An Intuitive Explanation of Fourier Theory | Hacker News Reader

An Intuitive Explanation of Fourier Theory

sharp.bu.edu

23 pointscharzom11 comments

Let's dumb it down a little further.

http://www.complextoreal.com/chapters/fft1.pdf

Check page two.

This is a good document. Signals and systems was one of the more interesting courses I took back in the day.

I graduated this past spring and after reading the stuff on this ladies site, I finally get what all those classes were about.

I'm glad to see things like this on Hacker News. Sure it has relatively little to do with the regular topics, but it's the kind of interesting thing that I'd like to find from people who populate here.

Digital Signal Processing/Intro to Signal Processing has been one of the most interesting classes I've taken so far.

Huh, I did signal processing and communication systems in college, and I don't recall anyone ever mentioning the lens thing. It says the distance from the image to the lens has to be "f" Is this the Nyquist frequency?

f is the focal length.

now I'm smacking myself. Yeah, should be obvious.

If this stuff excites you, read the first chapter of Joe Goodman's book, Introduction to Fourier Optics. That's the book I read to really understand fourier transforms.

I'm a bit confused. Is the DC term always in the center of 2D frequency image? If so, how does that provide any information about varying levels of background luminance?

The DC term is always at the lowest spatial frequency (DC.) So, if you plot your FT so that the DC term is in the middle, then the DC term is in the middle :)

It provides NO information about the varying levels, it tells you something like the sum of all the pixels / number of pixels. If you have a 10x10 uniform image, all pixels=1, the DC term will by 1/100.

Again, the DC Term is the absoloute lowest spatial frequency, hence it's DC.

The DC term also known as ao, Co, and Do (in the trigonometric, compact, and exponential forms) is the average value of the signal over its period (if it is periodic). It is the integral of the signal over one period divided by the period.

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