Fourier sine series

Question

p[t_] := (1/12) Sign[Sin[428 \[Pi] t]] + (11/12) Sign[
 Sin[428*2 \[Pi] t]]
 FourierSinSeries[p[t], t, 10]]

I want to expand this function but it takes forever. Is there anything wrong? Thank you.

Answer 1

Up to the documentation,

FourierSinSeries[(1/12) Sign[Sin[428 \[Pi] t]] + (11/12) Sign[
Sin[428*2 \[Pi] t]], t, 10, FourierParameters -> {1, 428}]

works quickly and well. The plot

Plot[(1/12) Sign[Sin[428 \[Pi] t]] + (11/12) Sign[
Sin[428*2 \[Pi] t]], {t, 0, 3/428}, WorkingPrecision -> 15]

gives insight into the above.