Time Shifting & Stretching: Questions Explained

[lennybogzy]

I have a question regarding time shifting, stretching etc. For example:

if I have y(t) = x(3t) does that mean that x(t) = y(t/3)?

if I have y(t)=(-1/2)x(-3t+2) does x(t) = -2y(t/3 -2) ?

 

[LCKurtz]

I have a question regarding time shifting, stretching etc. For example:

if I have y(t) = x(3t) does that mean that x(t) = y(t/3)?

Yes.

if I have y(t)=(-1/2)x(-3t+2) does x(t) = -2y(t/3 -2) ?

No. Let u = -3t+2 so t = (-1/3)(u-2). This gives

y((-1/3)(u-2))=(-1/2)x(u)

-2y((-1/3)(u-2)) = x(u). Replace the u by t and it's a little different than what you wrote.

 

[lennybogzy]

brilliant! thanks