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From: Willi =??B?TcO2aHJpbmc=?= on 13 Aug 2010 07:51
Golabi Doon wrote:

> Hello,
>
> Consider the function f(x) represented in phase/magnitude form sum_k
> (z_k)cos(k(x+p_k)) where z_k are negative real and p_k are real.
>
> Some operations on f have nice form, for example, we know sum_k (-k)
> (z_k)sin(k(x+p_k)) is the same df/dx. My question is, does sum_k (k)
> (z_k)cos(k(x+p_k)) have any meaning in terms of f ? This form is the
> same as f(x) except each term of the sum is multipled by "k".
>
> Regards
>
> Golabi
It is the Hilbert-transform of the derivative of f. If it exists.

Willi

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