For a visual of what I am talking about, please visit: http://webhost.etc.tuiasi.ro/cin/Downloads/Fourier/Fourier.html
and scroll down to the "Examples of Fourier Transforms" part
I am ask to explain why the Fourier transform on the rectangle function was similar to the Fourier transform on the trangular function.
The Attempt at a Solution
so here what I think, and I'm not totally sure about it. The FT of a rectangular function is sin and rhe FT of the trangular function is a sin^2. The FT are similar because both functions are even, symetric, and always positive. The rectangular function is a constant function, which gives the sin, while the trangular function is a linear function, which gives the sin^2. Maybe a x^2 function with bounds will give a sin^3? not really sure about that. Is my reasoning correct for why the two FTs are similar?