fix_fft.c

/* fix_fft.c - Fixed-point in-place Fast Fourier Transform  */
/*
  All data are fixed-point short integers, in which -32768
  to +32768 represent -1.0 to +1.0 respectively. Integer
  arithmetic is used for speed, instead of the more natural
  floating-point.

  For the forward FFT (time -> freq), fixed scaling is
  performed to prevent arithmetic overflow, and to map a 0dB
  sine/cosine wave (i.e. amplitude = 32767) to two -6dB freq
  coefficients. The return value is always 0.

  For the inverse FFT (freq -> time), fixed scaling cannot be
  done, as two 0dB coefficients would sum to a peak amplitude
  of 64K, overflowing the 32k range of the fixed-point integers.
  Thus, the fix_fft() routine performs variable scaling, and
  returns a value which is the number of bits LEFT by which
  the output must be shifted to get the actual amplitude
  (i.e. if fix_fft() returns 3, each value of fr[] and fi[]
  must be multiplied by 8 (2**3) for proper scaling.
  Clearly, this cannot be done within fixed-point short
  integers. In practice, if the result is to be used as a
  filter, the scale_shift can usually be ignored, as the
  result will be approximately correctly normalized as is.

  Written by:  Tom Roberts  11/8/89
  Made portable:  Malcolm Slaney 12/15/94 malcolm@interval.com
  Enhanced:  Dimitrios P. Bouras  14 Jun 2006 dbouras@ieee.org
*/

#define N_WAVE      1024    /* full length of Sinewave[] */
#define LOG2_N_WAVE 10      /* log2(N_WAVE) */

/*
  Henceforth "short" implies 16-bit word. If this is not
  the case in your architecture, please replace "short"
  with a type definition which *is* a 16-bit word.
*/

