Demo 4: Time Domain Operations on Signal

In this demo, we consider an example of a signal x(t) and examin various time domain operations, e.g., time shifting, time reversal and time scaling given by x(((t-a)/b)). Note that with b=1, we have x(t-a) which is a time shifting operation, i.e., x(t) is shifted at x=a; with a=0  and b=-1, we have x(-t) which is a time reversal of x(t); with a=0 and b>1, x(t) expands by a factor of b and with b<1, x(t) contracts/compresses by a factor of b.

y[t_]:=Piecewise[{{t,0≤t≤1},{1,1≤t≤3}}];
Manipulate[Plot[{y[t],y[(t-a)/b]},{t, -7, 7},Exclusions->None,PlotStyle->Thick, PlotRange -> All, GridLines->Automatic, AxesLabel->{t,x[(t-a)/b] }],{{a,0},-2,2,Appearance -> "Labeled"},{{b,1},-2,2, Appearance -> "Labeled"}, SaveDefinitions -> True]