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(Solved): Problem 8.2: O&W 7.22 The signal y(t) is generated by convolving a band-limited signal x_(1)(t) ...
Problem 8.2: O&W 7.22
The signal y(t) is generated by convolving a band-limited signal x_(1)(t) with another band-limited
signal x_(2)(t), that is,
y(t)=x_(1)(t)*x_(2)(t)
where
x_(1)(j\omega )=0 for |\omega |>1000\pi
x_(2)(j\omega )=0 for |\omega |>2000\pi
Impulse-train sampling is performed on y(t) to obtain
y_(p)(t)=\sum_(n=-\infty )^(\infty ) y(nT)\delta (t-nT)
Specify the range of values for the sampling period T to ensure that y(t) is recoverable from y_(p)(t).