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Question

Suppose that a continuous-time signal xc(t) (−∞ < t < ∞) is sampled every 0.5 seconds and yields the

discrete-time signal x[n] (n = . . . , −2, −1, 0, 1, 2, . . .) 

x[n]= { 6 n = -1

2 n = 0

-1 n = 1

0 otherwise }

where the n = 0 sample corresponds to t = 0. Let xr(t) be the recovered continuous-time signal when we apply sinc interpolation to x[n].

a) Give an equation for xr(t) that corresponds to the x[n] above.

b) Find xr(0.7).

c) Plot xr(t) over −2.2 ≤ t ≤ 2.2 using MATLAB.

d) On top of your plot in part c, plot the samples x[n] obtained during −2.2 ≤ t ≤ 2.2 using the relationship t = nT where T is the sampling period used to sample xc(t). Should the samples x[n] lie on the curve xr(t)? Explain. 

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