Can f(t) = u(t)5cos(2pi t) be represented directly as a fourier series?

Answer 1

yes, but only if u(t) is a periodic function. If f(t) is nonzero over a certain range of t only, it can be represented by a Fourier transform.

Answer 2

well the text in my notes just states that u(t) is a step function..and therefore how do i determine if its periodic .. To my understanding the unit step signal is not periodic..is that assumption right?

Answer 3

I believe then that this funtion can only be represented by fourier transform and laplace transform?

Answer 4

A Fourier series is periodic. If there is a single step function increase in u at some value of t, f(t) is not periodic. If the step function repeated each time t increases by 1, then f(t) would be periodic, and u(t) would be a kind of square wave. In that case you could use a Fouier series.

I am going to stop there. There may be more to u(t) than you are telling me.