Time Dependent Signals

[prakhars]

I wanted to know, what is the actual practical significance of having an time shifted signal.
i.e meaning of x(t-5) or x(t+6) in practical. and where can i see the effect of time shifted signals.

and also if a signal has a fixed frequency configuration then why its Fourier Transform differs when taken for a time shifted version.
i.e FT of x(t), is not as same as FT of x(t-5) although x(t-5) is the same signal as x(t), simply shifted in time ,....

 

[vvarlord]

when a signal is shifted in time it means the start time of signal is changed,and i don't think it's sth hard to be figured out
and for F transform when a signal is shifted the harmonics are the same and does not differ instead of the exponatioal coeficient which indicates the start time of signal
hope this helps

 

[albert22]

Time shifted signals are very important in the analysis of LTI (linear time invariant) systems and in DSP. Usually you can decompose a complicated signal into basic time shifted signals. And analyze each signal and then apply superposition. For example a rectangular pulse can be represented by two shifted unit steps.
Time shifted impulses are very important in DSP. Because discrete signal can be represented by a sum of time shifted weighted unit impulses.
The time shift property of the FT is F{x(t-a)} = X(jw) e^(-a jw) . Means that a shift in time corresponds to just a change in phase in the FT.

 

[permute]

one example might be "multi-path" in RF communications. In this case, the transmitter and receiver may not have a line-of-sight, but the signal may reflect off of several objects. It is possible that several paths are possible, and that only a few are really dominant.

A second example might be radar/sonar, where a pulse is sent out and a reflection of the pulse is measured later.