Determine which of the following digital transfer functions are physically realisable.

(a) \(G_{c}(z)=\frac{10\left(1+0.2 z^{-1}+0.5 z^{-2}ight)}{z^{-1}+z^{-2}+1.5 z^{-3}}\)

(b) \(G_{c}(z)=\frac{1.5 z^{-1}-z^{-2}}{1+z^{-1}+2 z^{-2}}\)

(c) \(G_{c}(z)=\frac{z+1.5}{z^{3}+z^{2}+z+1}\)

(d) \(G_{c}(z)=\frac{z^{-1}+2 z^{-2}+0.5 z^{-3}}{z^{-1}+z^{-2}}\)

(e) \(G_{c}(z)=0.1 z+1+z^{-1}\)

(f) \(G_{c}(z)=z^{-1}+z^{-2}\)