/* fix_fft.c - Fixed-point Fast Fourier Transform */ /* fix_fft() perform FFT or inverse FFT window() applies a Hanning window to the (time) input fix_loud() calculates the loudness of the signal, for each freq point. Result is an integer array, units are dB (values will be negative). iscale() scale an integer value by (numer/denom). fix_mpy() perform fixed-point multiplication. Sinewave[1024] sinewave normalized to 32767 (= 1.0). Loudampl[100] Amplitudes for lopudnesses from 0 to -99 dB. Low_pass Low-pass filter, cutoff at sample_freq / 4. All data are fixed-point short integers, in which -32768 to +32768 represent -1.0 to +1.0. 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 one in the lower half is reported as 0dB by fix_loud(). 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 the 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. TURBO C, any memory model; uses inline assembly for speed and for carefully-scaled arithmetic. Written by: Tom Roberts 11/8/89 Made portable: Malcolm Slaney 12/15/94 malcolm@interval.com Timing on a Macintosh PowerBook 180.... (using Symantec C6.0) fix_fft (1024 points) 8 ticks fft (1024 points - Using SANE) 112 Ticks fft (1024 points - Using FPU) 11 */ /* FIX_MPY() - fixed-point multiplication macro. This macro is a statement, not an expression (uses asm). BEWARE: make sure _DX is not clobbered by evaluating (A) or DEST. args are all of type fixed. Scaling ensures that 32767*32767 = 32767. */ #define dosFIX_MPY(DEST,A,B) { \ _DX = (B); \ _AX = (A); \ asm imul dx; \ asm add ax,ax; \ asm adc dx,dx; \ DEST = _DX; } #define FIX_MPY(DEST,A,B) DEST = ((long)(A) * (long)(B))>>15 #define N_WAVE 1024 /* dimension of Sinewave[] */ #define LOG2_N_WAVE 10 /* log2(N_WAVE) */ #define N_LOUD 100 /* dimension of Loudampl[] */ #ifndef fixed #define fixed short #endif extern fixed Sinewave[N_WAVE]; /* placed at end of this file for clarity */ extern fixed Loudampl[N_LOUD]; int db_from_ampl(fixed re, fixed im); fixed fix_mpy(fixed a, fixed b); /* fix_fft() - perform fast Fourier transform. if n>0 FFT is done, if n<0 inverse FFT is done fr[n],fi[n] are real,imaginary arrays, INPUT AND RESULT. size of data = 2**m set inverse to 0=dft, 1=idft */ int fix_fft(fixed fr[], fixed fi[], int m, int inverse) { int mr,nn,i,j,l,k,istep, n, scale, shift; fixed qr,qi,tr,ti,wr,wi,t; n = 1< 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 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>= 1; wi >>= 1; } for(i=m; i>= 1; qi >>= 1; } fr[j] = qr - tr; fi[j] = qi - ti; fr[i] = qr + tr; fi[i] = qi + ti; } } --k; l = istep; } return scale; } /* window() - apply a Hanning window */ void window(fixed fr[], int n) { int i,j,k; j = N_WAVE/n; n >>= 1; for(i=0,k=N_WAVE/4; i>1)); n <<= 1; for(k-=j; i>1)); } /* fix_loud() - compute loudness of freq-spectrum components. n should be ntot/2, where ntot was passed to fix_fft(); 6 dB is added to account for the omitted alias components. scale_shift should be the result of fix_fft(), if the time-series was obtained from an inverse FFT, 0 otherwise. loud[] is the loudness, in dB wrt 32767; will be +10 to -N_LOUD. */ void fix_loud(fixed loud[], fixed fr[], fixed fi[], int n, int scale_shift) { int i, max; max = 0; if(scale_shift > 0) max = 10; scale_shift = (scale_shift+1) * 6; for(i=0; i max) loud[i] = max; } } /* db_from_ampl() - find loudness (in dB) from the complex amplitude. */ int db_from_ampl(fixed re, fixed im) { static long loud2[N_LOUD] = {0}; long v; int i; if(loud2[0] == 0) { loud2[0] = (long)Loudampl[0] * (long)Loudampl[0]; for(i=1; i>4; off &= 0x000F; pa = MK_FP(seg,off); */ sum = 0L; while(n--) { a = *pa++; b = *pb++; FIX_MPY(a,a,b); sum += a; } if(sum > 0x7FFF) sum = 0x7FFF; else if(sum < -0x7FFF) sum = -0x7FFF; return (fixed)sum; #ifdef DOS /* ASSUMES hpa is already normalized so FP_OFF(hpa) < 16 */ asm push ds asm lds si,hpa asm les di,pb asm xor bx,bx asm xor cx,cx loop: /* intermediate values can overflow by a factor of 2 without causing an error; the final value must not overflow! */ asm lodsw . asm imul word ptr es:[di] asm add bx,ax asm adc cx,dx asm jo overflow asm add di,2 asm dec word ptr n asm jg loop asm add bx,bx asm adc cx,cx asm jo overflow asm pop ds return _CX; overflow: asm mov cx,7FFFH asm adc cx,0 asm pop ds return _CX; #endif } #if N_WAVE != 1024 ERROR: N_WAVE != 1024 #endif fixed Sinewave[1024] = { 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, -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, }; #if N_LOUD != 100 ERROR: N_LOUD != 100 #endif fixed Loudampl[100] = { 32767, 29203, 26027, 23197, 20674, 18426, 16422, 14636, 13044, 11626, 10361, 9234, 8230, 7335, 6537, 5826, 5193, 4628, 4125, 3676, 3276, 2920, 2602, 2319, 2067, 1842, 1642, 1463, 1304, 1162, 1036, 923, 823, 733, 653, 582, 519, 462, 412, 367, 327, 292, 260, 231, 206, 184, 164, 146, 130, 116, 103, 92, 82, 73, 65, 58, 51, 46, 41, 36, 32, 29, 26, 23, 20, 18, 16, 14, 13, 11, 10, 9, 8, 7, 6, 5, 5, 4, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, }; #ifdef MAIN #include #include #define M 4 #define N (1<