### Author Topic: Fourier coefficients  (Read 1236 times)

#### Jingxuan Zhang

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##### Fourier coefficients
« on: March 06, 2018, 08:06:25 PM »
Could anyone kindly inform me one more time the origin of the scalar multiple in finding Fourier coefficients? I know these are supposed be inner product, but I don't remember a scaling there.
Also, chap 4.3 remark 2 has some obvious typo. (Somewhere 2's in $L^2$'s are missing).

#### Victor Ivrii

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##### Re: Fourier coefficients
« Reply #1 on: March 07, 2018, 03:21:09 AM »
Well, it is $1/\|X_n\|^2$ with $X_n$ corresponding basis function.

#### Jingxuan Zhang

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##### Re: Fourier coefficients
« Reply #2 on: March 07, 2018, 06:58:39 AM »
As if when we do the projection of $b$ on $a$ in Euclidean space, the coefficient is given by $a\cdot b / ||a||^2$?

#### Victor Ivrii

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##### Re: Fourier coefficients
« Reply #3 on: March 07, 2018, 07:58:42 AM »
Exactly. I told you so