Digital Signal Processing (D.S.P.)

These programs realise the Least Mean Square (LMS) algorithm for the creation of an “Adaptive Filter”. The algorithm was invented in 1960 by Stanford University professor Bernard Widrow and his then Ph.D. student, Ted Hoff. Is considered to be a classic algorithm for addressing the problem. Here, two autonomous programs are presented. The first program apply the algorithm on a Sine-wave contaminated by noise, while the second program apply the algorithm on a Square-wave under the same conditions.

This program creates an “AM Modulated” signal with the frequency of the Carrier set at 100Hz and the frequency of the signal itself at 5Hz. The program is capable of displaying screenshots presenting details of the signal such as the “Carrier”, the “Signal” and the AM modulated signal in the Frequency Domain (the “Signal Spectrum”).

This collection of programs gives some examples on how to create "Digital Filters". All programs use the MATLAB function to create a "Filter" according to some appropriate parameters. The very last program in the collection (“Mirror Filter”) provides the necessary code to create a type of "Filters" which is not as well known in comparison with the others. This type of "Filters" is called "Mirror Filters" and has many applications, especially in the Telecommunications field. The mathematical expression of creating each of the "Filters" is given as part of each code.

The program generates a Sinusoidal Signal. In the program all the parameters are treated completely parametrically, in order for a greater understand of the creation mechanism to be achieved, and for the creation mechanism to be easier to modify.

These programs realise the Recursive Least Squares (RLS) algorithm for the creation of an “Adaptive Filter”. The algorithm first created by Plackett in 1950 (RLS was discovered by Carl Friedrich Gauss but lay unused or ignored until 1950 when Plackett rediscovered the original work of Gauss from 1821) and is considered to be a classic algorithm for addressing the problem. Here, two autonomous programs are presented. The first program apply the algorithm on a Sine-wave contaminated by noise, while the second program apply the algorithm on a Square-wave under the same conditions.

The program creates an IIR BAND STOP filter. The filter characteristics (Power Frequencies, Magnitude, and capacity in db) are given in the first two screenshots the program produces. The program is also capable of providing the “Ideal Filter” curve, which, unfortunately, is never mathematically feasible.

The program implements an FM modulated signal. By varying the values of some of the parameters in the mathematical equation generating the FM modulated signal, one can observe how these parameters affect the FM Frequency Band the most widespread dispersion of information through wireless communications. Useful conclusions can be drawn, also, if someone compares the FM modulated signal directly with the AM modulated signal.