/*
  Since we only use 3/4 of N_WAVE, we define only
  this many samples, in order to conserve data space.
*/
short Sinewave[N_WAVE-N_WAVE/4] = {
      0,    201,    402,    603,    804,   1005,   1206,   1406,
   1607,   1808,   2009,   2209,   2410,   2610,   2811,   3011,
   3211,   3411,   3611,   3811,   4011,   4210,   4409,   4608,
   4807,   5006,   5205,   5403,   5601,   5799,   5997,   6195,
   6392,   6589,   6786,   6982,   7179,   7375,   7571,   7766,
   7961,   8156,   8351,   8545,   8739,   8932,   9126,   9319,
   9511,   9703,   9895,  10087,  10278,  10469,  10659,  10849,
  11038,  11227,  11416,  11604,  11792,  11980,  12166,  12353,
  12539,  12724,  12909,  13094,  13278,  13462,  13645,  13827,
  14009,  14191,  14372,  14552,  14732,  14911,  15090,  15268,
  15446,  15623,  15799,  15975,  16150,  16325,  16499,  16672,
  16845,  17017,  17189,  17360,  17530,  17699,  17868,  18036,
  18204,  18371,  18537,  18702,  18867,  19031,  19194,  19357,
  19519,  19680,  19840,  20000,  20159,  20317,  20474,  20631,
  20787,  20942,  21096,  21249,  21402,  21554,  21705,  21855,
  22004,  22153,  22301,  22448,  22594,  22739,  22883,  23027,
  23169,  23311,  23452,  23592,  23731,  23869,  24006,  24143,
  24278,  24413,  24546,  24679,  24811,  24942,  25072,  25201,
  25329,  25456,  25582,  25707,  25831,  25954,  26077,  26198,
  26318,  26437,  26556,  26673,  26789,  26905,  27019,  27132,
  27244,  27355,  27466,  27575,  27683,  27790,  27896,  28001,
  28105,  28208,  28309,  28410,  28510,  28608,  28706,  28802,
  28897,  28992,  29085,  29177,  29268,  29358,  29446,  29534,
  29621,  29706,  29790,  29873,  29955,  30036,  30116,  30195,
  30272,  30349,  30424,  30498,  30571,  30643,  30713,  30783,
  30851,  30918,  30984,  31049,  31113,  31175,  31236,  31297,
  31356,  31413,  31470,  31525,  31580,  31633,  31684,  31735,
  31785,  31833,  31880,  31926,  31970,  32014,  32056,  32097,
  32137,  32176,  32213,  32249,  32284,  32318,  32350,  32382,
  32412,  32441,  32468,  32495,  32520,  32544,  32567,  32588,
  32609,  32628,  32646,  32662,  32678,  32692,  32705,  32717,
  32727,  32736,  32744,  32751,  32757,  32761,  32764,  32766,
  32767,  32766,  32764,  32761,  32757,  32751,  32744,  32736,
  32727,  32717,  32705,  32692,  32678,  32662,  32646,  32628,
  32609,  32588,  32567,  32544,  32520,  32495,  32468,  32441,
  32412,  32382,  32350,  32318,  32284,  32249,  32213,  32176,
  32137,  32097,  32056,  32014,  31970,  31926,  31880,  31833,
  31785,  31735,  31684,  31633,  31580,  31525,  31470,  31413,
  31356,  31297,  31236,  31175,  31113,  31049,  30984,  30918,
  30851,  30783,  30713,  30643,  30571,  30498,  30424,  30349,
  30272,  30195,  30116,  30036,  29955,  29873,  29790,  29706,
  29621,  29534,  29446,  29358,  29268,  29177,  29085,  28992,
  28897,  28802,  28706,  28608,  28510,  28410,  28309,  28208,
  28105,  28001,  27896,  27790,  27683,  27575,  27466,  27355,
  27244,  27132,  27019,  26905,  26789,  26673,  26556,  26437,
  26318,  26198,  26077,  25954,  25831,  25707,  25582,  25456,
  25329,  25201,  25072,  24942,  24811,  24679,  24546,  24413,
  24278,  24143,  24006,  23869,  23731,  23592,  23452,  23311,
  23169,  23027,  22883,  22739,  22594,  22448,  22301,  22153,
  22004,  21855,  21705,  21554,  21402,  21249,  21096,  20942,
  20787,  20631,  20474,  20317,  20159,  20000,  19840,  19680,
  19519,  19357,  19194,  19031,  18867,  18702,  18537,  18371,
  18204,  18036,  17868,  17699,  17530,  17360,  17189,  17017,
  16845,  16672,  16499,  16325,  16150,  15975,  15799,  15623,
  15446,  15268,  15090,  14911,  14732,  14552,  14372,  14191,
  14009,  13827,  13645,  13462,  13278,  13094,  12909,  12724,
  12539,  12353,  12166,  11980,  11792,  11604,  11416,  11227,
  11038,  10849,  10659,  10469,  10278,  10087,   9895,   9703,
   9511,   9319,   9126,   8932,   8739,   8545,   8351,   8156,
   7961,   7766,   7571,   7375,   7179,   6982,   6786,   6589,
   6392,   6195,   5997,   5799,   5601,   5403,   5205,   5006,
   4807,   4608,   4409,   4210,   4011,   3811,   3611,   3411,
   3211,   3011,   2811,   2610,   2410,   2209,   2009,   1808,
   1607,   1406,   1206,   1005,    804,    603,    402,    201,
      0,   -201,   -402,   -603,   -804,  -1005,  -1206,  -1406,
  -1607,  -1808,  -2009,  -2209,  -2410,  -2610,  -2811,  -3011,
  -3211,  -3411,  -3611,  -3811,  -4011,  -4210,  -4409,  -4608,
  -4807,  -5006,  -5205,  -5403,  -5601,  -5799,  -5997,  -6195,
  -6392,  -6589,  -6786,  -6982,  -7179,  -7375,  -7571,  -7766,
  -7961,  -8156,  -8351,  -8545,  -8739,  -8932,  -9126,  -9319,
  -9511,  -9703,  -9895, -10087, -10278, -10469, -10659, -10849,
 -11038, -11227, -11416, -11604, -11792, -11980, -12166, -12353,
 -12539, -12724, -12909, -13094, -13278, -13462, -13645, -13827,
 -14009, -14191, -14372, -14552, -14732, -14911, -15090, -15268,
 -15446, -15623, -15799, -15975, -16150, -16325, -16499, -16672,
 -16845, -17017, -17189, -17360, -17530, -17699, -17868, -18036,
 -18204, -18371, -18537, -18702, -18867, -19031, -19194, -19357,
 -19519, -19680, -19840, -20000, -20159, -20317, -20474, -20631,
 -20787, -20942, -21096, -21249, -21402, -21554, -21705, -21855,
 -22004, -22153, -22301, -22448, -22594, -22739, -22883, -23027,
 -23169, -23311, -23452, -23592, -23731, -23869, -24006, -24143,
 -24278, -24413, -24546, -24679, -24811, -24942, -25072, -25201,
 -25329, -25456, -25582, -25707, -25831, -25954, -26077, -26198,
 -26318, -26437, -26556, -26673, -26789, -26905, -27019, -27132,
 -27244, -27355, -27466, -27575, -27683, -27790, -27896, -28001,
 -28105, -28208, -28309, -28410, -28510, -28608, -28706, -28802,
 -28897, -28992, -29085, -29177, -29268, -29358, -29446, -29534,
 -29621, -29706, -29790, -29873, -29955, -30036, -30116, -30195,
 -30272, -30349, -30424, -30498, -30571, -30643, -30713, -30783,
 -30851, -30918, -30984, -31049, -31113, -31175, -31236, -31297,
 -31356, -31413, -31470, -31525, -31580, -31633, -31684, -31735,
 -31785, -31833, -31880, -31926, -31970, -32014, -32056, -32097,
 -32137, -32176, -32213, -32249, -32284, -32318, -32350, -32382,
 -32412, -32441, -32468, -32495, -32520, -32544, -32567, -32588,
 -32609, -32628, -32646, -32662, -32678, -32692, -32705, -32717,
 -32727, -32736, -32744, -32751, -32757, -32761, -32764, -32766,
};

