blob: 7ed8fdedf1a1200c0c1ddc10f21712b82ede113d [file] [log] [blame]
{real[0], imag[0], real[1], imag[1],..}
* * \par Lengths supported by the transform: * \par * Internally, the function utilize a Radix-8 decimation in frequency(DIF) algorithm * and the size of the FFT supported are of the lengths [ 64, 512, 4096]. * * * \par Algorithm: * * Complex Fast Fourier Transform: * \par * Input real and imaginary data: *
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
* where N is length of FFT * \par * Output real and imaginary data: *
* X(4r) = xa'+ j * ya'
* X(4r+1) = xb'+ j * yb'
* X(4r+2) = xc'+ j * yc'
* X(4r+3) = xd'+ j * yd'
*
* \par * Twiddle factors for Radix-8 FFT: *
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
*
* * \par * \image html CFFT.gif "Radix-8 Decimation-in Frequency Complex Fast Fourier Transform" * * \par * Output from Radix-8 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output. * \par * Butterfly CFFT equations: *
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
* yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
* xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
* yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
*
* * \par * where fftLen length of CFFT/CIFFT; ifftFlag Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT); * bitReverseFlag Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order); * pTwiddlepoints to array of twiddle coefficients; pBitRevTable points to the array of bit reversal table. * twidCoefModifier modifier for twiddle factor table which supports all FFT lengths with same table; * pBitRevTable modifier for bit reversal table which supports all FFT lengths with same table. * onebyfftLen value of 1/fftLen to calculate CIFFT; * * \par Fixed-Point Behavior * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function. * Refer to the function specific documentation below for usage guidelines. */ /* * @brief Core function for the floating-point CFFT butterfly process. * @param[in, out] *pSrc points to the in-place buffer of floating-point data type. * @param[in] fftLen length of the FFT. * @param[in] *pCoef points to the twiddle coefficient buffer. * @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. * @return none. */ void arm_radix8_butterfly_f32( float32_t * pSrc, uint16_t fftLen, const float32_t * pCoef, uint16_t twidCoefModifier) { uint32_t ia1, ia2, ia3, ia4, ia5, ia6, ia7; uint32_t i1, i2, i3, i4, i5, i6, i7, i8; uint32_t id; uint32_t n1, n2, j; float32_t r1, r2, r3, r4, r5, r6, r7, r8; float32_t t1, t2; float32_t s1, s2, s3, s4, s5, s6, s7, s8; float32_t p1, p2, p3, p4; float32_t co2, co3, co4, co5, co6, co7, co8; float32_t si2, si3, si4, si5, si6, si7, si8; const float32_t C81 = 0.70710678118f; n2 = fftLen; do { n1 = n2; n2 = n2 >> 3; i1 = 0; do { i2 = i1 + n2; i3 = i2 + n2; i4 = i3 + n2; i5 = i4 + n2; i6 = i5 + n2; i7 = i6 + n2; i8 = i7 + n2; r1 = pSrc[2 * i1] + pSrc[2 * i5]; r5 = pSrc[2 * i1] - pSrc[2 * i5]; r2 = pSrc[2 * i2] + pSrc[2 * i6]; r6 = pSrc[2 * i2] - pSrc[2 * i6]; r3 = pSrc[2 * i3] + pSrc[2 * i7]; r7 = pSrc[2 * i3] - pSrc[2 * i7]; r4 = pSrc[2 * i4] + pSrc[2 * i8]; r8 = pSrc[2 * i4] - pSrc[2 * i8]; t1 = r1 - r3; r1 = r1 + r3; r3 = r2 - r4; r2 = r2 + r4; pSrc[2 * i1] = r1 + r2; pSrc[2 * i5] = r1 - r2; r1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1]; s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1]; r2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1]; s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1]; s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1]; s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1]; r4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1]; s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1]; t2 = r1 - s3; r1 = r1 + s3; s3 = r2 - r4; r2 = r2 + r4; pSrc[2 * i1 + 1] = r1 + r2; pSrc[2 * i5 + 1] = r1 - r2; pSrc[2 * i3] = t1 + s3; pSrc[2 * i7] = t1 - s3; pSrc[2 * i3 + 1] = t2 - r3; pSrc[2 * i7 + 1] = t2 + r3; r1 = (r6 - r8) * C81; r6 = (r6 + r8) * C81; r2 = (s6 - s8) * C81; s6 = (s6 + s8) * C81; t1 = r5 - r1; r5 = r5 + r1; r8 = r7 - r6; r7 = r7 + r6; t2 = s5 - r2; s5 = s5 + r2; s8 = s7 - s6; s7 = s7 + s6; pSrc[2 * i2] = r5 + s7; pSrc[2 * i8] = r5 - s7; pSrc[2 * i6] = t1 + s8; pSrc[2 * i4] = t1 - s8; pSrc[2 * i2 + 1] = s5 - r7; pSrc[2 * i8 + 1] = s5 + r7; pSrc[2 * i6 + 1] = t2 - r8; pSrc[2 * i4 + 1] = t2 + r8; i1 += n1; } while(i1 < fftLen); if(n2 < 8) break; ia1 = 0; j = 1; do { /* index calculation for the coefficients */ id = ia1 + twidCoefModifier; ia1 = id; ia2 = ia1 + id; ia3 = ia2 + id; ia4 = ia3 + id; ia5 = ia4 + id; ia6 = ia5 + id; ia7 = ia6 + id; co2 = pCoef[2 * ia1]; co3 = pCoef[2 * ia2]; co4 = pCoef[2 * ia3]; co5 = pCoef[2 * ia4]; co6 = pCoef[2 * ia5]; co7 = pCoef[2 * ia6]; co8 = pCoef[2 * ia7]; si2 = pCoef[2 * ia1 + 1]; si3 = pCoef[2 * ia2 + 1]; si4 = pCoef[2 * ia3 + 1]; si5 = pCoef[2 * ia4 + 1]; si6 = pCoef[2 * ia5 + 1]; si7 = pCoef[2 * ia6 + 1]; si8 = pCoef[2 * ia7 + 1]; i1 = j; do { /* index calculation for the input */ i2 = i1 + n2; i3 = i2 + n2; i4 = i3 + n2; i5 = i4 + n2; i6 = i5 + n2; i7 = i6 + n2; i8 = i7 + n2; r1 = pSrc[2 * i1] + pSrc[2 * i5]; r5 = pSrc[2 * i1] - pSrc[2 * i5]; r2 = pSrc[2 * i2] + pSrc[2 * i6]; r6 = pSrc[2 * i2] - pSrc[2 * i6]; r3 = pSrc[2 * i3] + pSrc[2 * i7]; r7 = pSrc[2 * i3] - pSrc[2 * i7]; r4 = pSrc[2 * i4] + pSrc[2 * i8]; r8 = pSrc[2 * i4] - pSrc[2 * i8]; t1 = r1 - r3; r1 = r1 + r3; r3 = r2 - r4; r2 = r2 + r4; pSrc[2 * i1] = r1 + r2; r2 = r1 - r2; s1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1]; s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1]; s2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1]; s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1]; s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1]; s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1]; s4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1]; s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1]; t2 = s1 - s3; s1 = s1 + s3; s3 = s2 - s4; s2 = s2 + s4; r1 = t1 + s3; t1 = t1 - s3; pSrc[2 * i1 + 1] = s1 + s2; s2 = s1 - s2; s1 = t2 - r3; t2 = t2 + r3; p1 = co5 * r2; p2 = si5 * s2; p3 = co5 * s2; p4 = si5 * r2; pSrc[2 * i5] = p1 + p2; pSrc[2 * i5 + 1] = p3 - p4; p1 = co3 * r1; p2 = si3 * s1; p3 = co3 * s1; p4 = si3 * r1; pSrc[2 * i3] = p1 + p2; pSrc[2 * i3 + 1] = p3 - p4; p1 = co7 * t1; p2 = si7 * t2; p3 = co7 * t2; p4 = si7 * t1; pSrc[2 * i7] = p1 + p2; pSrc[2 * i7 + 1] = p3 - p4; r1 = (r6 - r8) * C81; r6 = (r6 + r8) * C81; s1 = (s6 - s8) * C81; s6 = (s6 + s8) * C81; t1 = r5 - r1; r5 = r5 + r1; r8 = r7 - r6; r7 = r7 + r6; t2 = s5 - s1; s5 = s5 + s1; s8 = s7 - s6; s7 = s7 + s6; r1 = r5 + s7; r5 = r5 - s7; r6 = t1 + s8; t1 = t1 - s8; s1 = s5 - r7; s5 = s5 + r7; s6 = t2 - r8; t2 = t2 + r8; p1 = co2 * r1; p2 = si2 * s1; p3 = co2 * s1; p4 = si2 * r1; pSrc[2 * i2] = p1 + p2; pSrc[2 * i2 + 1] = p3 - p4; p1 = co8 * r5; p2 = si8 * s5; p3 = co8 * s5; p4 = si8 * r5; pSrc[2 * i8] = p1 + p2; pSrc[2 * i8 + 1] = p3 - p4; p1 = co6 * r6; p2 = si6 * s6; p3 = co6 * s6; p4 = si6 * r6; pSrc[2 * i6] = p1 + p2; pSrc[2 * i6 + 1] = p3 - p4; p1 = co4 * t1; p2 = si4 * t2; p3 = co4 * t2; p4 = si4 * t1; pSrc[2 * i4] = p1 + p2; pSrc[2 * i4 + 1] = p3 - p4; i1 += n1; } while(i1 < fftLen); j++; } while(j < n2); twidCoefModifier <<= 3; } while(n2 > 7); } /** * @} end of Radix8_CFFT_CIFFT group */