**Convolution:**the resulting steady-state output of an input passed into a LTI system.

**Laplace Transform:**general form of Fourier transform, s = σ + jw. Displays frequency spectrum with decay (σ ≠ 0)

**Fourier Transform:**special case of Laplace transform, s = jw. Non-periodic and periodic signals. Displays frequency spectrum without decay (σ = 0). Phasors?

**Fourier Series:**Displays frequency spectrum of period signals

Okay, I understand that the Fourier Transform is a special case of the Laplace where there is no σ term, but when would you use either?

For instance, to produce a Bode plot of a system, you end up using the Laplace Transform, but could you not have just used the Fourier Transform? What is the difference in information that you receive for either case?

Also, for periodic signals, the Fourier Series states that it can be broken up into sinusoids, does this just tell which frequencies are going to be affected when passed into a system?

Thanks in advance,

JP