1
vote
1answer
38 views

How to find the Direct Discrete Laplace Transform of ${2n \choose n}$

Some time ago I developed a discrete version of the Laplace transform for the purpose of calculating sums and solve finite difference equations with constant coefficients. The notes below are a ...
3
votes
1answer
118 views

discretize a function using $z$-transform

I would like to discretize the following continuous function using $z$-transform: $$G(s)=\frac{s+1}{s^2+s+1}$$ The process I am using is to take the inverse Laplace transform of $\frac{G(s)}{s}$ and ...
3
votes
1answer
52 views

How do I apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$?

I want to apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$. I'm not able to do it in the standard way, because one term has $z^{-1}$ term and the other has $z$. What is the approach ...
0
votes
1answer
291 views

Solving a recurrence relation using Z transform

I'm trying to solve the following recurrence using Z transforms: For $n\in \mathbb{N}^{*}$ $T(n)=1\ for\ n< 4$ $T(n)=T(\lfloor \frac{n}{4} \rfloor)+T(\lfloor \frac{3n}{4} \rfloor)+n\ for\ n\geq ...
4
votes
0answers
7k views

Relationship Between The Z-Transform And The Laplace Transform

Below I've quoted Wikipedia's entry that relates the Z-Transform to the Laplace Transform. The part I don't understand is $z \ \stackrel{\mathrm{def}}{=}\ e^{s T}$; I thought $z$ was actually an ...
0
votes
2answers
137 views

Z-Transform Identity

I've come across an identity and would like to know if it has some sort of formal name or derivation or explanation or something! Also, I'm curious as to whether others are aware of such an identity. ...
3
votes
1answer
664 views

Discrete Laplace Tranform.

Yesterday ago I was reading how the Laplace Transform can be interpreted as the continuous analog of the discrete functional dependance of the power series $$f(x) = \sum a(n) x^n$$ This is to say, ...