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

http://www.FreedomUniversity.TV. 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. References can be found at the above website or specfically at my blog http://www.FreedomUniversity.TV/blog.

Category:

Education

Tags:

• z transform
• z transforms
• signal processing
• rational functions
• polynomial functions

[Alrekrify]

@silvermica There's an open window from a program called Camtasia.

[westwolf28]

Thank youuu!!!

[ItsaStringThing]

Very clear and easy to understand.. thanks

[29riteshkakkar]

Nice explanation...

[guitarfreak52903]

Microsoft Sam?

[silvermica]

Thanks for the informative video! Say, I'd like to know what software you're using to generate these videos.  Thanks!

[zxr250chris]

Thankyou. This was nice and easy to understand.

[vijaysuri]

thank you so much it sums up a lot....

[2snb]

nice

[chiquitoyou]

whare about ( 3a^2 b) (-5a^2 b^2)