calibcant/main.bib: Don't worry about four-deriv citation
Derivation:
F(d x(t) / dt) = F(x'(t))
= 1/sqrt(2 π) \int_{-∞}^∞ x'(t) \exp{-i ω t} dt
Using integration by parts:
\int v du = uv - \int u dv
with:
v = \exp{-iωt}
dv = -iω \exp{-iωt}
du = x'(t) dt
u = x(t)
gives:
F(x'(t)) = 1/sqrt(2 π) [
x(t)\exp{-iωt}|_{-∞}^∞ -
\int_{-∞}^{∞} x(t) iω\exp{-iωt} dt ]
= iω ⋅ 1/sqrt(2 π) \int_{-∞}^∞ x(t) \exp{-iωt} dt
= iω F(x(t))
Where the uv term drops out for any signal where x(t)→0 as |t|→∞.
For higher order differentials, just chain these together:
F(d^n x(t) / dt^n)
= iw F(d^{n-1} x(t) / dt^{n-1})
= …
= (iw)^n F(x(t))