Triangular Function - Maple Help

Triangular Function

Main Concept

A unit triangular function or the tent function is defined:

Fourier transform

The Fourier transform usually transforms a mathematical function of time, f(t), into a new function usually denoted by F($\mathrm{ω}$) 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) = $\mathrm{tri}\left(\frac{t}{\mathrm{\tau }}\right)$ is:

 where:  $\mathrm{\omega }$ hertz $\mathrm{τ}$   constant $=$ imaginary  number $\mathrm{tri}$ $=$ triangular function $\mathrm{sinc}$ $=$ sinc function $\left(\frac{\mathrm{sin}\left(x\right)}{x}\right)$

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

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