## Extremely Low Frequency Electro Magnetic Field Sensing (Part 4)

FFT posts are the far most visited pages from Arduinoos, and MicroELFEMF is one of the simplest and cheapest example of implementing this complex function. I got many requests and questions related to this subject, which drove me to publish some more explanations.

Understanding frequency bins is not trivial and I encourage you to read **this post**. This is an other attempt to make things clear and easy, thanks a to some simple equations:

For a known number of samples (N) and frequency resolution (f_res), we can get:

- sampling frequency (f_samp) = f_res . (N – 0.5)
- maximum frequency (f_max) = f_samp / 2

For a known number of samples (N) and sampling frequency (f_samp), we can get:

- frequency resolution (f_res) = f_samp /(N – 0.5)

On completion of the FFT transform, the center frequency of each bin is equal to:

center frequency (f_bin) = bin index . f_res

NB: bin index is base 0.

Lets apply these equations to some real life example.

Here is the request: “I want to perform measurement of ELF EMF with a frequency resolution of 10 in order to simplify the frequency picking at 50 Hz or 60 Hz. And as Arduino is not so fast, I will restrain the number of samples to 64″.

Then, the sampling frequency is, based on f_samp = f_res . (N – 0.5) = 10 . 63.5 = 635 Hz. The frequency spectrum will then range from 0 to 310 Hz in 32 bins. The signal from 50 Hz will be contained in a bin 5, and the signal from 60 Hz will be contained in bin 6.

Real life is not always as easy as measuring AC power . Picking any frequency may require the use of frequency interpolation, using 3 or more data points. The choice for the interpolating function depends very much on the “peak” shapes and will not be covered in this over simplified post.

Finally, here is the latest revision of the code

/* MicroELFEMFLED: Extremely Low Frequency Electro Magnetic Field Sensing A piece of wire must be attached to analog port 0 This wire detects the magnetic fields generated by the ambiant AC This signal is sampled in scan mode, filtered through a FFT. The 50 Hz signal is quantified and transformed in a blinking signal The sketch features self tuning of signal strength Copyright (C) 2012 Didier Longueville This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. */ #include <PlainADC.h> #include <PlainFFT.h> PlainADC PADC; /* Create ADC object */ PlainFFT FFT; /* Create FFT object */ /* Data acquisition parameters */ const uint16_t _samples = 64; const double _samplingFrequency = 635.0; const uint16_t _adcChannel = 0; /* From 0 to 5 on ATmega328 powered Arduinos */ const uint16_t _refVoltage = ADC_REF_VOL_DEFAULT; /* VCC: 5V */ /* Constants */ #define SCL_INDEX 0x00 #define SCL_TIME 0x01 #define SCL_FREQUENCY 0x02 /* Data acquisition vector */ uint8_t *_vBuffer; /* FFT vectors */ double *_vReal; double *_vImag; /* Local variables */ uint8_t _pinCtrlLed = PINB5; volatile uint8_t *_portCtrlLed = &PORTB; uint32_t _lastToggleTime = millis(); int16_t _signalStrength = 0; int16_t _minStrength = 32767; int16_t _maxStrength = 0; int16_t _maxInterval = 1000; int16_t _minInterval = 20; void setup() { Serial.begin(115200); /* Set data acquisition parameters */ _vBuffer = PADC.SetAcquisitionEngine(_adcChannel, _refVoltage, _samplingFrequency, _samples, ADC_DAT_FMT_DBL); /* Size imaginary vector */ _vImag = (double*)malloc(_samples * sizeof(double)); DDRB |= (1 << _pinCtrlLed); }; void loop() { uint32_t startAcquisition = millis(); /* Acquire data */ PADC.GetScanData(); /* Cast data in a doubles vector */ _vReal = reinterpret_cast<double*>(_vBuffer); /* Print raw data (optional) */ // PrintVector(_vReal, _samples, SCL_TIME); /* Suppress data offset */ FFT.SuppressOffset(_vReal, _samples); /* Clear imaginary vector */ FFT.ClearVector(_vImag, _samples); /* Window data: optional */ FFT.Windowing(_vReal, _samples, FFT_WIN_TYP_HAMMING, FFT_FORWARD); /* Compute FFT */ FFT.Compute(_vReal, _vImag, _samples, FFT_FORWARD); /* Compute magnitudes */ FFT.ComplexToReal(_vReal, _vImag, _samples, FFT_SCL_TYP_AMPLITUDE); // PrintVector(_vReal, (_samples >> 1), SCL_FREQUENCY); uint32_t acquisitionDuration = (millis() - startAcquisition); /* Get data corresponding to the target frequency, based on _samplingFrequency = 1270 and _samples = 64 */ _signalStrength = int16_t(*(_vReal + 5)); /* 50 Hz bin */ // _signalStrength = int16_t(*(_vReal + 6)); /* 60 Hz bin */ /* Self tuning */ if (_signalStrength < _minStrength) { _minStrength = _signalStrength; } if (_signalStrength > _maxStrength) { _maxStrength = _signalStrength; } double normalizedSignalStrength = double(_signalStrength - _minStrength) / (_maxStrength - _minStrength); // Serial.println((normalizedSignalStrength * 100.0), 1); /* Timing */ uint16_t interval = acquisitionDuration + ((_maxInterval - _minInterval) * (1.0 - normalizedSignalStrength)); /* Blink led */ while (millis() < (_lastToggleTime + interval)); _lastToggleTime = millis(); PORTB ^= (1 << _pinCtrlLed); /* Toggle control led on */ while (millis() < (_lastToggleTime + interval)); _lastToggleTime = millis(); PORTB ^= (1 << _pinCtrlLed); /* Toggle control led on */ // while(true); /* Loop once for debuging */ }; void PrintVector(double *vData, uint8_t bufferSize, uint8_t scaleType) { double freqInterval = (_samplingFrequency / (_samples - 0.5)); for (uint16_t i = 0; i < bufferSize; i++) { double abscissa; /* Print abscissa value */ switch (scaleType) { case SCL_INDEX: abscissa = double(i); break; case SCL_TIME: abscissa = (i / _samplingFrequency); break; case SCL_FREQUENCY: abscissa = (freqInterval * i); break; } Serial.print(abscissa, 6); Serial.print("\t"); Serial.print(vData[i], 4); Serial.println(); } Serial.println(); };

HTH

Will back EMF be a problem for the output pins that drive the motor?

Which motor?