booklet format - inaf iasf bologna

Temporal Data Analysis A.A. 2011/2012
= sinΩ Nyqt
Ω Nyq t
π Ω Nyqt
2π
cot πΩ Nyqt
2π
= sinΩ Nyq t 1 cos(Ω Nyq t/2)
2 sin(Ω Nyq t/2)
= 2sin(Ω Nyq t/2) cos(Ω Nyq t/2) 1 cos(Ω Nyq t/2)
2 sin(Ω Nyq t/2)
= cos 2 (Ω Nyq t/2)
Please note that we actually need all the summation terms of k from −∞ to +∞. If we had
taken only K = 0 and k = 1 into consideration we would have obtained
f (t) = 1 sinΩ Nyqt
Ω Nyq t
+ 0 sinΩ Nyq(t − ∆t)
Ω Nyq (t − ∆t)
= sinΩ Nyqt
Ω Nyq t
which would not correspond to the input of cos 2 (Ω Nyq t/2). We still would have, as before,
f (0) = 1 and f (k∆t) = 0, but for 0 < t < ∆t we would not have interpolated correctly, as sin x/x
decays slowly for large x while we want to get a periodic oscillation that does not decay as
input.
130 M.Orlandini