Let x a ( t ) be a time-limited signal: that is, x a ( t )

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Let x_a(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/T_s.

(a) Show that the function can be expressed as a Fourier series with coefficients c_k = 1/T_sX_a(k?F)

(b) Show that Xa(F) can be recovered from the samples X_a(k?F), - ?

(d) Show that if Ts ? 2?, perfect reconstruction of X_a(F) from the samples X(k?F) is possible using the interpolation formula

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Digital Signal Processing

ISBN: ?978-0133737622

3rd Edition

Authors: Jonh G. Proakis, Dimitris G.Manolakis

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Question Posted: May 26, 2011 02:59 AM

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Let x a ( t ) be a time-limited signal: that is, x a ( t )

Question:

(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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a x p t n xa t n T s is a periodic signal with period T s The Fourier ...View the full answer

Digital Signal Processing

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