Why do signals shift in opposite directions when time shifted in opposite ways?

[tina_singh]

when we have x(-t) and we time shift it say x(-t-2) it shifts toward the -ve t axis.. where as x(t-2) the function is shifted on the + axis..why is it so??

see when we say there are 2 functions x(t) and x(t-2) it means x(t-2) is delayed by 2 sec with respect to x(t) therefore it shifts in the positive x direction.. does'n't the same apply for x(-t) and x(-t-2) the second function is time delayed by 2 secs wid respect to the first so even it should shift to the positive x axis..isn't it?

 

[Azherbahai]

x(-t-2) has been time reversed so the opposite applies. It is best to think of these by drawing out simple arbitrary signal (like a pulse or step function) and remember that x(-t) is just reflecting it around the y-axis (think of the function as a rigid frame that can be rotated at the y-axis).