Nicolas

2006-Feb-23, 10:52 PM

OK so I've chosen a Master which includes all sorts of courses carrying fancy names, but it all boils down to stochastics. ugh. ANyway, I'm trying to get "to the bottom" of a course reader here, finding proofs for all formulas. There's just one page where I'm stuck with my proofs. I understand everything, but I can't prove it.

We start from the a/b definition of discrete Fourrier series:

http://upload.talk2.nl/files/168703temp.GIF

Some time after that, we're going to the complex form of this Fourrier Transform. I link to the 2 relevant sheets.

http://upload.talk2.nl/files/368140temp.GIF (http://upload.talk2.nl/files/368140temp.GIF)

http://upload.talk2.nl/files/419750temp.GIF (http://upload.talk2.nl/files/419750temp.GIF)

OK so in sheet 1:

*how do you prove that indeed that "c" notation is the same as the a/b notation? I'm stuck with an imaginary part that shouldn't be there...

*related to that, how do you "invent" the "c" complex form in the first place?

On sheet 2:

*you guessed it: prove the formula in the rectangle, below "it is easy to prove that..."

*How can I prove that 3.9 and 3.12 are each other's inverse?

---------------------

This is not homework, I just want to understand the basics to the bottom. I've searched on these 4 questions for a long time, but I'm unable to find them. It's strange, asit doesn't seem difficult compared to other proofs that I did find...

Any help is appreciated! I don't need explanations as to the Fourrier series itself, only how to (mathematically proof) the equality of the notations and the validity of the claims.

Edit: "Fourier"...

We start from the a/b definition of discrete Fourrier series:

http://upload.talk2.nl/files/168703temp.GIF

Some time after that, we're going to the complex form of this Fourrier Transform. I link to the 2 relevant sheets.

http://upload.talk2.nl/files/368140temp.GIF (http://upload.talk2.nl/files/368140temp.GIF)

http://upload.talk2.nl/files/419750temp.GIF (http://upload.talk2.nl/files/419750temp.GIF)

OK so in sheet 1:

*how do you prove that indeed that "c" notation is the same as the a/b notation? I'm stuck with an imaginary part that shouldn't be there...

*related to that, how do you "invent" the "c" complex form in the first place?

On sheet 2:

*you guessed it: prove the formula in the rectangle, below "it is easy to prove that..."

*How can I prove that 3.9 and 3.12 are each other's inverse?

---------------------

This is not homework, I just want to understand the basics to the bottom. I've searched on these 4 questions for a long time, but I'm unable to find them. It's strange, asit doesn't seem difficult compared to other proofs that I did find...

Any help is appreciated! I don't need explanations as to the Fourrier series itself, only how to (mathematically proof) the equality of the notations and the validity of the claims.

Edit: "Fourier"...