Final answer:
The z-transform of E(s) is not straightforward from its continuous Laplace domain representation. The computation requires the function to be discretized at intervals of T to obtain a sequence for the z-transform. The period T can be calculated using T = 1/f for a given frequency, but this is not directly applicable for finding the z-transform.
Step-by-step explanation:
The z-transform of a continuous function E(s) with a given sample period T, such as E(s) = 2 / (s^2 + s + 1) - 2 / (s^2 + 4), is not directly computed as this function is in the Laplace domain. To compute a z-transform, we typically begin with the time-domain signal or its s-domain representation if it's a result of the Laplace transform and then sample this signal at intervals of T to produce a discrete sequence. This sequence can then be converted into the z-domain using the definition of the z-transform.
In general, to find the period T of a signal, we could use the formula T = 1/f where f is the frequency. As per the provided strategy, if the frequency is given as f = 2s⁻¹, then the period T is calculated as T = 1/2. However, this scenario does not translate directly to finding the z-transform as z-transform deals with discrete-time signals rather than continuous ones.