Fourier Transform of Rectangular Functions

The Fourier transform of a rectangular function (or signal) is explored graphically using an applet.

Interactive Tutorial

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1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - The function f(t) to transform is in blue and the fourier transform of f(t) is in red.
3 - Use the slider on the left to change parameter a that contols the width of the rectangular function f(t) (blue).
4 - As you increase parameter a, the width of f(t) increases what happens to the shape of fourier transform? Does it get narrower or wider?
5 - As you decrease parameter a, the width of f(t) decreases what happens to the shape of fourier transform? Does it get narrower or wider?
6 - Use the definition of the Fourier transform to explain what you have observed above.