Simulation principles - P2prod/Filter-Modeling-Simulation GitHub Wiki

A filter is characterised by its response to a stimulus injected at its input. The most common input signals in time domain are:

  • step,
  • pulse.

Sometimes, we have:

  • ramp
  • exponential
  • periodic signals (such as sine, cosine, square, sawtooth, etc.) without or with decay.

As the two most commonly used are the step and the pulse, all modelling/simulation software comes with these ‘ready-to-use’ functions as standard, either natively or in an additional module or package in the case of Python.

I personally use echelon and implusion in this blog.

Among the software used for the examples, there are two families:

There are others that I won't go into here.

Some softwares ar capable to solve equations or systems of equation symbolically.

Some software packages are capable of solving equations or systems of equations symbolically. Its is the case of MATLAB (with Syms module), PYTHON (with SymPy package), MAPLE (natively) MATHEMATICA (natively), MATHCAD (natively). With these software packages, it is possible to process filters of order 2 or higher directly, whereas with the others it is necessary to convert a filter of order 2, for example, into a system of two equations of order 1. The symbolic results may differ when the filters processed are very complicated. I must emphasise that PYTHON with SymPy does very well. I'll give a few complex examples to illustrate this.

In conclusion, it is worth highlighting the remarkable versatility of MATHEMATICA, which makes use of highly sophisticated signal processing functions that, in some cases, can be considered to surpass those of MATLAB. The distinction between the two approaches (MATHEMATICA and MATLAB) lies in the use of specific functions for signal processing. In conclusion, it appears that one of the notable features of MATHEMATICA is its ability to produce a single file containing both the source code and the results, including graphical representations. Unlike MATLAB, which generates curves in independent files, MATHEMATICA offers an integrated approach to data analysis and visualisation.