PROBLEM 10.1*: Consider the system below where h[n] describes an arbitrary LTI s

Question

PROBLEM 10.1*: Consider the system below where h[n] describes an arbitrary LTI system x(t) IDEALrn yIn] IDEAL D-to-C C-to-D CONVERTER CONVERTER x(t) = A cos(950t) cos(200t) cos(600t) (a) Determine the Nyquist rate to sample x(t) (i.e., to avoid aliasing) (b) Assume now that = 2000 Hz (regardless of your answer for (a)) and the impulse response h[n] and its frequency response H(e1") have the form: 1, n=0, ,L-1 0,otherwise ja_sin(aL/2) e-j(L-1)/2 find the smallest value of such that the output is y(t) 0

Explanation / Answer

(a) x(t) can be written as

x(t) = Acos(2pi*475t)+B/2 cos(2pi*400t) +B/2 cos(2pi*200t)

The maximum frequency content in the signal x(t) is 475Hz

Therefore the nyquist rate required is fs=2fm=950Hz

Question (b)

y(t) is zero if and only if the system function h(n) =0, since the input is passed through h(n).

h(n) is zero for L =0 only.

Therefore smallest value of L is zero such that the output

y(t) =0.

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