== Headline text ==TIME INVARIANT SYSTEM A system is time invariant if for a signal X(t) or X[n] and time t0 , a shifted input of X(t-t0) yields in a shifted output Y(t-t0). Eg: y(t)=sin[x(t)] Proof: let an arbitary input X1 is taken,then;
Y1(t) =X1(t)
when the next input is taken,after the first input is shifted
X2(t)=X1(t-t0)
the output will be:
Y2(t)=sin[x2(t)]=sin[X1(t-t0)]
again, Y1(t-t0)=sin[X1(t-t0)]
thus we see that:
Y2(t)=Y1(t-t0)
== Headline text ==Time variant system Eg: Y[n]= nX[n]
As the above system has a time varying gain,hence it is time variant system.