/*
  FIX_MPY() - fixed-point multiplication & scaling.
  Substitute inline assembly for hardware-specific
  optimization suited to a particluar DSP processor.
  Scaling ensures that result remains 16-bit.
*/
inline short FIX_MPY(short a, short b)
{
	/* shift right one less bit (i.e. 15-1) */
	int c = ((int)a * (int)b) >> 14;
	/* last bit shifted out = rounding-bit */
	b = c & 0x01;
	/* last shift + rounding bit */
	a = (c >> 1) + b;
	return a;
}

/*
  fix_fft() - perform forward/inverse fast Fourier transform.
  fr[n],fi[n] are real and imaginary arrays, both INPUT AND
  RESULT (in-place FFT), with 0 <= n < 2**m; set inverse to
  0 for forward transform (FFT), or 1 for iFFT.
*/
int fix_fft(short fr[], short fi[], short m, short inverse)
{
	int mr, nn, i, j, l, k, istep, n, scale, shift;
	short qr, qi, tr, ti, wr, wi;

	n = 1 << m;

	/* max FFT size = N_WAVE */
	if (n > N_WAVE)
		return -1;

	mr = 0;
	nn = n - 1;
	scale = 0;

	/* decimation in time - re-order data */
	for (m=1; m<=nn; ++m) {
		l = n;
		do {
			l >>= 1;
		} while (mr+l > nn);
		mr = (mr & (l-1)) + l;

		if (mr <= m)
			continue;
		tr = fr[m];
		fr[m] = fr[mr];
		fr[mr] = tr;
		ti = fi[m];
		fi[m] = fi[mr];
		fi[mr] = ti;
	}

	l = 1;
	k = LOG2_N_WAVE-1;
	while (l < n) {
		if (inverse) {
			/* variable scaling, depending upon data */
			shift = 0;
			for (i=0; i<n; ++i) {
				j = fr[i];
				if (j < 0)
					j = -j;
				m = fi[i];
				if (m < 0)
					m = -m;
				if (j > 16383 || m > 16383) {
					shift = 1;
					break;
				}
			}
			if (shift)
				++scale;
		} else {
			/*
			  fixed scaling, for proper normalization --
			  there will be log2(n) passes, so this results
			  in an overall factor of 1/n, distributed to
			  maximize arithmetic accuracy.
			*/
			shift = 1;
		}
		/*
		  it may not be obvious, but the shift will be
		  performed on each data point exactly once,
		  during this pass.
		*/
		istep = l << 1;
		for (m=0; m<l; ++m) {
			j = m << k;
			/* 0 <= j < N_WAVE/2 */
			wr =  Sinewave[j+N_WAVE/4];
			wi = -Sinewave[j];
			if (inverse)
				wi = -wi;
			if (shift) {
				wr >>= 1;
				wi >>= 1;
			}
			for (i=m; i<n; i+=istep) {
				j = i + l;
				tr = FIX_MPY(wr,fr[j]) - FIX_MPY(wi,fi[j]);
				ti = FIX_MPY(wr,fi[j]) + FIX_MPY(wi,fr[j]);
				qr = fr[i];
				qi = fi[i];
				if (shift) {
					qr >>= 1;
					qi >>= 1;
				}
				fr[j] = qr - tr;
				fi[j] = qi - ti;
				fr[i] = qr + tr;
				fi[i] = qi + ti;
			}
		}
		--k;
		l = istep;
	}
	return scale;
}

