Fourier Transform of Quadratic Pulse.
A Rectangular pulse of width t and height 1/t has spectrum sinc(wt/2).
If this pulse is convolved with itself, the result is a triangular pulse with
This proceedure can be repeated to produce pulses with Fourier Transform which reduces
more rapidly with frequency. If the rectangular pulse is convolved with the triangular
pulse, the result is a quadratic pulse with spectrum sinc(wt/2)3.
The effect is shown in the applet below.
The quadratic pulse is shown as the magenta curve and its spectrum as the cyan curve.
The yellow curve shows the pulse which is reconstructed from a finite width of the
spectrum. The result shows that the pulse shape is retained when passed through a filter
of relatively narrow bandwidth.
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COPYRIGHT © 2005 Cuthbert Nyack.