Clickbank Products


April 2014
« Apr    

Clickbank Products

Overview and Introduction to the z-Transform (Polynomial & Rational Functions)

We introduce the z-transform bringing polynomials and rational functions to help analyze linear discrete-time systems. The discrete-time convolution (or FIR convolution) is equivalent to polynomial multiplication and algebraic operations in the z transform domain can be translated as combining or decomposing linear time-invariant (LTI) systems. The most common z-transforms are rational functions, that is, the numerator polynomial divided by the denominator polynomial.

We consider three representations of signals and systems. The first one, the time-domain or n-domain, involves sequences, impulse responses and differences. The next representation is the frequency or w-domain (omega-domain). Here, we consider frequency responses and spectrum descriptions. Finally and most important when analyzing discrete-time systems is the z-domain. This consist of z transforms, operators, and poles and zeros.

One application of the z-transform is the use of the discrete-time convolution mentioned earlier. Here, the operation in the z-domain or z-transform domain involves multiplication between two polynomials. We’ll see its the multiplication between the z transform of the input signal and the z-transform of the system or filter.

The above application shows the value of having three different domain representation. A difficult analysis in one domain (discrete-time convolution) is simpler to analyze in the other domain (in this case the z-transform domain involving polynomial multiplication).

Therefore, having increased understanding will result form developing skills for moving from one representation to another. The z transform domain exists primarily for its mathematical convenience in analyzing and synthesizing discrete-time signals and systems.

Several videos will be presented elaborating the importance of the z transform. Below are some references on the digital signal processing using z transforms.

Some of the links in the post above are “affiliate links.” This means if you click on the link and purchase the item, we will receive an affiliate commission. Regardless, we only recommend products or services we believe will add value to our readers.

Related posts:

  1. Laplace Transform Video Tutorial and Inverse Laplace Transform Tutorial – Part 1 Here is one of my early videos I did using...
  2. Matlab Examples: Review of Discrete Convolution Sum Using Matlab Here is a review of the discrete convolution sum including...
  3. Laplace Transform Tutorial with Examples (Constant and Ramp Functions) Here is the first of a series of videos on...
  4. Laplace Transform Examples – Part 2 Laplace Transform is one of the most important analytical tools...
  5. Convolution Sum for Discrete-Time Systems Below is an introduction to the convolution sum for discrete-time...

Leave a Reply