Question 22.30: Given that the z transform of cos(ak) is z(z-cos a)/z²-2z c......
Given that the z transform of cos (ak) is
\frac{z(z-\cos a)}{z^2-2 z \cos a+1}find the z transform of \mathrm{e}^{-2 k} \cos (a k).
Step-by-Step
Since b = 2, the complex translation theorem states that we replace z by e^{2z} in the z transform F(z).
F\left(\mathrm{e}^2 z\right)=\frac{\mathrm{e}^2 z\left(\mathrm{e}^2 z-\cos a\right)}{\mathrm{e}^4 z^2-2 \mathrm{e}^2 z \cos a+1}is therefore the required transform.
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