The input image is the spatial domain equivalent of the sinusoid which is in temporal domain. The variable used to represent an input image pixel in the above formula is x n,m.
In Scilab, two-dimensional Fourier transform is executed through the command fft2(img) where img is the image variable.
In measuring physical signals, one need to know the signal frequency, the sampling rate must be twice the frequency of the signal. The sampling interval must be equal or less than the inverse of the sampling rate.
a) Light from a fluorescent lamp is known to flicker at 120Hz. What should be the threshold sampling interval for accurate FT analysis?
The threshold sampling interval dt should be dt = 1/(2*120Hz) or 0.00417 s.
b) What is the effect of increasing the number of samples N in the FT?
Guess: Increasing the number of samples N would also change the time interval dt. This would make the FT more accurate as it is based on the assumption that the signal is infinite and periodic.
Right answer: increasing the number of samples N means decreasing the sampling interval. This makes the FFT resolution better so that the peaks become narrower.
Decreasing the sampling interval Δt in the FT would increase the number of samples N for the same time period. This would make the FT more accurate.
number of samples N?
Fixing the total time interval T but increasing the number of samples is also good because it fixes the number
SELF-EVALUATION: 9/10. The guesses were not always correct but the simulations were carried out correctly.
[1] Dr. Maricor Soriano's lecture notes
[2] http://homepages.inf.ed.ac.uk/rbf/HIPR2/fourier.htm.
[3] Nyquist Theorem, http://searchcio-midmarket.techtarget.com/sDefinition/0,,sid183_gci812005,00.html
1 comment:
You get a 10 here. For me its more important you made a good guess and learned from your mistake than not to make a guess at all.
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