What Is the Correct Magnitude of a Rectangular Result in Fourier Transform?

[iskorpit]

fourier transform simple question?? pls help

can anyone help me in finding the Fourier transform of this signal?? i need quick help

 

[cepheid]

Welcome to PF.

You already posted this in the Engineering subforum, where it belongs. Don't double post -- it is considered spamming.

We can certainly help you out, but we're not going to do your work for you (please read forum rules). What equations or concepts are applicable to this problem (e.g. what is the definition of the Fourier transform of a discrete time signal)? What have you done so far on this problem? The template that you deleted when you posted this was there for a reason, namely because it is an excellent, systematic way to approach any given problem.

 

[iskorpit]

i know when signals in multiplication we can take the convolution of their Fourier transforms to find the Fourier transform of the signal but there is a third term 1/pi*n which i don't know how to find its Fourier transform so that confused me

 

[iskorpit]

and i am sorry for my bad usage of the forum, as you know i am a novice user

 

[Phyisab****]

Try using Latex by clicking the sigma icon on the reply box $$\frac{like}{this.}$$

 

[cepheid]

...but there is a third term 1/pi*n which i don't know how to find its Fourier transform so that confused me

Whether you consider it to be a product of two or of three functions depends largely on how you choose to define those functions. Do you by any chance happen to know the Fourier transform of

$$\frac{\sin W n}{\pi n}$$​

where W is a constant? Hint: there is a name for this function.

 

[iskorpit]

oh =) i couldn't see the sinc function but then i think the answer is the convolution of the Fourier transforms of sinc and cos but i can't realize how to take their convolution

 

[cepheid]

oh =) i couldn't see the sinc function but then i think the answer is the convolution of the Fourier transforms of sinc and cos but i can't realize how to take their convolution

Hey, are you by any chance using the textbook Signals and Systems by Oppenheim, Willsky, and Nawab?

Edit: and by the way, this convolution should be particularly easy. What's the result of a convolution with a delta function?

 

[iskorpit]

yes but this question is from an old midterm i don't know if it is also in my book? if it is in the book it would be perfect if u could tell me the question number

 

[iskorpit]

i think that convolution of a signal with a delta is again itself but i have a confusion about the transform of cos? is it a dirac at $$7*pi/2$$ and $$-7*pi/2$$ with magnitude pi

 

[cepheid]

yes but this question is from an old midterm i don't know if it is also in my book? if it is in the book it would be perfect if u could tell me the question number

I have no idea if this question is in your book. I was just going to point out that the textbook has a pretty good explanation of how the discrete-time FT of a product leads to a "periodic convolution," (a convolution in which the limits of integration are finite) and how to calculate such a convolution. I have a 2nd edition. Therefore, for me, the chapter on Discrete-Time Fourier Transforms is Chapter 5. The section on "The Multiplication Property" would be very useful for you to look at (section 5.5 in my edition). In particular, the very first example in that section tells you how to carry out a periodic convolution (it's example 5.15 in my edition).

 

[cepheid]

i think that convolution of a signal with a delta is again itself but i have a confusion about the transform of cos? is it a dirac at $$7*pi/2$$ and $$-7*pi/2$$ with magnitude pi

Not quite. If you look in the same chapter I mentioned in my previous post for a table entitiled "Basic Discrete-Time Fourier Transform Pairs", you'll see that the FT of

$$\cos \omega_0 n$$​

is given. What is $\omega_0$ in this example?

 

[iskorpit]

ok thank u very much but at last i wanted to make things clear if we look only in one period is it a convolution of a square and two diracs?

 

[iskorpit]

i think Wo is $$7*pi/2$$ am i wrong??

 

[iskorpit]

i have found the same question in my book and i understood my mistake but i could't understand something. book says that the rectangular which is the result of the convolution has a height 1.i don't know how to call it maybe i should say magnitude.but i know that in the Fourier transform if cos(won) there is a pi multiplier.so i think the height or =) magnitude of the rectangular has to be pi. am i wrong?