Jean-Francois Genat · 1.91 · Université Pierre et Marie Curie Paris 6

Using a 256Hz sampling frequency sets the highest signal frequency at fs=128Hz (Shannon-Nyquist), sufficient in your case. The lowest frequency point is determined by the number of samples. For example, processing 1024 signal points using a 10-bit FFT would set the first frequency point above DC at 256Hz/1024 = 0.25 Hz. The most famous textbook on the subject : Digital Signal Processing, by Oppenheim and Schafer, http://www.amazon.com/Digital-Signal-Processing-Alan-Oppenheim/dp/0132146355 A more recent and wavelets oriented: A Wavelet Tour of Signal Processing by Stéphane Mallat http://www.ceremade.dauphine.fr/~peyre/wavelet-tour/ Do not forget to window your signals (Hamming, Hanning, Kaiser, Cosine...) to avoid DC aliases in the frequency domain due to folding discontinuity. Cheers !

Using a 256Hz sampling frequency sets the highest signal frequency at fs=128Hz (Shannon-Nyquist), sufficient in your case. The lowest frequency point is determined by the number of samples. For example, processing 1024 signal points using a 10-bit FFT would set the first frequency point above DC at 256Hz/1024 = 0.25 Hz.

The most famous textbook on the subject : Digital Signal Processing, by Oppenheim and Schafer,

http://www.amazon.com/Digital-Signal-Processing-Alan-Oppenheim/dp/0132146355

A more recent and wavelets oriented: A Wavelet Tour of Signal Processing by Stéphane Mallat

http://www.ceremade.dauphine.fr/~peyre/wavelet-tour/

Do not forget to window your signals (Hamming, Hanning, Kaiser, Cosine...) to avoid DC aliases in the frequency domain due to folding discontinuity.

Cheers !

I am not sure what resource you have, but I would suggest Matlab with the signal processing module which should give you access to both the FFT as well as filters and a little filter design tutorial.

Another route would be "Numerical Recipes" by Press, Teukolsky, Vettering, and Flannery. This has a dedicated chapter on the FFT and some information in the following chapter on filtering. It is very practical and does not go into much theory or background.

For more in-depth background I like "The Fast Fourier Transform and Its Applications" by Brigham.

I am trying to extract modulation frequency. For example I have a current signal with 50Hz fundamental which is enveloped in say 5Hz,20Hz and 35 Hz modulating frequencies.Now I want to separate it as 5 Hz modulation with 50Hz fundamental inside,20Hz with 50Hz fundamental inside and so on.

I use Visual Basic 2010 express and FAMOS (which is a easy to use signal processing software like MATLAB) . So i interface commands from FAMOS to do the DSP operation and sequence it with Visual Basic programming to get a flow,so the input signal which contains 50Hz with various modulating frequencies can be detected by FFT (modulation freq extraction is already done by squaring and band pass filtering process)

After this I was considering using a low pass of 5Hz to extract this freq and another low pass of 20Hz,but this time even the 5Hz is included. I was wondering if some one can give me a clue as to how I can filter just one particular modulating frequency from a group.

What You need to do depends on the type of modulation. Assuming that You got Your FFT right. If the modulation is AM, the 5Hz will show up as 45 and 55 Hz in Your spectra if the AM is DSB. USB or LSB will give You just one sideband frequency. The amplitude is evident from the spectra. If the frequency is just added to the 50Hz, it can be filtered out by bandpass filters or a phase lock in amplifier if the signal is in a lot of noise. A bandpass filter in software or hardware will only work if You have an added or demodulated frequency, not modulation. Then the signal needs to be demodulated first. Sorry if I state the obvious, but I don´t understand exactly what You mean by extracting the frequencies. Amplitude, phase and frequency over time as the goal is just my guess. The problem should be easy at such a low frequency if the signal is not extremely noisy. A DSP is perhaps overkill. Sometimes a tunable bandpassfilter in hardware that receives commands from the processor can be a good solution to filtering out added varying frequencies. I think AD and maxim has several suitable chips. I have in the past used their switched capacitor varieties in some applications with good results. The simpler ones are controlled by clocking with a multiple of the desired frequency, which could be controlled from the FFT.

