(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

show whether the system

y(t) = x(2t) is time variant or not

2. Relevant equations

a system is time invariant if a time shift in the input signals results in an identical time shift in the output signal, that is if y[n] is the output of a discrete-time, time invariant system when x[n] is the input, then y[n-n0] is the output when x[n-n0] is applied

3. The attempt at a solution

first of all I have the answer on my book(oppenheim) but I can't understand what he does

what I tried to do is

suppose we apply a signal

x1(t) and we get an output of y1(t) = x1(2t)

now, suppose we apply a signal x2(t) = x1(t-t0)

we get an output of y2(t) = x2(t) = x1(2t - 2t0) = y1(t-t0)

hence it's time invariant

now, the book says it's time variant, and also it creates graphs to prove this point and I don't understand how he proves this..

what am I doing wrong?

thanks in advance

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Time invariance

**Physics Forums | Science Articles, Homework Help, Discussion**