Question

Write, as a series, the z-transform of the number sequence generated by sampling the time function e(t) = every seconds. beginning at t = 0. Can you express this transform in closed form?

Answer 1

The z-transform of a sequence generated by sampling the time function e(t) = e^t every second, starting at t = 0, can be expressed as a series. However, it cannot be expressed in closed form as it is an infinite series.

Step-by-step explanation:

The z-transform of a sequence generated by sampling the time function e(t) = e^t every second, starting at t = 0, can be expressed as a series. The z-transform converts a discrete-time signal into a continuous complex variable function. In this case, the z-transform would be:

Z(e(t)) = e^t + e^(-s) + e^(-2s) + ... = Σ(e^(-s))^n, where n goes from 0 to infinity and s is the complex variable.

Unfortunately, the z-transform of this sequence cannot be expressed in closed form because it is an infinite series.