Fourier Transform - Definitive Answer Required

[thomas49th]

Homework Statement

Here is a signal

$$\frac{5000}{\pi}sinc^{2}(50t) + \frac{10000}{\pi}sinc^{2}(50t)cos(100t)$$

Find it's Fourier transform and draw it

Homework Equations

Standard Fourier transformations

The Attempt at a Solution

Well
$$\frac{5000}{\pi}sinc^{2}(50t)$$ = triangle(w/100)

So $$\frac{5000}{\pi}sinc^{2}(50t) + \frac{10000}{\pi}sinc^{2}(50t)cos(100t)$$

I get triangle(w/100) + 2(triangle(w+100/100)+triangle((w-100)/100)

However the answer says that there is no 2 (highlighted in red). Why note. The Fourier transform of cos(100t) is pi * [d(w+100) + d(w-100)] is it not? Where has the 2 gone?

where d is dirac

Thanks
Thomas

 

[vela]

Which Fourier transform convention are you using? There are several. See http://en.wikipedia.org/wiki/Fourier_transform. I think you might be mixing up the transforms from two different conventions.

 

[thomas49th]

$$G(w) =\int g(t) e^{-jwt}dw$$

 

[vela]

Well, after messing around in Mathematica, I can see the two shouldn't be there. Show us your work so we can see where the problem lies.

 

[thomas49th]

From the mark scheme associated with the question
I did the same except got a 2 outside the last 2 terms...I didn't get a flat part in the middle (as the triangle sides didn't add to 1)