Triangular Function
Main Concept
A unit triangular function or the tent function is defined:
tritτ = Δtτ ={ 0 t≥τ21− 2 t τt<τ2
Fourier transform
The Fourier transform usually transforms a mathematical function of time, f(t), into a new function usually denoted by F(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) = tritτ is:
Fω = ∫−∞∞tritτ e−j ω t ⅆt = τ2 sinc2ωτ4
where:
ω
=
hertz
τ
constant
j
imaginary
number
tri
triangular function
sinc
sinc function sinxx
Adjust the value of t to observe the change in the fourier transform
τ =
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