I would like some help clearing up some confusion.
The fourier transform of a triangular pulse with base $2T_b$ is given as,
$T_bsinc^2(\pi f T_b)$
You can also get this result by realizing that 2 square pulses each with width $T_b$ convolved together make a triangular pulse with width $2T_b$.
The fourier transform of a square pulse with width $T_b$ is given as,
$T_bsinc(\pi f T_b)$
Using the property,
Convolution in time $<=======>$ Multiplication in frequency
You can find that the convolution of two square pulses together, is just their fourier transforms multiplied together. Thus, a triangular pulse of width $2T_b$ is just the fourier transforms of two square pulses multiplied together, right?
Using this result I find that the fourier transform of the triangular pulse is,
$T_b^2 sinc^2(\pi f T_b)$
Though this does not seem correct as it has an extra factor of $T_b$,
Could someone please clear my confusion?