[SOLVED] Time Shift and Scaling Properties

Hello there,

Below is the question and my attempted solution. My concern regards part 1, 2, 3 and 4.



Q1. I think 1 and 2 are correct, right?
Q2. For 3, if I do time scaling followed by replacing t by t - 5, I get another graph. Which approach should I use? How do I know if I should time scale first or time shift?
Q3. I have no idea what is asked as well as what to do in part 4?

Thanks

About questions 1 to 3, you just have to equals the argument of the time-scaled/shifted function to each point of the original function. That is:

1. t1/10=-1 ==> t1=-10, t2/10=1 ==> t2=10, t3/10=2 ==> t3=20 you graph is correct (pure time scaling)
2. t1/10-5=-1 ==> t1=40, t2/10-5=1 ==> t2=60, t3/10-5=2 ==> t3=70 that is shift right by 5 before, then scale by 10
3. (t1-5)/10=-1 ==> t1=-5, (t2-5)/10=1 ==> t2=15, (t3-5)/10=2 ==> t3=25 that is scale by 10 before, then shift right by 5

so you inverted graph 2 with graph 3.

About part 4 I think is asked to find which one of the three functions is periodic.

Our function has a total duration of 2-(-1)=3

the first is the summation of infinite x(t) shifted by 3 so is exactly x(t) periodicized (I don't know if this term is correct in English)
the second one is the summation of infinite x(t) shifted by 4, the is a periodic function different from x(t) there is an added
the third one is the summation of infinite x(t) shifted by 2, then there will be superposition between a shifted x(t) and the following

I assume there are three different results for (4) the t-4l has copies every 4 t's apart. Same goes for the others t-3l every three apart and the t-2l has overlapping graphs.

ads-ee said:

I assume there are three different results for (4) the t-4l has copies every 4 t's apart. Same goes for the others t-3l every three apart and the t-2l has overlapping graphs.

Click to expand...

Sorry ads-ee, I was modifying my post just when you posted yours

Thanks! I understand 1-3.

About part 4, turns out all the three are preodic, and we just have to repeat the graph at
four to the right and four units to left (for 1)
for the one with ...3l, it'll just be a bit more closer

and for the last part, the triangular regions overlap!

Thanks for your answers guys

dzafar said:

About part 4, turns out all the three are preodic, and we just have to repeat the graph at
four to the right and four units to left (for 1)
for the one with ...3l, it'll just be a bit more closer

and for the last part, the triangular regions overlap!

Click to expand...

Which is exactly what I said in my post, though probably in a rather cryptic way.