Am I missing something with exponential Fourier series?

AI Thread Summary
The discussion revolves around difficulties in understanding and efficiently calculating exponential Fourier series in a signal processing class. The user expresses frustration with the lengthy process of deriving general expressions for different n values after performing integrals. They currently rely on converting to trigonometric form, which they find slow and cumbersome. The user seeks shortcuts or clearer methods to simplify the process, particularly regarding the transition from the integral to the final expression. Overall, they are looking for assistance in grasping the concepts and improving their calculation efficiency.
slashrulez
Messages
7
Reaction score
0
Hi, I'm in a signal processing class, and I'm having some trouble with complex numbers. As an example, I've attached a pretty simple question about an exponential Fourier series.

I don't find these questions particularly hard, it just takes me ridiculously long to do them. I mean, after I take the integral, it literally took me 10 minutes to actually figure out how to get the general expression for different n values and whatnot. It just seems like it should be much easier, so I'm wondering if there's some kind of shortcut I'm missing.

My current method is pretty slow, and I just rewrite everything in trigonometric form and work from there. I can't think of any other way to do it, but it takes an awful long time. When I look at the work in that example, I don't really know what's going on. I don't know how they go to from the integral to that expression in one step, and I don't even know what the symbol attached to the npi/2 is.

Can anyone help me out? Thanks.
 
Mathematics news on Phys.org
Whoops, it looks like I forgot to attach the picture
 

Attachments

  • Untitled.jpg
    Untitled.jpg
    20.5 KB · Views: 477
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top