Question

Find the Z – Transform of sinh ⁡nθ.

(a) \(\frac{sinh⁡θ}{z^2-2z cosh⁡θ+1} \)

(b) \(\frac{1}{2}  \frac{sinh⁡θ}{z^2-2z cosh⁡θ+1} \)

(c) \(\frac{z sinh⁡θ)}{z^2-2z cosh⁡θ+1} \)

(d) \(\frac{z(z-sinh⁡θ)}{z^2-2z cosh⁡θ+1} \)

I have been asked this question by my school principal while I was bunking the class.

My query is from Linear Difference Equations and Z topic in portion Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Right choice is (a) \(\frac{sinh⁡θ}{z^2-2z cosh⁡θ+1} \)

For explanation: The first step to solve this is to expand the function sinh⁡nθ. The expansion of this function is of the form a^n. First we have to find the Z-Transform of 1 and then we have to use damping rule. To, get the answer, we take L.C.M.