,
  0xB3C0, 0x9930, 0xB27F, 0x9A22, 0xB140, 0x9B17, 0xB005, 0x9C11,
  0xAECC, 0x9D0E, 0xAD97, 0x9E0F, 0xAC65, 0x9F14, 0xAB36, 0xA01C,
  0xAA0A, 0xA129, 0xA8E2, 0xA238, 0xA7BD, 0xA34C, 0xA69C, 0xA463,
  0xA57E, 0xA57E, 0xA463, 0xA69C, 0xA34C, 0xA7BD, 0xA238, 0xA8E2,
  0xA129, 0xAA0A, 0xA01C, 0xAB36, 0x9F14, 0xAC65, 0x9E0F, 0xAD97,
  0x9D0E, 0xAECC, 0x9C11, 0xB005, 0x9B17, 0xB140, 0x9A22, 0xB27F,
  0x9930, 0xB3C0, 0x9843, 0xB505, 0x9759, 0xB64C, 0x9674, 0xB796,
  0x9592, 0xB8E3, 0x94B5, 0xBA33, 0x93DC, 0xBB85, 0x9307, 0xBCDA,
  0x9236, 0xBE32, 0x9169, 0xBF8C, 0x90A1, 0xC0E9, 0x8FDD, 0xC248,
  0x8F1D, 0xC3A9, 0x8E62, 0xC50D, 0x8DAB, 0xC673, 0x8CF8, 0xC7DB,
  0x8C4A, 0xC946, 0x8BA0, 0xCAB2, 0x8AFB, 0xCC21, 0x8A5A, 0xCD92,
  0x89BE, 0xCF04, 0x8927, 0xD079, 0x8894, 0xD1EF, 0x8805, 0xD367,
  0x877B, 0xD4E1, 0x86F6, 0xD65C, 0x8676, 0xD7D9, 0x85FA, 0xD958,
  0x8583, 0xDAD8, 0x8511, 0xDC59, 0x84A3, 0xDDDC, 0x843A, 0xDF61,
  0x83D6, 0xE0E6, 0x8377, 0xE26D, 0x831C, 0xE3F4, 0x82C6, 0xE57D,
  0x8276, 0xE707, 0x822A, 0xE892, 0x81E2, 0xEA1E, 0x81A0, 0xEBAB,
  0x8163, 0xED38, 0x812A, 0xEEC6, 0x80F6, 0xF055, 0x80C8, 0xF1E4,
  0x809E, 0xF374, 0x8079, 0xF505, 0x8059, 0xF695, 0x803E, 0xF827,
  0x8027, 0xF9B8, 0x8016, 0xFB4A, 0x800A, 0xFCDC, 0x8002, 0xFE6E);
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