|
|
/* ----------------------------------------------------------------------
|
|
|
* Copyright (C) 2010 ARM Limited. All rights reserved.
|
|
|
*
|
|
|
* $Date: 15. July 2011
|
|
|
* $Revision: V1.0.10
|
|
|
*
|
|
|
* Project: CMSIS DSP Library
|
|
|
* Title: arm_cfft_radix4_q31.c
|
|
|
*
|
|
|
* Description: This file has function definition of Radix-4 FFT & IFFT function and
|
|
|
* In-place bit reversal using bit reversal table
|
|
|
*
|
|
|
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
|
|
|
*
|
|
|
* Version 1.0.10 2011/7/15
|
|
|
* Big Endian support added and Merged M0 and M3/M4 Source code.
|
|
|
*
|
|
|
* Version 1.0.3 2010/11/29
|
|
|
* Re-organized the CMSIS folders and updated documentation.
|
|
|
*
|
|
|
* Version 1.0.2 2010/11/11
|
|
|
* Documentation updated.
|
|
|
*
|
|
|
* Version 1.0.1 2010/10/05
|
|
|
* Production release and review comments incorporated.
|
|
|
*
|
|
|
* Version 1.0.0 2010/09/20
|
|
|
* Production release and review comments incorporated.
|
|
|
*
|
|
|
* Version 0.0.5 2010/04/26
|
|
|
* incorporated review comments and updated with latest CMSIS layer
|
|
|
*
|
|
|
* Version 0.0.3 2010/03/10
|
|
|
* Initial version
|
|
|
* -------------------------------------------------------------------- */
|
|
|
#include "arm_math.h"
|
|
|
|
|
|
|
|
|
/**
|
|
|
* @ingroup groupTransforms
|
|
|
*/
|
|
|
|
|
|
/**
|
|
|
* @addtogroup CFFT_CIFFT
|
|
|
* @{
|
|
|
*/
|
|
|
|
|
|
/**
|
|
|
* @details
|
|
|
* @brief Processing function for the Q31 CFFT/CIFFT.
|
|
|
* @param[in] *S points to an instance of the Q31 CFFT/CIFFT structure.
|
|
|
* @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
|
|
|
* @return none.
|
|
|
*
|
|
|
* \par Input and output formats:
|
|
|
* \par
|
|
|
* Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
|
|
|
* Hence the output format is different for different FFT sizes.
|
|
|
* The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
|
|
|
* \par
|
|
|
* \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT"
|
|
|
* \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"
|
|
|
*
|
|
|
*/
|
|
|
|
|
|
void arm_cfft_radix4_q31(
|
|
|
const arm_cfft_radix4_instance_q31 * S,
|
|
|
q31_t * pSrc)
|
|
|
{
|
|
|
if(S->ifftFlag == 1u)
|
|
|
{
|
|
|
/* Complex IFFT radix-4 */
|
|
|
arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle,
|
|
|
S->twidCoefModifier);
|
|
|
}
|
|
|
else
|
|
|
{
|
|
|
/* Complex FFT radix-4 */
|
|
|
arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle,
|
|
|
S->twidCoefModifier);
|
|
|
}
|
|
|
|
|
|
|
|
|
if(S->bitReverseFlag == 1u)
|
|
|
{
|
|
|
/* Bit Reversal */
|
|
|
arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
|
|
|
}
|
|
|
|
|
|
}
|
|
|
|
|
|
/**
|
|
|
* @} end of CFFT_CIFFT group
|
|
|
*/
|
|
|
|
|
|
/*
|
|
|
* Radix-4 FFT algorithm used is :
|
|
|
*
|
|
|
* 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
|
|
|
*
|
|
|
*
|
|
|
* 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'
|
|
|
*
|
|
|
*
|
|
|
* Twiddle factors for radix-4 FFT:
|
|
|
* Wn = co1 + j * (- si1)
|
|
|
* W2n = co2 + j * (- si2)
|
|
|
* W3n = co3 + j * (- si3)
|
|
|
*
|
|
|
* Butterfly implementation:
|
|
|
* xa' = xa + xb + xc + xd
|
|
|
* ya' = ya + yb + yc + yd
|
|
|
* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
|
|
|
* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
|
|
|
* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
|
|
|
* yc' = (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)
|
|
|
*
|
|
|
*/
|
|
|
|
|
|
/**
|
|
|
* @brief Core function for the Q31 CFFT butterfly process.
|
|
|
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type.
|
|
|
* @param[in] fftLen length of the FFT.
|
|
|
* @param[in] *pCoef points to twiddle coefficient buffer.
|
|
|
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
|
|
|
* @return none.
