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Hello guys,
I am using an NRF chip with Cortex M4. Currently I am reading data from an accelerometer (12 signed bit ADC) and I have to get peak velocity. For that I am using the Omega arithmetic algorithm, as follows:
- remove offset from raw data (acceleration) and shift values with 4 bits; copy the array in a x2 length array with interleaving 0 complex values;
- do a CFFT on the new array;
- try to divide each complex value by (0 + 2*pi*df I); now we have velocity in frequency domain;
- to inverse CFFT, calculate magnitude, remove offset and shift back 4 bytes;
- check for peak velocity and convert data into mm/s value;
I used a test array (sine wave of ~208 hz with peak value of 2048 - that is the max signed value for signed 12 bits) , sampling frequency of 3332hz and a total of 4096 samples. Problem is that if I divide my complex values with 2*pi*f (according to the complex division formulas), I get very low values in the frequency domain for real and complex parts, and the final array has inside it a bunch of zeroes and -1. I am not getting back a sine wave in time domain.
Does anybody has an idea if I should shift with some bits or something the values before doing the Inverse CFFT? Here is a part of the code below:
Many thanks!
#define FFT_LENGTH 4096 #define NUMBER_OF_VIBRATION_MEASUREMENTS 4096 .... static q15_t fft_data_out[FFT_LENGTH*2]; static q15_t fft_data_in[FFT_LENGTH]; memcpy(&fft_data_in[0], &p_edwin_service->vibrations.raw[0], sizeof(p_edwin_service->vibrations.raw)); // copy adc data to in buffer #ifdef USE_TEST_DATA memcpy(fft_data_in, test_data, sizeof(test_data)); // for test only #endif arm_shift_q15(fft_data_in, 4, fft_data_in, NUMBER_OF_VIBRATION_MEASUREMENTS); q15_t mean2 = 0; arm_mean_q15(fft_data_in, NUMBER_OF_VIBRATION_MEASUREMENTS, &mean2); mean2 = -mean2; arm_offset_q15(fft_data_in, mean2, fft_data_in, NUMBER_OF_VIBRATION_MEASUREMENTS); NRF_LOG_INFO("mean before fft %d", mean2) for (uint32_t i = 0; i < FFT_LENGTH; i++) { fft_data_out[(i * 2)] = fft_data_in[i]; fft_data_out[(i*2)+1] = 0; } arm_cfft_q15(&arm_cfft_sR_q15_len4096, fft_data_out, 0, NORMAL_DATA_ORDER); // fft // divide by 2 pi f to_velocity_freq(fft_data_out); // TODO remove low frequency values arm_cfft_q15(&arm_cfft_sR_q15_len4096, fft_data_out, 1U, NORMAL_DATA_ORDER); // inverse fft memset(fft_data_in, 0, NUMBER_OF_VIBRATION_MEASUREMENTS); //magnitude q15_t *pSrc3 = fft_data_out; q15_t *pDst3 = fft_data_in; for (uint32_t i = 0; i < FFT_LENGTH; i++) { q15_t re = *pSrc3++; q15_t im = *pSrc3++; *pDst3++ = fast_usqrt((q31_t)(re * re) + (q31_t)(im * im)); } //mean mean = 0; arm_mean_q15(fft_data_in, NUMBER_OF_VIBRATION_MEASUREMENTS, &mean); mean = -mean; arm_offset_q15(fft_data_in, mean, fft_data_in, NUMBER_OF_VIBRATION_MEASUREMENTS); arm_shift_q15(fft_data_in, -4, fft_data_in, NUMBER_OF_VIBRATION_MEASUREMENTS); //shift // get max peak in time domain float pk_v_from_time = pk_vel_time(fft_data_in) * (float)p_edwin_service->range/(float)(2048.0); NRF_LOG_INFO("Velocity PK from OMEGA arithmetic= " NRF_LOG_FLOAT_MARKER, NRF_LOG_FLOAT( pk_v_from_time ));
void to_velocity_freq(q15_t *signal) { int N=4096; float tmp=0; float df = 0; float tmp1 = 0; for (int n = 0; n < N/2; n++) { df = n * (3332.0/(float)(NUMBER_OF_VIBRATION_MEASUREMENTS)); tmp =0.0; tmp1= 0.0; if (df != (float)0.0){ tmp = (float)signal[n*2] / (2*pi*df); tmp1= (-1)*(float)(signal[n*2+1]) /(2*pi*df); } signal[n*2] = (q15_t) __SSAT((q31_t) (tmp), 16); signal[n*2+1] = (q15_t) __SSAT((q31_t) (tmp1), 16); } for (int n = N/2, y = (-1)*N/2; n < N; n++, y++) { df = y * (3332.0/(float)(NUMBER_OF_VIBRATION_MEASUREMENTS)); tmp =0.0; tmp1= 0.0; if (df != (float)0.0){ tmp = (float)signal[n*2] / (2*pi*df); tmp1= (-1)*(float)(signal[n*2+1]) /(2*pi*df); } signal[n*2] = (q15_t) __SSAT((q31_t) (tmp), 16); signal[n*2+1] = (q15_t) __SSAT((q31_t) (tmp1), 16); } }
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