FFT
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This applet lets you experiment with approximating a function or "bit pattern" by a Fourier series. The coefficients of the Fourier series are computed using a "discrete Fast Fourier Transform" algorithm (see "Resources"). 

FFT of Arbitrary Function: This applet lets you enter an arbitrary function and compute its Fourier coefficients. It shows how the resulting Fourier series approximates the original function.
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FFT of "Bit Pattern": This applet illustrates signal distortion when sending digital (bit) patterns representing a character (coded as the 8-bit ASCI code) though a wire that includes a "low-pass" filter (i.e. high frequencies are filtered out). ALT="Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is ignoring the <APPLET> tag!

 
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About "function FFT": Almost any periodic function can be represented as a Fourier series. This applet computes the Fourier coefficients and shows how the corresponding Fourier series approximates the original function. Note in particular:
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More Fourier coefficients result in a better approximation by the Fourier series 

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Functions with sharp corners need a lot of Fourier coefficient for a good approximation and have oscillating Fourier representation.

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About "bitwise FFT": Start the applet and press any key. The key is converted into its ASCII code, then into a bit pattern corresponding to that ASCII code. That pattern is "sent" through a wire that may include a "low-pass" filter which distorts the signal. The more frequencies are filtered out, the harder it becomes to reconstruct the original signal. 

Operators:
+, -, *, /, ^
Functions:
sin, cos, tan, ln, log, abs, int, frac, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, ceil, floor, round, exp, sqr, sqrt, sign, fact

Other:
(, ), <, >, <=, >=, and, or
Conditionals:
if(test,if_true,if_false)
Constants
pi, e

Parser © 1996, Yanto Suryono

 

Created by Bert Wachsmuth

SHU Thinklets Version 1.1 (last modified 11/30/2003)
(c) 2000-2003, Math and Computer Science @ Seton Hall
All Rights Reserved (bgw)