|
|
|
*/
|
|
|
|
|
|
void arm_radix4_butterfly_q31(
|
|
|
q31_t * pSrc,
|
|
|
uint32_t fftLen,
|
|
|
q31_t * pCoef,
|
|
|
uint32_t twidCoefModifier)
|
|
|
{
|
|
|
uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
|
|
|
q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
|
|
|
|
|
|
|
|
|
/* Total process is divided into three stages */
|
|
|
|
|
|
/* process first stage, middle stages, & last stage */
|
|
|
|
|
|
|
|
|
/* start of first stage process */
|
|
|
|
|
|
/* Initializations for the first stage */
|
|
|
n2 = fftLen;
|
|
|
n1 = n2;
|
|
|
/* n2 = fftLen/4 */
|
|
|
n2 >>= 2u;
|
|
|
i0 = 0u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
j = n2;
|
|
|
|
|
|
/* Calculation of first stage */
|
|
|
do
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* input is in 1.31(q31) format and provide 4 guard bits for the input */
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = (pSrc[(2u * i0)] >> 4u) + (pSrc[(2u * i2)] >> 4u);
|
|
|
/* xa - xc */
|
|
|
r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
|
|
|
/* ya - yc */
|
|
|
s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1);
|
|
|
/* (xa + xc) - (xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
/* yb + yd */
|
|
|
t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2);
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* yb - yd */
|
|
|
t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
|
|
|
/* xb - xd */
|
|
|
t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
|
|
|
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = 2u * ia1;
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
|
|
|
((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
|
|
|
((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r1 = r2 + t1;
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r2 = r2 - t1;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s1 = s2 - t2;
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s2 = s2 + t2;
|
|
|
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
|
|
|
((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
|
|
|
((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
|
|
|
|
|
|
/* index calculation for the coefficients */
|
|
|
ia3 = 3u * ia1;
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
|
|
|
((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
|
|
|
((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
|
|
|
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
/* Updating input index */
|
|
|
i0 = i0 + 1u;
|
|
|
|
|
|
} while(--j);
|
|
|
|
|
|
/* end of first stage process */
|
|
|
|
|
|
/* data is in 5.27(q27) format */
|
|
|
|
|
|
|
|
|
/* start of Middle stages process */
|
|
|
|
|
|
|
|
|
/* each stage in middle stages provides two down scaling of the input */
|
|
|
|
|
|
twidCoefModifier <<= 2u;
|
|
|
|
|
|
|
|
|
for (k = fftLen / 4u; k > 4u; k >>= 2u)
|
|
|
{
|
|
|
/* Initializations for the first stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
/* Calculation of first stage */
|
|
|
for (j = 0u; j <= (n2 - 1u); j++)
|
|
|
{
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = ia1 + ia1;
|
|
|
ia3 = ia2 + ia1;
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
for (i0 = j; i0 < fftLen; i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1) >> 2u;
|
|
|
/* xa + xc -(xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb - yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
/* (xb - xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
|
|
|
((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1u;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
|
|
|
((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u;
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r1 = r2 + t1;
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r2 = r2 - t1;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s1 = s2 - t2;
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s2 = s2 + t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
|
|
|
((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
|
|
|
((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
|
|
|
((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
|
|
|
((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
|
|
|
}
|
|
|
}
|
|
|
twidCoefModifier <<= 2u;
|
|
|
}
|
|
|
|
|
|
/* End of Middle stages process */
|
|
|
|
|
|
/* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
|
|
|
/* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
|
|
|
/* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
|
|
|
/* data is in 5.27(q27) format for the 16 point as there are no middle stages */
|
|
|
|
|
|
|
|
|
/* start of Last stage process */
|
|
|
|
|
|
/* Initializations of last stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
|
|
|
/* Calculations of last stage */
|
|
|
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xb */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
/* xa - xb */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xc + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1);
|
|
|
/* (xa + xb) - (xc + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2);
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb-yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
/* (xb-xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = r1;
|
|
|
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = s1;
|
|
|
|
|
|
/* (xa+yb-xc-yd) */
|
|
|
r1 = r2 + t1;
|
|
|
/* (xa-yb-xc+yd) */
|
|
|
r2 = r2 - t1;
|
|
|
|
|
|
/* (ya-xb-yc+xd) */
|
|
|
s1 = s2 - t2;
|
|
|
/* (ya+xb-yc-xd) */
|
|
|
s2 = s2 + t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = r1;
|
|
|
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = s1;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = r2;
|
|
|
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = s2;
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
/* output is in 11.21(q21) format for the 1024 point */
|
|
|
/* output is in 9.23(q23) format for the 256 point */
|
|
|
/* output is in 7.25(q25) format for the 64 point */
|
|
|
/* output is in 5.27(q27) format for the 16 point */
|
|
|
|
|
|
/* End of last stage process */
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
/**
|
|
|
* @brief Core function for the Q31 CIFFT butterfly process.
