Question

could someone help me with fourier?

Answer 1

I dont understand the parseval's identity...

for example this question:
Consider the periodic block function f(t) with period pi and for some a∈R with 0 < a< pi, and the period block function g(t) with period pi and some b∈R with 0<b<pi. Assume a≤b

Use parseval's identity to show that:
∞
Σ (sin(na)*sin(nb) )/n^2
n=1

is the same as

(a( pi - b))/2

Answer 2

\[\sum_{n=1}^\infty {\frac{\sin(n*a) * \sin(n*b)}{n^2}}\]\[ = \frac{a(\pi - b)}{2}\]

Answer 3

yeahhh i have typed that.. but could you explain it?

Answer 4

http://www.youtube.com/watch?v=gvdf5n-zI14&feature=player_embedded

Answer 5

This expression on the right
\[ a(\pi - b)/2 \]
looks like a convolution and then the expression on the left looks like the product of two Fourier series as you might expect from a convolution.

Answer 6

Ah ... and now I see what the functions are you are convoluting; they're given to you.

So the convolution formula applied to those two functions gives you the infinite sum; explicitly integrating the convolution of the two functions gives you the RHS expression.

Then use Parseval's theorem to set them equal.

Answer 7

JamesJ could you be more specific? So i have use the convolution integral?

Answer 8

Can you tell me exactly what are the two functions given to you in the problem? As written they're not well defined.

Answer 9

I think on the left side with the Σ thats just a sommation of a and b. And i dont know that the other is, im afraid of...

Answer 10

I mean these functions:
Consider the periodic block function f(t) with period pi and for some a∈R with 0 < a< pi, and the period block function g(t) with period pi and some b∈R with 0<b<pi. Assume a≤b

Answer 11

owhh ... there are 2 periodic signals a and b, both signals are block functions

Answer 12

Can you write them out for me explicitly?

Answer 13

the period is \[\omega0 = 2\]

fn = sin(na)/(n*pi)
f0 = a/pi

gn = sin(nb)/(n*pi)
g0 = b/pi

Answer 14

that what i calculated

Answer 15

Sorry, I'm still not getting it. What is a periodic block function?