Answer: No, z1(t) and z2(t) Not Same Signal

[jeir35]

Homework Statement

Let z1(t) be the signal x(t) delayed by 4 sconds and then sped up by a factr of 3. Let
z2(t) be the signal x(t) sped up by a factr of 3 and then delayed by 4 sconds. Do z1(t)
and z2(t) represent the same signal?

Homework Equations

The Attempt at a Solution

My answer was no they are not the same

for the first part
x1(t) = x(t-4) for the delay of 4 secs

then sped up
x2(t) = x1(3t)

so y1= x(3t-4) or x(3(t-4/3)

for the second part

x1(t)=x(3t) sped up
and x2(t) = x1(t-4) delayed by 4 secs

so y2= x(3(t-4)) or x(3t-12)

Is my math correct?

 

[Redbelly98]

Welcome to PF

Yes, that looks correct. You probably meant "z1" and "z2" where you wrote "y1" and "y2", but you do have the right idea.

 

[jeir35]

thanks for the verification!