Michele Riccio
mbed-os 6.10 versione
Diff: cmsis_dsp/TransformFunctions/arm_cfft_radix2_f32.c
- Revision:
- 1:fdd22bb7aa52
- Child:
- 2:da51fb522205
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/cmsis_dsp/TransformFunctions/arm_cfft_radix2_f32.c Wed Nov 28 12:30:09 2012 +0000
@@ -0,0 +1,511 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010 ARM Limited. All rights reserved.
+*
+* $Date: 15. February 2012
+* $Revision: V1.1.0
+*
+* Project: CMSIS DSP Library
+* Title: arm_cfft_radix2_f32.c
+*
+* Description: Radix-2 Decimation in Frequency CFFT & CIFFT Floating point processing function
+*
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Version 1.1.0 2012/02/15
+* Updated with more optimizations, bug fixes and minor API changes.
+*
+* Version 1.0.3 2010/11/29
+* Initial version
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**
+ * @ingroup groupTransforms
+ */
+
+/**
+ * @defgroup Radix2_CFFT_CIFFT Radix-2 Complex FFT Functions
+ *
+ * \par
+ * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
+ * Computational complexity of CFFT reduces drastically when compared to DFT.
+ * \par
+ * This set of functions implements CFFT/CIFFT
+ * for Q15, Q31, and floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output.
+ * Complex input is stored in input buffer in an interleaved fashion.
+ *
+ * \par
+ * The functions operate on blocks of input and output data and each call to the function processes
+ * <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values.
+ * \par
+ * The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
+ * <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
+ *
+ * \par Lengths supported by the transform:
+ * \par
+ * Internally, the function utilize a radix-2 decimation in frequency(DIF) algorithm
+ * and the size of the FFT supported are of the lengths [16, 32, 64, 128, 256, 512, 1024, 2048, 4096].
+ *
+ *
+ * \par Algorithm:
+ *
+ * <b>Complex Fast Fourier Transform:</b>
+ * \par
+ * Input real and imaginary data:
+ * <pre>
+ * x(n) = xa + j * ya
+ * x(n+N/2 ) = xb + j * yb
+ * </pre>
+ * where N is length of FFT
+ * \par
+ * Output real and imaginary data:
+ * <pre>
+ * X(2r) = xa'+ j * ya'
+ * X(2r+1) = xb'+ j * yb'
+ * </pre>
+ * \par
+ * Twiddle factors for radix-2 FFT:
+ * <pre>
+ * Wn = cosVal + j * (- sinVal)
+ * </pre>
+ *
+ * \par
+ * \image html CFFT_Radix2.gif "Radix-2 Decimation-in Frequency Complex Fast Fourier Transform"
+ *
+ * \par
+ * Output from Radix-2 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.
+ * \par
+ * <b> Butterfly CFFT equations:</b>
+ * <pre>
+ * xa' = xa + xb
+ * ya' = ya + yb
+ * xb' = (xa-xb)* cosVal + (ya-yb) * sinVal
+ * yb' = (ya-yb)* cosVal - (xa-xb) * sinVal
+ * </pre>
+ *
+ *
+ * <b>Complex Inverse Fast Fourier Transform:</b>
+ * \par
+ * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.
+ *
+ * \par
+ * <b> Modified Butterfly CIFFT equations:</b>
+ * <pre>
+ * xa' = xa + xb
+ * ya' = ya + yb
+ * xb' = (xa-xb)* cosVal - (ya-yb) * sinVal
+ * yb' = (ya-yb)* cosVal + (xa-xb) * sinVal
+ * </pre>
+ *
+ * \par Instance Structure
+ * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.
+ * There are separate instance structure declarations for each of the 3 supported data types.
+ *
+ * \par Initialization Functions
+ * There is also an associated initialization function for each data type.
+ * The initialization function performs the following operations:
+ * - Sets the values of the internal structure fields.
+ * - Initializes twiddle factor table and bit reversal table pointers
+ * \par
+ * Use of the initialization function is optional.
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.
+ * Manually initialize the instance structure as follows:
+ * <pre>
+ *arm_cfft_radix2_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};
+ *arm_cfft_radix2_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
+ *arm_cfft_radix2_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
+ * </pre>
+ * \par
+ * where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
+ * <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
+ * <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
+ * <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
+ * <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
+ * <code>onebyfftLen</code> 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.
+ */
+
+
+/**
+ * @addtogroup Radix2_CFFT_CIFFT
+ * @{
+ */
+
+/**
+ * @details
+ * @brief Processing function for the floating-point Radix-2 CFFT/CIFFT.
+ * @param[in] *S points to an instance of the floating-point Radix-2 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.
