Help me understand LTI systems

SkyEye

Can someone help me understand some of the concepts associated with Fourier transforms? I get the math part, but I have difficulty conceptually understanding some of the basic concepts like why exp(jx) = cos x + j sin x or how the Fourier transforms in continuous and discrete time vary so much.

L|ama

Euler's formula is most easily proved by looking at the power series for e^ix. e^x = sum from n=0 to inf of x^n/n!, if you chuck in ix instead of x there and then expand and gather the imaginary terms and real terms you get the power series cosx and i times the power series for sinx. If you need something more conceptual than that, I can't really help much. You can sort of look at complex exponentiation as rotation in the complex plane projected onto the real axis (like phasors, if you've ever dealt with those).