[Signals and Systems] What's the signinfance of negative time?

[snshusat161]

Hello all,
This one thought came to my mind just now. What's the physical significance of signal representation in negative time, i mean second and third quadrant.

So for example, sin(t) and sin(t).u(t) aren't they same for all practical purposes?

I know, mathematically they are different. But I'm trying to visualize the difference in terms of practical usage.

 

[cpscdave]

Not sure if this is along the lines of what you are asking.
But when we covered this material the prof mentioned that while you can physically have negative time in a system (obviously) but the inclusion of negative time made the calculations of much of the math vastly easier.

 

[dbelgiovane]

It is useful for setting up a reference frame for looking at the impulse response of your system. The negative time could represent anything transient which has occurred before a time frame of interest. the step function u(t) multiplied by a function makes everything before equal to zero allowing the system's reference frame to begin, you can easily delay when this occurs by looking at u(t-delay) by some delayed period. It is pretty much a convention to distinguish regions which we care about and it represents that the system is causal and done not depend on past inputs which is a requirement for many systems.

 

[Baluncore]

Representing a signal in negative time, reversed time order, has a simple elegant effect in the frequency domain.
It takes the conjugate of the signal phase vectors.