Contents
What is the difference between Fourier transform and Z transform?
Fourier transforms are for converting/representing a time-varying function in the frequency domain. Z-transforms are very similar to laplace but are discrete time-interval conversions, closer for digital implementations. They all appear the same because the methods used to convert are very similar.
What is s domain used for?
S domain is used for solving the time domain differential equations easily by applying the Laplace for the differential equations.
Why do we use S domain?
It is a mathematical domain where, instead of viewing processes in the time domain modeled with time-based functions, they are viewed as equations in the frequency domain. It is used as a graphical analysis tool in engineering and physics.
Why do we need the Z transform?
The z-transform is an important signal-processing tool for analyzing the interaction between signals and systems. A significant advantage of the z-transform over the discrete-time Fourier transform is that the z-transform exists for many signals that do not have a discrete-time Fourier transform.
When displayed in the time domain (the interactive example easily allows that by dragging both poles to the -1 location in the z-plane, which coincides with the PI/T contour line), it is shown that the continuous time signal is sampled just twice per period.
This article focuses on the relationship between the Laplace domain (s-domain) and z-domain representations of continuous-time and discrete-time transfer functions. The following two-pole continuous transfer function is used in the interactive demo above and throughout this article: The continuous-time transfer function has two poles and no zeros.
How is the z plane related to the s plane?
Your browser does not support the HTML5 canvas tag. This code calculates plots the s-plane, z-plane, and time-domain waveforms. This article focuses on the relationship between the Laplace domain (s-domain) and z-domain representations of continuous-time and discrete-time transfer functions.
What is the damping factor of the z plane?
Therefore, the damping coefficient is zero for poles located on the unit circle. Locations closer to the inner contours in the Z-plane or farther in the left-side in the Laplace-plane correspond to a higher damping factor. E.g., a version of the transfer function with natural frequency of 12.7 rad/s and damping factor of 0.1 would be: