Jorge, Thanks, and a happy new year back to you! Re your e-mail--- ... This isn't something I know much about, but glancing at the article in Wikipedia on...
I think this is one correct way to visualize the DFT.   Above, on the right, the values are complex numbers: the hue (red to purple) shows the modulus,...
Here, to be consistent, I've plotted the original real-valued function the same way as the complex DFT: red is for positive sign ("argument" of 0) and the hue...
Here's the standard way for visualizing complex functions, with higher modulus in brighter colors, and the argument shown by hues going from red for 0 degrees...
Just trying to get some more insight into how the DFT is behaving by playing around with various simple starting functions. Here I'm trying the contour map of...
Hi Jorge, Signal processing is usually done with numerical evaluation for example with GNU-Octave [1] or Matlab [2]. But naturally these programs and their...
Chris's efforts on the DFT and Jorge's query show how far this topic has come since I first looked into it - about 1970 after a psychology professor studying...
Thanks, George. Can't take any credit for the equations, but at least I think I showed that GC 3.5 can help quite a bit with visualization. Right now, it's...
Chris! (and others) Many Thanks for this nice surprise when I opened the e-mail. As always, what a knowledgeable and helpful person you are! I will have a...
Jorge, Glad to help. I've always wondered how Photoshop and other similar programs manage to sharpen up an out-of-focus image. It seems like magic. If I have...
When sampling you should also remember the Nyquist rule for sampling frequency. Although I guess in this case you are resampling an already sampled image and...
Pete, Thanks very much for the advice, which I'll keep in mind. I'm not sure exactly how to determine the frequencies involved in the simple graphs I'm using;...
What is the current version of GC? I currently have version 3.2, and was wondering if there is an upgrade. I could not find anything on Pacific Tech's web...
... It looks like there's a problem with the server right now.   On Feb 2, 2008, at 4:50 PM, tlylab wrote: I'm using GC to check my calculus, but when I...
... simplification if complains it can not connect to the integral server? The integral server is not maintained my Pacific Tech. I don't know its current...
... The key idea here is to remember that the u and v parameters are used to "leave tracks". The rotation matrix leaves a track as it rotates around the...
How does one go about creating a sphere from a circle? As always, the key idea is to think of the t parameter as leaving a trace of the curve, and the u and v...
[Not sure this one got through, so I'm resending it.] How does one go about creating a sphere from a circle? As always, the key idea is to think of the t...
The online integration site that GC used to hook up to is offline, but here's a workaround: Go to http://integrals.wolfram.com/ index.jsp, type in the function...
Using the online version of the Abramowitz and Stegun reference, I came across a series for the Fresnel integrals which didn't involve the Bessel functions at...
Here, I fixed the colors via two color maps. Since we're going in the negative direction to the left of the y-axis, the signs of the areas are reversed. Also,...
The Cornu spiral (or "clothoid") is the curve whose curvature increases steadily with distance along it, or, more concisely, whose curvature is equal to its...
Here's a version of the clothoid where the red dot's projection on the y-axis traces out the Fresnel sine analog, S( ), on an imaginary "moving tape"---the...
Chris- You should set up a simple web site that archives all of these great examples! I keep copies of most of what you send, but frankly, I can't keep it...
Thanks for the encouragement! I plan to get down to putting things on a website soon. Don't like to take away from the time for actually doing the math,...
Appreciate the feedback and the encouragement. Any chance I could turn to you with the occasional website question. I've got Freeway as my website builder, and...
