Lecture of 30 September 1994

Using Maple to Evaluate Fourier Transforms

Discrete One-Dimensional FFTs

Execute the command xmaple
Get information on FFTs by selecting Help Browser from the Help menu, (This can be issued from the keyboard as (Alt-H B). Then asking for help on the Topic "Miscellaneous", Subtopic "FFT".
Then follow the instructions about what to type to the maple system.

The example of Figure 3.5 in the text can be verified by evaluating the following: readlib(FFT); x := array([2.,3.,4.,4.]); y := array([0,0,0,0]); FFT(2,x,y); print(x); print(y); One oddity, Maple yields the following values for x and y: [13. -2. -1. -2.] [0 1. 0 -1.] What could explain this difference?

Symbolic Evaluation of the Fourier Transform

Maple also provides the ability to carry out symbolic evaluation of the Fourier transform as in the following example: readlib(fourier); fourier(1,x,u); which results in 2 pi Dirac(u).

Using Khoros to Evaluate Image FFTs

You can set your account up to use Khoros as follows:

Copy the file /cis/wave1/khoros/dotfiles/Xdefaults.snazzy into the file named cantata in your XAPPLRESDIR.
If you don't already have an XAPPLRESDIR, create a directory ~/.resources and place following line in your .cshrc file
setenv XAPPLRESDIR ~/.resources Your XAPPLRESDIR will now be the directory ~/.resources
Add the following lines at the end of your .cshrc file: # stuff to make khoros work setenv KHOROS_HOME /cis/wave1/khoros set path=($KHOROS_HOME/bin $path) source $KHOROS_HOME/dotfiles/khoros_env #
If you want to immediately run the cantata visual programming environment, you must execute the following unix commands: source ~/.cshrc rehash

Cantata is a visual programming environment that brings together a number of program utilities. You can create glyphs that correspond to programs, and connect up their input and output streams with wires. Menus (in green boxes) let you choose different kinds of glyphs that correspond to separate programs that carry out different kinds of processes.

To see an image, you must input it and display it. To do this you can

Select Input Data File from the INPUT SOURCES menu
Click on one of the image names in the input_file box then press the Glyph button to make a glyph called images
Select Display Image from the OUTPUT menu
Click on the Glyph button in the display box to make a glyph called put_update.
Click (with left button) on the output arrow of the images glyph and then click on the top input arrow of the put_update glyph to connect them with a wire.
Press the (red) RUN button to execute the flowgraph you've drawn.

To view the Fourier Transform of an image like ball.xv or visual_mtf.xv or airport.xv, you must select Transforms from the IMAGE PROCESSING menu, then manipulate the output of the transform appropriately (perhaps by using a Data Conversion from the CONVERSIONS menu to get from complex to real by taking the magnitude, then squaring this and taking its log).

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