+ */
+
+void arm_cfft_radix2_f32(
+ const arm_cfft_radix2_instance_f32 * S,
+ float32_t * pSrc)
+{
+
+ if(S->ifftFlag == 1u)
+ {
+ /* Complex IFFT radix-2 */
+ arm_radix2_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
+ S->twidCoefModifier, S->onebyfftLen);
+ }
+ else
+ {
+ /* Complex FFT radix-2 */
+ arm_radix2_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
+ S->twidCoefModifier);
+ }
+
+ if(S->bitReverseFlag == 1u)
+ {
+ /* Bit Reversal */
+ arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+ }
+
+}
+
+
+/**
+ * @} end of Radix2_CFFT_CIFFT group
+ */
+
+
+
+/* ----------------------------------------------------------------------
+** Internal helper function used by the FFTs
+** ------------------------------------------------------------------- */
+
+/*
+ * @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_radix2_butterfly_f32(
+ float32_t * pSrc,
+ uint32_t fftLen,
+ float32_t * pCoef,
+ uint16_t twidCoefModifier)
+{
+
+ int i, j, k, l;
+ int n1, n2, ia;
+ float32_t xt, yt, cosVal, sinVal;
+
+#ifndef ARM_MATH_CM0
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ // loop for groups
+ for (i = 0; i < n2; i++)
+ {
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+
+ /* Twiddle coefficients index modifier */
+ ia = ia + twidCoefModifier;
+
+ /* index calculation for the input as, */
+ /* pSrc[i + 0], pSrc[i + fftLen/1] */
+ l = i + n2;
+
+ /* Butterfly implementation */
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+ pSrc[2u * l] = xt * cosVal + yt * sinVal;
+
+ pSrc[2u * l + 1u] = yt * cosVal - xt * sinVal;
+
+ } // groups loop end
+
+ twidCoefModifier = twidCoefModifier << 1u;
+
+ // loop for stage
+ for (k = fftLen / 2; k > 2; k = k >> 1)
+ {
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ // loop for groups
+ for (j = 0; j < n2; j++)
+ {
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = j; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+ pSrc[2u * l] = xt * cosVal + yt * sinVal;
+
+ pSrc[2u * l + 1u] = yt * cosVal - xt * sinVal;
+
+ } // butterfly loop end
+
+ } // groups loop end
+
+ twidCoefModifier = twidCoefModifier << 1u;
+ } // stages loop end
+
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = 0; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
+
+ pSrc[2u * l] = xt;
+
+ pSrc[2u * l + 1u] = yt;
+
+ } // groups loop end
+
+#else
+
+ //N = fftLen;
+ n2 = fftLen;
+
+ // loop for stage
+ for (k = fftLen; k > 1; k = k >> 1)
+ {
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ // loop for groups
+ for (j = 0; j < n2; j++)
+ {
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = j; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+ pSrc[2 * l] = (cosVal * xt + sinVal * yt); // >> 15;
+ pSrc[2 * l + 1] = (cosVal * yt - sinVal * xt); // >> 15;
+
+ }
+ }
+ twidCoefModifier = twidCoefModifier << 1u;
+ }
+
+#endif // #ifndef ARM_MATH_CM0
+
+}
+
+
+void arm_radix2_butterfly_inverse_f32(
+ float32_t * pSrc,
+ uint32_t fftLen,
+ float32_t * pCoef,
+ uint16_t twidCoefModifier,
+ float32_t onebyfftLen)
+{
+
+ int i, j, k, l;
+ int n1, n2, ia;
+ float32_t xt, yt, cosVal, sinVal;
+
+#ifndef ARM_MATH_CM0
+
+ //N = fftLen;
+ n2 = fftLen;
+
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ // loop for groups
+ for (i = 0; i < n2; i++)
+ {
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+ pSrc[2u * l] = xt * cosVal - yt * sinVal;
+
+ pSrc[2u * l + 1u] = yt * cosVal + xt * sinVal;
+
+ } // groups loop end
+
+ twidCoefModifier = twidCoefModifier << 1u;
+
+ // loop for stage
+ for (k = fftLen / 2; k > 2; k = k >> 1)
+ {
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ // loop for groups
+ for (j = 0; j < n2; j++)
+ {
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = j; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+ pSrc[2u * l] = xt * cosVal - yt * sinVal;
+
+ pSrc[2u * l + 1u] = yt * cosVal + xt * sinVal;
+
+ } // butterfly loop end
+
+ } // groups loop end
+
+ twidCoefModifier = twidCoefModifier << 1u;
+ } // stages loop end
+
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = 0; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) * onebyfftLen;
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) * onebyfftLen;
+
+ pSrc[2u * l] = xt * onebyfftLen;
+
+ pSrc[2u * l + 1u] = yt * onebyfftLen;
+
+ } // butterfly loop end
+
+#else
+
+ //N = fftLen;
+ n2 = fftLen;
+
+ // loop for stage
+ for (k = fftLen; k > 2; k = k >> 1)
+ {
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ // loop for groups
+ for (j = 0; j < n2; j++)
+ {
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = j; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = pSrc[2 * i] + pSrc[2 * l];
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = pSrc[2 * l + 1] + pSrc[2 * i + 1];
+
+ pSrc[2u * l] = xt * cosVal - yt * sinVal;
+
+ pSrc[2u * l + 1u] = yt * cosVal + xt * sinVal;
+
+ } // butterfly loop end
+
+ } // groups loop end
+
+ twidCoefModifier = twidCoefModifier << 1u;
+ } // stages loop end
+
+ n1 = n2;
+ n2 = n2 >> 1;
+ ia = 0;
+
+ cosVal = pCoef[ia * 2];
+ sinVal = pCoef[(ia * 2) + 1];
+ ia = ia + twidCoefModifier;
+
+ // loop for butterfly
+ for (i = 0; i < fftLen; i += n1)
+ {
+ l = i + n2;
+ xt = pSrc[2 * i] - pSrc[2 * l];
+ pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) * onebyfftLen;
+
+ yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
+ pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) * onebyfftLen;
+
+ pSrc[2u * l] = xt * onebyfftLen;
+
+ pSrc[2u * l + 1u] = yt * onebyfftLen;
+
+ } // butterfly loop end
+
+#endif // #ifndef ARM_MATH_CM0
+
+}