$8.$ Short answers

A$.$ Is an adaptive filter linear?$$ Is an adaptive filter shift$-$invariant?$$ Is an adaptive filter causal? Justify your answers.

B$.$ Matlab provides tools to create digital Butterworth, Chebyshev, and Elliptic filters.$$ Why does it not provide a digital Bessel filter?$$ Is it possible to create a digital Bessel filter?

C$.$ A design is required for a second$-$order digital bandpass filter with passband centered at $\mathrm{.}317$ cycles per sample.$$ Is the following design appropriate?$$ Justify your answer.

yn$=0\mathrm{.}5$ xn$-$yn$-1-1\mathrm{.}5$y$($n$-2)$

D$.$ A continuous periodic signal of period $14$ milliseconds is sampled at $500$ Hz$.$ What is the lowest$-$frequency harmonic of the continuous signal to be aliased, and what frequency does it appear to be after sampling?$$ Justify your answer.