Comments on: Fourier transforms

By: Steve

Steve — Fri, 03 Sep 2010 20:01:42 +0000

Jagan—It will be a 2-D sinusoid. See this page for an example.

By: Jagan

Jagan — Fri, 13 Aug 2010 06:21:38 +0000

Hi Steve,
Suppose there is a only one frequency content say at (u0,v0)in the 2-D Fourier transform domain. How will the image looks like?
-jagan

By: Steve

Steve — Mon, 19 Apr 2010 19:02:25 +0000

Simon—Try using the function fsamp2 in the Image Processing Toolbox. Yes, h always exists for a system that performs linear, shift-invariant filtering, whether it is lowpass or highpass. h is the impulse response of such a system. You might try experimenting with Signal Processing Toolbox routines to design 1-D highpass filters if you want to see what they look like. Then you can use Image Processing Toolbox filter design routines to transform the 1-D prototype filters into 2-D filters.

By: Simon Peter Silk

Simon Peter Silk — Thu, 15 Apr 2010 19:43:44 +0000

Hi Steve,

I’ve been working on some image filtering as part of a course project, and I’ve been working out of the book Digital Image Processing Using Matlab (DIPUM).

Regarding frequency domain filtering, if I’ve made a frequency domain filter H, how do I find its space domain equivalent h so that I can calculate g=f*h using imfilter, which is often faster for small masks (/kernels)? Assume H has been calculated by the method outlined in DIPUM, meaning it is the same size as the image f that I want to filter.

A secondary question is does h always exists if H does? It seems to me that it should, and for low pass filtering, it’s easy to picture h as an averaging filter, and H as a low-pass frequency cutoff. But for high pass filtering, it’s just as easy to picture H as a high-pass frequency cutoff, but I can’t easily picture a space domain equivalent.

I’ve also noticed DIPUM covers LP filters under both Spatial Filtering (Chap 3) and Frequency Domain Processing (Chap 4), but HP filters only seem to be discussed under the latter.

Any thoughts? Thanks.

By: Steve

Steve — Tue, 02 Mar 2010 13:21:24 +0000

Juan—Your English is fine, but the question is pretty vague. The quote you give isn’t nearly detailed enough to turn into an actual computational procedure, and I’m not sure what you mean by changing the scale of the variable.

By: juan pablo

juan pablo — Mon, 01 Mar 2010 02:40:00 +0000

HI,
I am working with fft2 for filtering an image, the procedure after Goodman’s fourier Optics, is:” take the fourier transform of the image (source of light) and multiply by the filter function, and…” (here is my question) is necesary to change a variable after the fft is done, that means, I have a matrix that has the information but I don`t know how to change the scale of the variable
Sorry if my english is not good. Hope you can help me
thanks

By: Steve

Steve — Mon, 07 Dec 2009 22:50:25 +0000

Cris—My initial introduction to signals and systems was also via Oppenheim, Willsky, and Young.

By: Cris Luengo

Cris Luengo — Mon, 07 Dec 2009 22:23:02 +0000

That’s funny. I learned following Oppenheim, Willsky & Young. That’s the same Oppenheim as in Oppenheim & Schafer. I’m guessing my choice of terminology has changed a bit over the years? :)

By: Steve

Steve — Mon, 07 Dec 2009 18:21:27 +0000

Cris—I made a note to demonstrate how to do 1-D and 2-D DTFT plots.

Also, my viewpoint might not be all that different from yours. I tend to think in terms of the DTFT (what you call DFT) as well, and I think of frequency components rather than basis functions. But I view the DFT (what you call Fourier series of discrete-time periodic signal) as a discrete transform of a finite-length signal, and the resulting DFT coefficients simply sample the DTFT (as long as the DFT length is sufficiently long).

By: Steve

Steve — Mon, 07 Dec 2009 15:54:11 +0000

Cris—I am also from a signal processing background. From your description, what you call the DFT I call the DTFT (discrete-time Fourier transform). That is the terminology used, for example, in Discrete-Time Signal Processing by Oppenheim and Schafer. Since Ron Schafer led the signal processing research group at Georgia Tech while I was there, it is natural that I am accustomed to that terminology. ;-)

This is the kind of thing I had mind when I said last week that I was afraid of writing about Fourier transforms. In my experience even very knowledgeable signal processing people can have a hard time discussing Fourier transforms with each other, at least until they figure out the terminology roadblocks.