[MCU] Qmath做FFT

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//*****************************************************************************

// QmathLib_signal_FFT_ex4: Qmath signal generator and complex FFT example.

//

// Generate an input signal based on an array of wave descriptors. Each wave

// descriptor is composed of a frequency, amplitude and phase angle. The

// input signal is constructed with a size of SAMPLES and assumes a sample

// frequency defined by SAMPLE_FREQUENCY. The real component of the input

// consists of the summation of all the waves at that time index and the

// imaginary component is set to zero.

//

// The input array is passed into the complex FFT function which performs

// the FFT in-place using radix-2. The result of the cFFT is stored in the

// input array and is scaled by SAMPLES.

//

// The result is used to calculate the magnitude and phase angle at each

// frequency bin up to SAMPLES/2 (Nyquist frequency). The magnitude and phase

// angles are stored in data memory and should approximate the original

// signal composition. Because the input signal did not have any imaginary

// components the magnitude will be halved. The results can be printed with

// the printf function if ALLOW_PRINTF is defined.

//

// B. Peterson

// Texas Instruments Inc.

// May 2014

// Built with CCS version 6.0.0.00190 and IAR Embedded Workbench version 6.10.1

//*****************************************************************************

#include "msp430.h"

#include <stdio.h>

#include <stdlib.h>

#include <stdint.h>



/* Select the global Q value and include the Qmath header file. */

#define GLOBAL_Q    12

#include "QmathLib.h"



/* Specify the sample size and sample frequency. */

#define SAMPLES                 64      // <= 256, power of 2

#define SAMPLE_FREQUENCY        8192    // <= 16384



/* Access the real and imaginary parts of an index into a complex array. */

#define RE(x)           (((x)<<1)+0)    // access real part of index

#define IM(x)           (((x)<<1)+1)    // access imaginary part of index



/*

 * Input and result buffers. These can be viewed in memory or printed by

 * defining ALLOW_PRINTF.

 */

_q qInput[SAMPLES*2];                   // Input buffer of complex values

_q qMag[SAMPLES/2];                     // Magnitude of each frequency result

_q qPhase[SAMPLES/2];                   // Phase of each frequency result



/* Misc. definitions. */

#define PI      3.1415926536



/* Structure that describes a single wave to be used to construct the signal */

typedef struct wave {

    int16_t     frequency;              // Frequency in Hz

    _q          amplitude;              // Amplitude of the signal

    _q          phase;                  // Phase angle in radians

} wave;



/*

 * Specify wave structures that will be used to construct the input signal to

 * the complex FFT function.

 */

const wave signals[] = {

/*   Frequency (Hz)     Magnitude       Phase angle (radians) */

    {128,               _Q(0.5),        _Q(PI/2)},

    {512,               _Q(2.0),        _Q(0)},

    {2048,              _Q(1.333),      _Q(-PI/2)}

};



/* Calculate the number of wave structures that have been provided. */

#define NUM_WAVES       (sizeof(signals)/sizeof(wave))



//#define ALLOW_PRINTF                    // allow usage of printf to print results

#ifdef ALLOW_PRINTF

    char cMagBuffer[10];                // Character buffer for printing magnitude

    char cPhaseBuffer[10];              // Character buffer for printing phase

    char cFrequencyBuffer[10];          // Character buffer for printing frequency

#endif



extern void cFFT(_q *input, int16_t n);



int main(void)

{

    int16_t i, j;                       // loop counters

    _q qWaveCurrentAngle[NUM_WAVES];    // input angles for each signal

    

    /* Disable WDT. */

    WDTCTL = WDTPW + WDTHOLD;

    

    /* Set the initial input angles. */

    for (i = 0; i < NUM_WAVES; i++) {

        qWaveCurrentAngle[i] = signals[i].phase;

    }

    

    /* Construct the input signal from the wave structures. */

    for (i = 0; i < SAMPLES; i++) {

        qInput[RE(i)] = 0;

        qInput[IM(i)] = 0;

        for (j = 0; j < NUM_WAVES; j++) {

            /*

             * input[RE] += cos(angle)*amplitude

             * angle += 2*pi*freq/sample_freq

             */

            qInput[RE(i)] += _Qmpy(_Qcos(qWaveCurrentAngle[j]), signals[j].amplitude);

            qWaveCurrentAngle[j] += _Qmpy(_Q(2*PI), _Qdiv(signals[j].frequency, SAMPLE_FREQUENCY));

            if (qWaveCurrentAngle[j] > _Q(PI)) {

                qWaveCurrentAngle[j] -= _Q(2*PI);

            }

        }

    }

    

    /*

     * Perform a complex FFT on the input samples. The result is calculated

     * in-place and will be stored in the input buffer.

