MHB Half wave symmetry and integrals

[fernlund]

If I have a periodic wave x(t) with half-wave symmetry, it means that:

x(t + T0/2) = -x(t)

where T0 is the period of the wave. Would this automatically lead to the conclusion that

X(t + T0/2) = -X(t)

where X'(t) = x(t), i.e X(t) is the integral of x(t).

?

 

[Ackbach]

If I have a periodic wave x(t) with half-wave symmetry, it means that:

x(t + T0/2) = -x(t)

where T0 is the period of the wave. Would this automatically lead to the conclusion that

X(t + T0/2) = -X(t)

where X'(t) = x(t), i.e X(t) is the integral of x(t).

?

I think so. Can you integrate $x(t+T_0/2)=-x(t)$ on both sides w.r.t. $t$, and obtain your result?

 

[fernlund]

I think so. Can you integrate $x(t+T_0/2)=-x(t)$ on both sides w.r.t. $t$, and obtain your result?

Yeah, it's correct for all of the examples I can think of. Thanks!