Howtosignalprocessing
- How do you find time-invariant?
- What makes a system time-invariant?
- How do I know if my system is time variant or not?
- How do I know if my signal is LTI?
How do you find time-invariant?
A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).
What makes a system time-invariant?
y(t − τ ) = (H(x))(t− τ ). A time-invariant system is one whose behavior (its response to inputs) does not change with time.
How do I know if my system is time variant or not?
To assess whether a system is time-varying or not, follow these steps: replace u(t) with u(t−τ) on one side of the equation, replace y(t) with y(t−τ) on the other side of the equation, and then check if they are equal.
How do I know if my signal is LTI?
A signal x[n] is causal if and only if x[n] = 0 for all n < 0. x[n] is causal if and only if x[n]u[n] = x[n] (think about it). An LTI system is causal if and only if its impulse response h[n] is causal. All real-world systems are causal; otherwise they could see into the future!
