Consider a real, odd, and periodic signal x(t) whose Fourier series representation may
Chapter 7, Problem 7.8(choose chapter or problem)
Consider a real, odd, and periodic signal x(t) whose Fourier series representation may be expressed as
\(x(t)=\sum_{k=0}^{5}\left(\frac{1}{2}\right)^{k} \sin (k \pi t)\)
Let \(\hat{x}(t)\) represent the signal obtained by performing impulse-train sampling on x(t) using a sampling period of T = 0. 2.
(a) Does aliasing occur when this impulse-train sampling is performed on x(t)?
(b) If \(\hat{x}(t)\) is passed through an ideallowpass filter with cutoff frequency \(\pi / T\) and passband gain T, determine the Fourier series representation of the output signal g(t).
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