Let x a ( t ) be a time-limited signal: that is, x a ( t )
Question:
Let xa(t) be a time-limited signal: that is, xa(t) = 0 for |t| > ?, with Fourier transform Xa(F). The function Xa(F) is sampled with sampling interval ?f = 1/Ts.
(a) Show that the function can be expressed as a Fourier series with coefficients ck = 1/TsXa(k?F)
(b) Show that Xa(F) can be recovered from the samples Xa(k?F), - ?
(c) Show that if Ts a(F).
(d) Show that if Ts ? 2?, perfect reconstruction of Xa(F) from the samples X(k?F) is possible using the interpolation formula
Transcribed Image Text:
(a) Σ X,(1 - nT,) X,11) (d) sin{(n/& F(F-k&F)] (7/8 FXF-k&F) x, (k8 F)- X,(F) =
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Related Book For
Digital Signal Processing
ISBN: ?978-0133737622
3rd Edition
Authors: Jonh G. Proakis, Dimitris G.Manolakis
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