**Find Z transform of F[K] =Cos(ak) u[k] :**

F(z) = Z (cos(ak) u(k) )

= Z ( ½ (e

^{jak}+e^{-jak}) u(K) )
= ½ (Z (e

^{jak }u(k) ) + Z (e^{-jak}) u(K) )
=½ ( Z/ Z-e

^{ja}+ Z/ Z-e^{-ja})
= ½ ( Z/ Z-e

^{ja }*^{ }Z-e^{-ja}/ Z-e^{-ja}+ Z/ Z-e^{-ja}* Z-e^{-ja}/ Z-e^{-ja})
=½ ( Z

^{2}- Ze^{-ja}/ Z^{2}- Ze^{ja}– Ze^{-ja}+1 + Z^{2}- Ze^{ja}/ Z^{2}- Ze^{ja}– Ze^{-ja}+1)
=½ (2Z

^{2}– (Ze^{ja}– Ze^{-ja}) / Z^{2}- Ze^{ja}– Ze^{-ja}+1)
= ½(2Z

^{2}– 2Zcos(a)/ Z^{2}-2Zcos(a) +1
= Z (Z-cos(a)) / Z

^{2}-2Zcos(a) +1**Find Z transform of F[K] =Cos(ak) u[k] :**

F(z) = Z (cos(ak) u(k) )

= Z ( ½ (e

^{jak}+e^{-jak}) u(K) )
= ½ (Z (e

^{jak }u(k) ) + Z (e^{-jak}) u(K) )
=½ ( Z/ Z-e

^{ja}+ Z/ Z-e^{-ja})
= ½ ( Z/ Z-e

^{ja }*^{ }Z-e^{-ja}/ Z-e^{-ja}+ Z/ Z-e^{-ja}* Z-e^{-ja}/ Z-e^{-ja})
=½ ( Z

^{2}- Ze^{-ja}/ Z^{2}- Ze^{ja}– Ze^{-ja}+1 + Z^{2}- Ze^{ja}/ Z^{2}- Ze^{ja}– Ze^{-ja}+1)
=½ (2Z

^{2}– (Ze^{ja}– Ze^{-ja}) / Z^{2}- Ze^{ja}– Ze^{-ja}+1)
= ½(2Z

^{2}– 2Zcos(a)/ Z^{2}-2Zcos(a) +1
= Z (Z-cos(a)) / Z

^{2}-2Zcos(a) +1