The filter is the sum of the last 3 signal samples. The signal is a pulse set of three ones. The signal arrives 1 sample at a time. Notice the coefficients of the multiplied polynomials are equal to the signal output values at times 0 through 4. If Read more…
Topological Network Theory References Graph Theory and Its Engineering Applications By Wai-Kai Chen Books by Sundaram Seshu ( google search: inauthor:"Sundaram Seshu" ) Linear Graphs and Network Theory PDF – Sundaram Seshu Linear Graphs and Network Theory DjVu – Sundaram Seshu Linear Network Analysis – Seshu; Norman Balabanian Topological Read more…
What is most interesting about the following geometric proof is that it uses a shearing transform. This transform exploits the fact that a parallelogram of equal height and length has equal area. This gives it a fluid pouring aspect. Alot of different proofs of Pythagorean theorem.
The 2 dimensional determinant of a matrix can be interpreted as the area of a parallelogram as shown in the following diagram. This carries on through higher dimensions. Below depicts a 3 variable system. The rows r1, r2, r3 are vectors each. The various summations taken 1, 2 and 3 Read more…
I found another math rendering plugin refered to here: http://www.illigal.uiuc.edu/web/kumara/2007/04/10/latex-math-plugin-for-wordpress/ It is based on LaTeX. Note To Self: Kumara Sastry appears to be an interesting an talented person. He studies in the area of genetic algorithms. An idea I have is to study talented people and make a blog and the Read more…
13=1 13+23=9 = 32 13+23+33=36 = 62 13+23+33+43=100 = 102 13+23+33+43+53=225 = 152 …. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16…. These are triangular numbers are in bold: 1+2 =3 1+2+3=6 1+2+3+4=10 ( n(n+1)/2 )2= n2(n+1)2/4 A question I have in my mind is that Fermat’s last theorem states: If an integer n is greater than Read more…
Research Links The Maximum Entropy Principle – The distribution with the maximum entropy is the distribution nature chooses Maximum Entropy Distribution for Random Variable of Extent [0,Infinity] and a Mean Value Mu Quantum Harmonic Oscillator: Wavefunctions Hermite polynomials In many physical systems the question arises what is the probability Read more…
How to display mathcad files in a webpage. Export MathCad document as HTML
The beautiful equation tying pi, 1, 0, e and i all together. You have to love that. I am using wpmathpub. The wpmathpub math publisher plugin for WordPress.org blogs is now available directly from WordPress.org’s plugin site. The WordPress.org hosted version manages several promotional and support features: Overview of the Read more…
In a previous article entropy was defined as the expected number of bits in a binary number required to enumerate all the outcomes. This was expressed as follows: entropy= H(x)= In physics ( nature ) it is found that the probability distribution that represents a physical process is the Read more…