Fourier transform of triangular function

[tronxo]

Im kind of stuck in one of my signals problems. A triangular function defined as: V(t)= (-A/T)t + A when 0< t< T; V(t)= (A/T)t + A when -T< t< 0; otherwise, the function is 0. I have to find the Fourier transform of this function. Could anyone help me??

 

[chroot]

A triangle function is the convolution of two rectangle functions. You presumably already know what the FT of a rectangle function is, and you know how convolution in the time domain relates to multiplication in the Fourier domain.

- Warren

 

[tronxo]

thank you for ur time, warren, but I am still having problems with it. The problem is, even though i know, as you say before, that a triangle function is the convolution of two rect functions, i don't know how to identify which rect functions are related to this particular example.
thank you again, Alex

 

[chroot]

Plot the triangle function, and look at its endpoints. Notice that when you convolve two functions with endpoints (a, b) and (c, d), the resulting convolution has endpoints (a+b, c+d).

- Warren

 

[tronxo]

Thanks again
Alex