$)$ Given an arbitrary rational transfer function H$($z$),$ a minimum$-$phase system Hmin$($z$)$ with a magnitude

identical to that of H$($z$)$ does not necessarily exist.

$($b$)$ Bilinear transform is not suitable for designing digital filters with piece$-$wise linear but non$-$constant

magnitude responses, e$.$g$.,$ a differentiator.

$($c$)$ A causal and stable analog Butterworth filter cannot have any poles on the imaginary axis on the s$-$plane.

$($d$)$ A rectangular window can only provide a fixed ripple size and transition bandwidth that are not ad$-$

justable.

$($e$)$ A rational LTI system is BIBO stable if its ROC excludes the unit circle.

$($f$)$ If a rational X$($z$)$ has $5$ poles with $4$ distinct magnitudes, X$($z$)$ may correspond to the z$-$transform of $4$

different signals, among which one is right$-$sided, one is left$-$sided, and two are two$-$sided.

$($g$)$ A Type $3$ linear$-$phase FIR filter is not suitable for designing a bandstop filter.

$($h$)$ A stable and causal allpass filter must have all its poles inside the unit circle, but its zeros may be inside

or outside the unit circle