     */

    cFFT(qInput, SAMPLES);

    

    /* Calculate the magnitude and phase angle of the results. */

    for (i = 0; i < SAMPLES/2; i++) {

        qMag[i] = _Qmag(qInput[RE(i)], qInput[IM(i)]);

        qPhase[i] = _Qatan2(qInput[IM(i)], qInput[RE(i)]);

    }

    

    /* Print the results. */

#ifdef ALLOW_PRINTF

    for (i = 0; i < SAMPLES/2; i++) {

        _Qtoa(cMagBuffer, "%2.4f", qMag[i]);

        _Qtoa(cPhaseBuffer, "%2.4f", qPhase[i]);

        _Q1toa(cFrequencyBuffer, "%5.0f", _Q1mpyI16(_Q1(SAMPLE_FREQUENCY/SAMPLES), i));

        printf("%sHz: mag = %s, phase = %s radians\n",

               cFrequencyBuffer, cMagBuffer, cPhaseBuffer);

    }

#endif

    

    return 0;

}



extern void cBitReverse(_q *input, int16_t n);



/*

 * Perform in-place radix-2 DFT of the input signal with size n.

 *

 * This function has been written for any input size up to 256. This function

 * can be optimized by using lookup tables with precomputed twiddle factors for

 * a fixed sized FFT, using Q15 format for the twiddle factors and inlining the

 * multiplication steps with direct access to the MPY32 hardware peripheral.

 */

void cFFT(_q *input, int16_t n)

{

    int16_t s, s_2;                     // step

    uint16_t i, j;                      // loop counters

    _q qTAngle;                         // twiddle factor angle

    _q qTIncrement;                     // twiddle factor increment

    _q qTCos, qTSin;                    // complex components of twiddle factor

    _q qTempR, qTempI;                  // temp result complex pair

    

    /* Bit reverse the order of the inputs. */

    cBitReverse(input, n);

    

    /* Set step to 2 and initialize twiddle angle increment. */

    s = 2;

    s_2 = 1;

    qTIncrement = _Q(-2*PI);

    

    while (s <= n) {

        /* Reset twiddle angle and halve increment factor. */

        qTAngle = 0;

        qTIncrement = _Qdiv2(qTIncrement);

        

        for (i = 0; i < s_2; i++) {

            /* Calculate twiddle factor complex components. */

            qTCos = _Qcos(qTAngle);

            qTSin = _Qsin(qTAngle);

            qTAngle += qTIncrement;

            

            for (j = i; j < n; j += s) {

                /* Multiply complex pairs and scale each stage. */

                qTempR = _Qmpy(qTCos, input[RE(j+s_2)]) - _Qmpy(qTSin, input[IM(j+s_2)]);

                qTempI = _Qmpy(qTSin, input[RE(j+s_2)]) + _Qmpy(qTCos, input[IM(j+s_2)]);

                input[RE(j+s_2)] = _Qdiv2(input[RE(j)] - qTempR);

                input[IM(j+s_2)] = _Qdiv2(input[IM(j)] - qTempI);

                input[RE(j)] = _Qdiv2(input[RE(j)] + qTempR);

                input[IM(j)] = _Qdiv2(input[IM(j)] + qTempI);

            }

        }

        /* Multiply step by 2. */

        s_2 = s;

        s = _Qmpy2(s);

    }

}



/*

 * Perform an in-place bit reversal of the complex input array with size n.

 * Use a look up table to speed up the process. Valid for size of 256 and

 * smaller.

 */

void cBitReverse(_q *input, int16_t n)

{

    uint16_t i, j;                      // loop counters

    int16_t i16BitRev;                  // index bit reversal

    _q qTemp;

    

    extern const uint8_t ui8BitRevLUT[256];

    

    /* In-place bit-reversal. */

    for (i = 0; i < n; i++) {

        i16BitRev = ui8BitRevLUT[i];

        for (j = n; j < 256; j <<= 1) {

            i16BitRev >>= 1;

        }

        if (i < i16BitRev) {

            /* Swap inputs. */

            qTemp = input[RE(i)];

            input[RE(i)] = input[RE(i16BitRev)];

            input[RE(i16BitRev)] = qTemp;

            qTemp = input[IM(i)];

            input[IM(i)] = input[IM(i16BitRev)];

            input[IM(i16BitRev)] = qTemp;

        }

    }

}



/* 8-bit reversal lookup table. */

const uint8_t ui8BitRevLUT[256] = {

    0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0, 

    0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8, 

    0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4, 

    0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC, 

    0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2, 

    0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,

    0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6, 

    0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,

    0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,

    0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9, 

    0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,

    0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,

    0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3, 

    0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,

    0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7, 

    0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF

};