# Homework Help: Fourier Transform

1. Dec 11, 2017

### jaus tail

1. The problem statement, all variables and given/known data

2. Relevant equations
if x(t) --> X(W)
then
x(-t) --> X(-W)
and
x(t+a)-->ejwX(W)

3. 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?

2. Dec 11, 2017

### 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

3. Dec 11, 2017

### jaus tail

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

4. Dec 12, 2017

### jaus tail

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

5. Dec 12, 2017

### Abhishek kumar

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

6. Dec 12, 2017

### jaus tail

Thanks. But I dont 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.

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7. Dec 12, 2017

### Abhishek kumar

A
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

8. Dec 12, 2017

### 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?

9. Dec 12, 2017

### Abhishek kumar

-Jw

10. Dec 12, 2017

### 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.

11. Dec 12, 2017

### jaus tail

12. Dec 12, 2017

### Abhishek kumar

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.

13. Dec 12, 2017

Thanks.