A periodic voltage signal has period and is defined on one period by for

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier series and periodic decomposition

Problem

A periodic voltage signal

V(x)

has period

L

and is defined on one period by

V(x) = V_0(x/L)^2

for

-L/2 \le x < L/2

, extended periodically outside that interval. ((a)) Without computing any integral, state which of the real Fourier coefficients

a_0

a_n

(

n \ge 1

) and

b_n

(

n \ge 1

) must vanish, using only the parity of

V(x)

. ((b)) Test whether the half-period shift

V(x+L/2)

equals

V(x)

-V(x)

, and say whether this predicts any further coefficients to vanish.

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