December 2019 – Fundamentals of Linear Control: A Concise Approach

Z-transform and rational functions as a database for sequences

The Z-transform is essentially a clever database that can store and operate on the values of a discrete-time signal. The inverse Z-transform can be used to query the database.

Sampling. Part III

In previous posts we have explored sampling of continuous-time signals and introduced the Z-transform as a tool to work with discrete-time signals. In this post we address the other end of the process, that is the reconstruction of a signal from its samples.

Discrete-time systems and the Z-transform. Part I

The Z-transform does to discrete-time signals and systems what the Laplace transform does to a continuous-time signals and systems.

Sampling. Part II

In an earlier post we discussed how to obtain the continuous-time Laplace and Fourier transforms of a sampled signal based on the Laplace and Fourier transforms of the original signal. We shall now explore other relationships between those transforms and the Z-transform of the sampled signal.

Sampling. Part I

Modern control systems are typically implemented in computers that work with periodic samples of signals, that is discrete-time signals, rather than continuous-time signals. A system that produces samples of a given signal is a linear system, albeit a time-varying one. In this post, which starts a series exploring the issue of sampling and discretization, we delve into the nature of a system that can produce such signal samples. More will follow.