Hope any of this helps.

@ Mr.Isberg: I am working with this digitally,with FAMOS a signal processing software interfaced with Visual Basic programing.

1. I have a 50Hz signal (non-stationary in nature,from WIND Turbine)with Modulation over it (Current signal is modulated depending on the flow of wind hence the subsequent amplitude change of the 50Hz,changes in power depending on the wind ).

2. This signal contains more than one modulating frequency.

The signal is demodulated by squaring with itself,which extracts this modulating frequency and doubling the 50Hz to 100Hz.

3. A High pass and Low pass digital filter is implemented (to get rid of the 100Hz and DC components from squaring). This gives me only the modulating frequency.

4. NOw there are more than one modulating freq and I want to do an FFT after Windowing to know what frequencies are present and then extract each of this modulating frequency individually.

5.Now I want to add this single extracted Modulating freq to 50Hz again.

So instead of having 3 modulating frequency on a 50Hz signal in a 10min Window sample,now I have 3 different signal,each with 50Hz and one modulating frequency in each in a 10mins window.

6.Now I have my signals ready for further processing.

I am working with the flicker meter digital algorithm to see which frequency is leading to maximum disturbance in the light bulb.(Perceptibilty value,Pst)

I am not sure what kind of filter I should use to separate frequency as low as 1Hz and 2Hz that might be present and to do it accurately.And how can this be automated,so after the FFT the program recognizes the freq present and adjusts this filter in such a way that it extracts this frequency. I am very confused at this point.

OK so the object of the game is to separate the disturbances in order to generate a signal to do tests of a particular frequency at the time in hardware. One way of doing this that comes to my mind could be to do an averaged FFT over a time window directly on the modulated 50 Hz signal. If the physical effect is as You describe it, the modulation should be almost pure envelope modulated AM with a low modulation index. That means that You could do Your processing directly in the frequency domain by an algorithm that identifies and deletes the appropriate sidebands corresponding each of the different frequencies. Doing a reverse FFT would then give You the original signals back including the 50Hz modulated with just one of the frequencies. FM should be absent at Your frequencies if the generator is synchronous. This is of course assuming that Your disturbances are fairly sinusoidal, eg pure frequencies. If the frequency peaks are broad the problem is somewhat more difficult. Then identification and windowing becomes more difficult.

A new spectral estimator and transform may be of interest. The Fourier Transform models the autocorrelation function based on sinusoids to form the power spectrum. Instead, the new estimator averages lags in the autocorrelation function to form the power spectrum. The basis vectors are the periodic components of the signal at each frequency. So, there is no need for filtering or windowing to obtain specific components. The FT depends on rate / time interval, this new estimator depends on rate / period squared. So you can have short time intervals for analysis and still maintain frequency resolution. Please see for example -

Ciaccio EJ, Biviano AB, Garan H.Computational method for high resolution spectral analysis of fractionated atrial electrograms. Comput Biol Med. 2013;43:1573-1582.

Ciaccio EJ, Biviano AB, Whang W, Coromilas J, Garan H. A new transform for the analysis of complex fractionated atrial electrograms. BioMed Eng OnLine. 2011;10:35.

I have attached a really simple IDL routine (IDL is similar to Fortran, in syntax, if you are not familiar with it) that allows one to perform a bandpass filter on an input array of vectors. I wrote it to perform Fourier filters, so no fancy convolutions or anything tricky.

The power_of_2.pro routine just zero-pads the input so that the output contains an integer power of 2 number of elements prior to using the FFT routine in IDL (makes FFT run significantly faster). Let me know if you have any questions (and most importantly, let me know if you happen upon a bug in the routine).