Fourier transform time shift

1. Jul 8, 2006

EvLer

I am given this signal:
x(t) = sin(4(t-1))
and I need to find X(jw), i.e. it's FT, so I am confused whether I shift by 1 or by 4, in other words whether I multiply F{sin(4t)} by e^(4jw) or by e^(1jw)

which one is it? I am thinking it's 4jw.... is it right?

2. Jul 8, 2006

HallsofIvy

Staff Emeritus
Aarg! Those engineers and their jmaginary numbers!

I hope you will bear with me as I use "i" rather than "j". I just can't force myself to that heresy.

sin(4(t-1))= sin(4t- 4). Looks to me like you need to shift by 4.

3. Jul 9, 2006

:tongue2:

thanks

4. Jul 9, 2006

EvLer

a bit off topic

perhaps i should have started a different thread, but since HallsofIvy has mentioned, i couldn't help but ask: is there any tiniest difference between i and j, i.e. are we, engineers, underestimate imaginary numbers in some way?
It always comes up and i just would like to satisfy my curiosity.

5. Nov 19, 2009

bhupala

Mr EvLer,

There is no big deal in taking j instead of i for imaginary numbers. For engineers, 'i' represents current. To avoid confusion engineers take 'j' for imaginary part.