Triangular Function - Maple Programming Help

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Triangular Function

Main Concept

A unit triangular function or the tent function is defined:

trit&tau; &equals; Δt&tau; &equals;&lcub; 0 t&tau;21 2 t &tau;t<&tau;2

Fourier transform

The Fourier transform usually transforms a mathematical function of time, f(t), into a new function usually denoted by F(&omega;) whose arguments is frequency with units of cycles/sec (hertz) or radians per second. This new function is known as the Fourier transform. The Fourier transform is a mathematical transformation used within many applications in physics and engineering. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.

 

Triangular functions are useful in signal processing as a representation of ideal signals.

 

The Fourier transform of f(t) = tritτ is:  

F&omega; &equals; tritτ ej &omega; t &DifferentialD;t &equals; τ2 sinc2&omega;&tau;4

where:

 

ω

&equals; 

hertz

&tau; 

&equals; 

constant

j 

&equals;

imaginary 

number

tri

&equals;

triangular function

sinc

&equals;

sinc function sinxx

 

Adjust the value of t to observe the change in the fourier transform

&tau; &equals;

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