- #1

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Any comments will be appreciated.

- Thread starter caduceus
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- #1

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Any comments will be appreciated.

- #2

mathman

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|f(x)| is not integrable over (-oo,oo). so the Fourier integral cannot be properly defined.

- #3

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Because that is a sinusoidal function. What is there to analyze?

Any comments will be appreciated.

You want to find the sinusoidal functions that make up a non sinusoidal function.

- #4

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- #5

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Prof Brad Osgood has some excellent Fourier transform lectures on iTunesU

(The Fourier Transform and its Applications).

In particular, there's a few lectures (~lectures 10-14 I think) on distributions and Schwartz functions that help show how Fourier transforms of sines, exponentials, deltas, ... can be better justified. Suprisingly (to me after having seen and given up trying to understand Functional analysis), the basics required for application are not actually all that difficult, mostly requiring a change in approach, and an extra level of indirection.

Some lecture notes to go with the lectures can be found here:

http://www.stanford.edu/class/ee261/book/all.pdf [Broken]

(chapter 4 covers distributions).

(The Fourier Transform and its Applications).

In particular, there's a few lectures (~lectures 10-14 I think) on distributions and Schwartz functions that help show how Fourier transforms of sines, exponentials, deltas, ... can be better justified. Suprisingly (to me after having seen and given up trying to understand Functional analysis), the basics required for application are not actually all that difficult, mostly requiring a change in approach, and an extra level of indirection.

Some lecture notes to go with the lectures can be found here:

http://www.stanford.edu/class/ee261/book/all.pdf [Broken]

(chapter 4 covers distributions).

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- #6

Meir Achuz

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The Fourier integral gives two delta functions. That is good enough for physicists.

Any comments will be appreciated.

- #7

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following are two equations

$fk(k1) = \frac{1}{nj} \sum_{j=1}^{nj} c_j(j) \exp (i k1 x_j(j))$\\

$where \frac {-ms}{2} <k1 < \frac{ms-1}{2}$

a) what is k1

b) what is x_j(j)

c) what is c_j(j)

Is this a forward transform

d) What will be the inverse transform, and is inverse tranform means we are evaluating fourier series

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