Origin Ver. and Service Release (Select Help-->About Origin): 8.5.0 SR1
Operating System: Windows XP
Hi, dear Sir,
I'm not sure if that's proper to discuss this issue here. It's actually about the algorithm of the FFT from FFTW library which is used in the new-version Origin.
For simplicity, let me just assume my data is from a digital photo detector (Aavalanche photodiode, PerkinElmer Inc.) collecting scattering photons from a laser, whose intensity is attenuated low enough and amplitude-modulated at a certain frequency. I basically want to extract the amplitude from FFT spectrum of the data at the modulated frequency.
The data, photon arrival times, will be like (assuming the resolution is 1us)
0.000547
0.000610
0.001438
0.002106
0.002386
0.002610
0.002681
0.002780
...
...
...
99.998750
99.999547
Each data point here is the photon arrival time, implying when the detector gets a photon.
To get the FFT spectrum, I first bin the above photon arrival data, importing the binned data into Origin, and then execute the FFT operation to find the amplitude at the modulated frequency.
The problem I found is that sometimes the amplitude at the modulated frequency is pretty sensitive to the photon number I collected. For example, I have a 500Hz modulation data set with 299726 photon number. Binning it in 100 usec, importing into Origin, and trying find the FFT amplitude at 500 Hz give me 0.04 (arbitrary unit, normalized). It, however, gives me 0.06 if I truncate the last 726 points, which will leave me a photon number of 299000.
0.06 is actually closer to the expected value, but I don't why the FFT sometimes is sensitive to a such small change in the photon number, and therefore a small change in the number of bins in the binned data.
Truncating the bin to power of 2 (radix-2) does sometimes help, but I found for most of the cases radix-2 algorithm gives me a larger fluctuation than mix-radix. I also try different FFT library, like the one from GSL, but it actually shows the same results.
If possible, can you give me some suggestion about any tricks picking out the bin size/number such that the FFT amplitude will be closer to what we expect?
By the way, if you need the data I'll be glad to send you a copy.
Thanks,
Jung-Cheng
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Accuracy of FFT
Posted - 04/14/2011 : 9:56:39 PM