|
|
|
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type.
|
|
|
* @param[in] fftLen length of the FFT.
|
|
|
* @param[in] *pCoef points to twiddle coefficient buffer.
|
|
|
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
|
|
|
* @return none.
|
|
|
*/
|
|
|
|
|
|
|
|
|
/*
|
|
|
* Radix-4 IFFT algorithm used is :
|
|
|
*
|
|
|
* CIFFT uses same twiddle coefficients as CFFT Function
|
|
|
* x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
|
|
|
*
|
|
|
*
|
|
|
* IFFT is implemented with following changes in equations from FFT
|
|
|
*
|
|
|
* 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
|
|
|
*
|
|
|
*
|
|
|
* 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'
|
|
|
*
|
|
|
*
|
|
|
* Twiddle factors for radix-4 IFFT:
|
|
|
* Wn = co1 + j * (si1)
|
|
|
* W2n = co2 + j * (si2)
|
|
|
* W3n = co3 + j * (si3)
|
|
|
|
|
|
* The real and imaginary output values for the radix-4 butterfly are
|
|
|
* xa' = xa + xb + xc + xd
|
|
|
* ya' = ya + yb + yc + yd
|
|
|
* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
|
|
|
* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
|
|
|
* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
|
|
|
* yc' = (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)
|
|
|
*
|
|
|
*/
|
|
|
|
|
|
void arm_radix4_butterfly_inverse_q31(
|
|
|
q31_t * pSrc,
|
|
|
uint32_t fftLen,
|
|
|
q31_t * pCoef,
|
|
|
uint32_t twidCoefModifier)
|
|
|
{
|
|
|
uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
|
|
|
q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
|
|
|
|
|
|
/* input is be 1.31(q31) format for all FFT sizes */
|
|
|
/* Total process is divided into three stages */
|
|
|
/* process first stage, middle stages, & last stage */
|
|
|
|
|
|
/* Start of first stage process */
|
|
|
|
|
|
/* Initializations for the first stage */
|
|
|
n2 = fftLen;
|
|
|
n1 = n2;
|
|
|
/* n2 = fftLen/4 */
|
|
|
n2 >>= 2u;
|
|
|
i0 = 0u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
j = n2;
|
|
|
|
|
|
do
|
|
|
{
|
|
|
|
|
|
/* input is in 1.31(q31) format and provide 4 guard bits for the input */
|
|
|
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = (pSrc[2u * i0] >> 4u) + (pSrc[2u * i2] >> 4u);
|
|
|
/* xa - xc */
|
|
|
r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
|
|
|
/* ya - yc */
|
|
|
s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1);
|
|
|
/* (xa + xc) - (xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
/* yb + yd */
|
|
|
t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2);
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* yb - yd */
|
|
|
t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
|
|
|
/* xb - xd */
|
|
|
t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
|
|
|
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = 2u * ia1;
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
|
|
|
((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[2u * i1 + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
|
|
|
((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r1 = r2 - t1;
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s1 = s2 + t2;
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
|
|
|
((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
|
|
|
((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
|
|
|
|
|
|
/* index calculation for the coefficients */
|
|
|
ia3 = 3u * ia1;
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
|
|
|
((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
|
|
|
((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
|
|
|
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
/* Updating input index */
|
|
|
i0 = i0 + 1u;
|
|
|
|
|
|
} while(--j);
|
|
|
|
|
|
/* data is in 5.27(q27) format */
|
|
|
/* each stage provides two down scaling of the input */
|
|
|
|
|
|
|
|
|
/* Start of Middle stages process */
|
|
|
|
|
|
twidCoefModifier <<= 2u;
|
|
|
|
|
|
/* Calculation of second stage to excluding last stage */
|
|
|
for (k = fftLen / 4u; k > 4u; k >>= 2u)
|
|
|
{
|
|
|
/* Initializations for the first stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
for (j = 0; j <= (n2 - 1u); j++)
|
|
|
{
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = ia1 + ia1;
|
|
|
ia3 = ia2 + ia1;
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
for (i0 = j; i0 < fftLen; i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1) >> 2u;
|
|
|
/* xa + xc -(xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb - yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
/* (xb - xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32u)) -
|
|
|
