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In article <1158268781.777153.136000@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Sandro <sandro.grassia@xxxxxxxxxxxxxxxx> wrote:
>
>Robert Israel ha scritto:
>
>> In article <1158177772.707332.288140@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>> <sandro.grassia@xxxxxxxxxxxxxxxx> wrote:
>But my question is still without answer....
>
> I know that if f(t) with period T [ f(t)=f(t+T) ; T minimum value]
>satisfy:
> f(t+T)=-f(t)
You mean f(t+T/2) = -f(t)
> than f(t) has only odd armonics.
>
> What special has g(t) if g(t) has only even armonics?
In other words, since it seems your "only even harmonics"
[ please note the "h" in the English word, by the way ]
does not include the fundamental, you're saying you have
a function of the form
g(t) = a_1 cos(2 pi t /T - phi_0)
+ sum_k a_{2k} cos(4 pi k t/T - phi_{2k})
Then
g(t) - g(t+T/2) = 2 a_1 cos(2 pi t/T - phi_0)
is a pure sinusoid of period T. If g is twice differentiable,
g"(t) - g"(t+T/2) = (2 pi/T)^2 (g(t) - g(t+T/2))
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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