/*
  fix_fftr() - forward/inverse FFT on array of real numbers.
  Real FFT/iFFT using half-size complex FFT by distributing
  even/odd samples into real/imaginary arrays respectively.
  In order to save data space (i.e. to avoid two arrays, one
  for real, one for imaginary samples), we proceed in the
  following two steps: a) samples are rearranged in the real
  array so that all even samples are in places 0-(N/2-1) and
  all imaginary samples in places (N/2)-(N-1), and b) fix_fft
  is called with fr and fi pointing to index 0 and index N/2
  respectively in the original array. The above guarantees
  that fix_fft "sees" consecutive real samples as alternating
  real and imaginary samples in the complex array.
*/
int fix_fftr(short f[], int m, int inverse)
{
	int i, N = 1<<(m-1), scale = 0;
	short tt, *fr=f, *fi=&f[N];

	if (inverse)
		scale = fix_fft(fi, fr, m-1, inverse);
	for (i=1; i<N; i+=2) {
		tt = f[N+i-1];
		f[N+i-1] = f[i];
		f[i] = tt;
	}
	if (! inverse)
		scale = fix_fft(fi, fr, m-1, inverse);
	return scale;
}

fix_fft.h

#ifndef FIX_FFT_H
#define FIX_FFT_H

int fix_fftr(short*, int, int);

#endif

main.c

#include <stdio.h>
#include <stdlib.h>
#include "fix_fft.h"

FILE*fp;

#define FFT_SAMP (9)

char help[] = "usage: <in> <out> <inverse? 1 : 0>";
int main(int argc, char** argv)
{
	if(argc < 3){
		printf("%s\n", help);
		return 0;
	}
	/* Try to open the given file */
	fp = fopen(argv[1], "rb");
	if(!fp) {
		printf("File not found!\n");
		return 0;
	}
	fseek(fp, 0, SEEK_END);
	unsigned int Sz = ftell(fp);
	rewind(fp);
	short* inBuf = (short*)malloc((1<<FFT_SAMP)*2);
	if(!inBuf){
		fclose(fp);
		return 1;
	}

	/* try to create a file */
	FILE* out = fopen(argv[2], "wb");
	if(out==NULL){
		fclose(fp);
		free(inBuf);
		printf("%s couldn't be created!\n", argv[2]);
	}
	
	int i = 0;
	while((i+(1<<FFT_SAMP)*2) < Sz) {
		fread(inBuf, 1, (1<<FFT_SAMP)*2, fp);
		fix_fftr(inBuf, FFT_SAMP, 0);
		if(argv[3][0]=='1')
			fix_fftr(inBuf, FFT_SAMP, 1);
		fwrite(inBuf, 1, (1<<FFT_SAMP)*2, out);
		i+= (1<<FFT_SAMP)*2;
	}
	fclose(fp);
	fclose(out);
	free(inBuf);
	return 1;
}

Can you provide example input text file?

When I do 128 point FFT， the result is supposed to be a length of 65 complex numbers. However, the output of fixed_fft is just 64 complex number. Thus, I wonder which component is discarded, the DC component or the Nyquist component?

When I do 128 point FFT， the result is supposed to be a length of 65 complex numbers. However, the output of fixed_fft is just 64 complex number. Thus, I wonder which component is discarded, the DC component or the Nyquist component?

Not even 65 samples, the output of FFT is of the same length as input. Half of the data is redundant for non-complex inputs, because for real inputs it is Hermitian symmetric.

if we change N_WAVE value =256 , how to generate Sinewave table.

if we change N_WAVE value =256 , how to generate Sinewave table.

Same question here. Any ideas? Thanks.

I found one solution here in this code repo rxseger/rx_tools: rx_fm, rx_power, and rx_sdr tools for receiving data from SDRs, based on rtl_fm, rtl_power, and rtl_sdr from librtlsdr, but using the SoapySDR vendor-neutral SDR support library instead, intended to support a wider range of devices than RTL-SDR, especially in this file and lines:

https://github.com/rxseger/rx_tools/blob/811b21c4c8a592515279bd19f7460c6e4ff0551c/src/rtl_power.c#LL234C1-L255C1

There is a function to generate the Sin Table depend on the FFT size.

Also, the code is mentioned here: jj's useful and ugly FFT page