((int32_t) (((q63_t) s1 * si2) >> 32u))) >> 1u;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] =
|
|
|
(((int32_t) (((q63_t) s1 * co2) >> 32u)) +
|
|
|
((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r1 = r2 - t1;
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s1 = s2 + t2;
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
|
|
|
((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
|
|
|
((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[(2u * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
|
|
|
((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
|
|
|
((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
|
|
|
}
|
|
|
}
|
|
|
twidCoefModifier <<= 2u;
|
|
|
}
|
|
|
|
|
|
/* End of Middle stages process */
|
|
|
|
|
|
/* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
|
|
|
/* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
|
|
|
/* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
|
|
|
/* data is in 5.27(q27) format for the 16 point as there are no middle stages */
|
|
|
|
|
|
|
|
|
/* Start of last stage process */
|
|
|
|
|
|
|
|
|
/* Initializations of last stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
|
|
|
/* Calculations of last stage */
|
|
|
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xc + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1);
|
|
|
/* (xa + xb) - (xc + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2);
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb-yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
/* (xb-xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = r1;
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = s1;
|
|
|
|
|
|
/* (xa - xc) - (yb-yd) */
|
|
|
r1 = r2 - t1;
|
|
|
|
|
|
/* (xa - xc) + (yb-yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb-xd) */
|
|
|
s1 = s2 + t2;
|
|
|
|
|
|
/* (ya - yc) - (xb-xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = r1;
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = s1;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = r2;
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = s2;
|
|
|
|
|
|
}
|
|
|
|
|
|
/* output is in 11.21(q21) format for the 1024 point */
|
|
|
/* output is in 9.23(q23) format for the 256 point */
|
|
|
/* output is in 7.25(q25) format for the 64 point */
|
|
|
/* output is in 5.27(q27) format for the 16 point */
|
|
|
|
|
|
/* End of last stage process */
|
|
|
}
|
|
|
|
|
|
|
|
|
/*
|
|
|
* @brief In-place bit reversal function.
|
|
|
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type.
|
|
|
* @param[in] fftLen length of the FFT.
|
|
|
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
|
|
|
* @param[in] *pBitRevTab points to bit reversal table.
|
|
|
* @return none.
|
|
|
*/
|
|
|
|
|
|
void arm_bitreversal_q31(
|
|
|
q31_t * pSrc,
|
|
|
uint32_t fftLen,
|
|
|
uint16_t bitRevFactor,
|
|
|
uint16_t * pBitRevTable)
|
|
|
{
|
|
|
uint32_t fftLenBy2, fftLenBy2p1, i, j;
|
|
|
q31_t in;
|
|
|
|
|
|
/* Initializations */
|
|
|
j = 0u;
|
|
|
fftLenBy2 = fftLen / 2u;
|
|
|
fftLenBy2p1 = (fftLen / 2u) + 1u;
|
|
|
|
|
|
/* Bit Reversal Implementation */
|
|
|
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
|
|
|
{
|
|
|
if(i < j)
|
|
|
{
|
|
|
/* pSrc[i] <-> pSrc[j]; */
|
|
|
in = pSrc[2u * i];
|
|
|
pSrc[2u * i] = pSrc[2u * j];
|
|
|
pSrc[2u * j] = in;
|
|
|
|
|
|
/* pSrc[i+1u] <-> pSrc[j+1u] */
|
|
|
in = pSrc[(2u * i) + 1u];
|
|
|
pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
|
|
|
pSrc[(2u * j) + 1u] = in;
|
|
|
|
|
|
/* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
|
|
|
in = pSrc[2u * (i + fftLenBy2p1)];
|
|
|
pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
|
|
|
pSrc[2u * (j + fftLenBy2p1)] = in;
|
|
|
|
|
|
/* pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
|
|
|
in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
|
|
|
pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
|
|
|
pSrc[(2u * (j + fftLenBy2p1)) + 1u];
|
|
|
pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
|
|
|
|
|
|
}
|
|
|
|
|
|
/* pSrc[i+1u] <-> pSrc[j+1u] */
|
|
|
in = pSrc[2u * (i + 1u)];
|
|
|
pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
|
|
|
pSrc[2u * (j + fftLenBy2)] = in;
|
|
|
|
|
|
/* pSrc[i+2u] <-> pSrc[j+2u] */
|
|
|
in = pSrc[(2u * (i + 1u)) + 1u];
|
|
|
pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
|
|
|
pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
|
|
|
|
|
|
/* Reading the index for the bit reversal */
|
|
|
j = *pBitRevTable;
|
|
|
|
|
|
/* Updating the bit reversal index depending on the fft length */
|
|
|
pBitRevTable += bitRevFactor;
|
|
|
}
|
|
|
}
|
|
|
|
