Why am I getting the wrong answer for the Fourier transform time-shift property?

[jaus tail]

Homework Statement

Homework Equations

if x(t) --> X(W)
then
x(-t) --> X(-W)
and
x(t+a)-->e^jwX(W)

The Attempt at a Solution

I'm getting right answer for 1st part. For second part book says right answer is C.
Where am I wrong?[/B]

 

[Abhishek kumar]

First you calculate x(t) by inverse Fourier tansform then by substituting t=-t and t=-t-1 you will get the result

 

[jaus tail]

So as per rules
if f(t)----> Fourier---> F(jw)
then f(t-to) ----> e^stoF(jw)
So then if there is now any more x(3(t-to)) then does the change reflect in e^sto also or is that a constant and only F(jw) becomes 1/|a| F(jw/a)?

 

[jaus tail]

This is what I tried for second part. But book answer is c

 

[Abhishek kumar]

x(-t) --> X(-W)

So as per rules
if f(t)----> Fourier---> F(jw)
then f(t-to) ----> e^stoF(jw)
So then if there is now any more x(3(t-to)) then does the change reflect in e^sto also or is that a constant and only F(jw) becomes 1/|a| F(jw/a)?

So as per rules
if f(t)----> Fourier---> F(jw)
then f(t-to) ----> e^stoF(jw)
So then if there is now any more x(3(t-to)) then does the change reflect in e^sto also or is that a constant and only F(jw) becomes 1/|a| F(jw/a)?

Yes you can apply this property. i told you in previous post to recheck ur answer by that method.

 

[jaus tail]

Thanks. But I don't know how to use inverse Fourier method. What answer are you getting? B or C?
It could be book answer is wrong.

I wanted to ask a doubt on fourier?
If we have to use time shift property followed by time scaling property then does the exponential part also change?

I can't find any solved examples. In laplace there were a few unsolved examples but then my answer matched when I didn't consider e^(-Ts) as part of new F(S). As in the second circle drawn above.

 

[Abhishek kumar]

A

Thanks. But I don't know how to use inverse Fourier method. What answer are you getting? B or C?
It could be book answer is wrong.

I wanted to ask a doubt on fourier?
If we have to use time shift property followed by time scaling property then does the exponential part also change?
View attachment 216565
I can't find any solved examples. In laplace there were a few unsolved examples but then my answer matched when I didn't consider e^(-Ts) as part of new F(S). As in the second circle drawn above.

Just multiply by e^-jw to the answer you got in previous problem.In only time shift exponential term come you can do it by simple integration

 

[jaus tail]

That gives answer but should it be e^-jw or e^(+jw)
since x(-t-1) = x(-(t+1))
So I'm not sure how to go ahead with this. Should it be +jw or -jw?

 

[Abhishek kumar]

That gives answer but should it be e^-jw or e^(+jw)
since x(-t-1) = x(-(t+1))
So I'm not sure how to go ahead with this. Should it be +jw or -jw?

-Jw

 

[jaus tail]

In original post I've used time shift property first and then time scaling. Can u help me as to why I'm not getting right answer there? I've pasted pic.

 

[jaus tail]

If I go by the last post over here then I get a different answer:
https://dsp.stackexchange.com/quest...de-of-a-function-affect-its-fourier-transform
here a = b = -1.

 

[Abhishek kumar]

In original post I've used time shift property first and then time scaling. Can u help me as to why I'm not getting right answer there? I've pasted pic.

You have done right but you choose option b and option b is not matching to you result may be in option c there is print mistake with minus sing in first term.

 

[jaus tail]

Thanks.