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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
};
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