Difference equation Definition and 89 Threads

I wish to solve a non constant coefficents difference equation $(x+1)y_{x+1}-(r+x)y_{x}+ry_{x-1}=0$ where r is a constant. Is there a characteristic equation and generic solution for this ?

http://dl.dropbox.com/u/33103477/Nicotine.png N_{t+1} = N_t - \frac{1.02}{100}N_t + 0.02 OR N_{t+1} = N_t - \frac{1}{100}N_t + 0.02 The first equation considers counts the amount the body absorbs everyday to include the amount ingested that day, the other doesn't. The answers are...

I've been told that to calculate the difference equation of an LTI system, you simply take the sample values of the impulse response as the coefficients of the x[n-k] terms in the difference equation. i.e. if h[n] = {1, 0.5, 0.25, 0.125} for n>=0, then y[n] = x[n]...

Dear friends of MHB in this thread some aspects of the difference equation of degree greater than one are investigated. For size limitation the tutorial is divided into several sections. As for the part I, suggestions, observations, requests of clarification and improvements are welcome...

Homework Statement Solve the difference equation: an+2 - 5an+1 + 6an = 4n Subject to a0 = 0 & a1 = 1 Homework Equations an = Arn The Attempt at a Solution I got two solutions for the first part for when it is homogeneous by substituting an = Arn into the equation and solving for...

Dear friends of MHB some months ago I wrote for MHF a tutorial on the Difference equations and the reason of that was the difficulties I noticed in the treatment of difference equations, an important chapter of Discrete Maths that [may be...] is a little unfairly undervaluated. Request by the...

Homework Statement Solve the difference equation Homework Equations y[n+2]-3y[n+1]+2y[n]==4n*2^n, n>=0 y0=0,y1=1 The Attempt at a Solution 1. Homogenous solution: Characteristic equation => r^2-3r+2==0 <=> r1=1,r2=2 => yhn = C1*1^n+C2*2^n 2. Particular solution: ypn = ? I...

Hello. I have been given a transfer function for a digital system, and I need to find the difference equation for that system. I have attached a pdf with my work. I would be grateful if someone could take a look at it, and see if I am along the right lines. Thanks in advance, and happy...

Homework Statement Solve the first order difference equation. Homework Equations x[n] - x[n-1] = n(n+1)/2 x[1] = 1 The Attempt at a Solution Homogenous solution: Characteristic equation: r - 1 = 0 <=> r = 1 => yhn = C * 1^n = C Particular solution: ypn = ? I'm supposed to...

Homework Statement y[n] - (2/3)y[n-1] = x[n] what is y[n] if x[n] = diracdelta[n] The Attempt at a Solution for some reason, i argued that y[n-1] = diracdelta[n-1] so y[n] = diracdelta[n] + (2/3)diracdelta[n-1] Im pretty sure this is wrong, anybody can help?

Homework Statement Find the particular solution. y(k+2) + y(k+1) -6y(k) = 3^(k) Homework Equations The Attempt at a Solution Still need to be answered Question (1): Before finding the particular solution, is it true that we should ALWAYS get the homogeneous solution...

Homework Statement Verify that the response of the system governed by the 1st order different equation y(k)=bu(k)+ay(k-1) is given by this solution y(k)=\frac{b}{1+a}\left [ (-1)^{k}+a^{k+1} \right ] for u(k) = (-1)^k The Attempt at a Solution The solution said we can verify this...

I designed four different transfer function to differentiate and accumulate a given function. In my example, the given function is sin() between [0, 6*PI]. Dashed blue line: The original input function (i.e.; sin(t)) Red line: Integration of sin(t) with initial value of -1.0. (H(s) = 1/s)...

This is a bit of a shot in the dark, but has anybody ever encountered a theory which can tell me what the solution of this equation: A_n = nA_{n-2} + nA_{n-3} behaves like, as n\to\infty? For convenience, you can set A_n = 1 for n = 0, \ldots, 3. Without the term on the right, it goes...

At+1=(At+r)/(At+r+1) A1=constant I know I can set At+1=At=A and solve for a special solution. What would be a general solution? I am not taking a course in Difference Equation, and this is not my homework but I encounter a similar question and I reduce it to this form. Thanks

How do you solve the system z(t+1)=Az(t)+b where A is a 2x2 matrix and z(t+1), z(t), b are 2x1 matricies? I solved the homogeneous solution: z(t)=P(D^t)(P^-1)z(0) where D is the diagonal matrix of eigenvalues of A and P is the matrix of eigenvectors. I tried to solve the nonhomogeneous...

Homework Statement In analogy with differential equations, the difference equation x_{k}=x_{k-1}+x_{k-2} has two solutions x_{k}=\beta^{k} for some \beta\neq0. Determine the two possible values of \beta. Homework Equations x_{k}=x_{k-1}+x_{k-2} x_{k}=\beta^{k} \beta\neq0 The...

Hi, Im trying to go back and relearn material from a signals class I took to prepare for my controls class. In the controls class we always deal with CT systems, whereas in the systems class we focused on DT. My prof derived a frequency response that was H(w) = 1/(1-a*exp(i*w)). This...

This question is for a DSP class. I hope that I am posting somewhere appropriate. So given the impulse response: h[n]=((0.5)^n-(0.25)^n)u[n] find y[n]. Where do I start? I don't need an answer, just a nudge in the right direction.

I want to find q501 for the difference equation: qn=qn-1 - 0.001 q2n-2 n≥2, q0=1, q1=2 I thought it's easier to do this on Matlab & I tried to write a script file for this problem: k=0.001 q(1)=1 q(2)=2 for n=1:502 q_n=q_n-1-k*(q_n-2)^2 end I don't know why my code...

While working on another problem, the following difference equation came up. s_{n}=\frac{1}{r_{1}-r_{1}^{n}}}\sum_{k=1}^{n-1}s_{k}B_{n,k}\left( r_{1},r_{2},...,r_{n-k+1}\right) The B_{n,k} are (nonlinear) polynomials in the variables r_{1}, ..., r_{n,k-n+1} that don't involve the s's...

Homework Statement Given difference equation T(a+2)-7T(a+1) +6T(a)= 6f Find the general solution of this equation Homework Equations I have found the auxiliary equation be A(1)^n+B(6)^n But seems can't find the particular solution of that question. Is it impossible to do this...

http://e.imagehost.org/0218/question.jpg I think I've managed to create the finite difference equation in part a), but I'm not sure how to turn this into a matrix equation. Any advice would be appreciated!

In the following link: http://electron6.phys.utk.edu/QM1/modules/m2/square_potentials.htm what does the difference equation mean, and how is it gotten from the previous step?

Homework Statement This is a question about one single step of a solution of a long equation. http://www.geocities.com/link_herooftime/math.jpg where P, U and V are variables. a, b, c, d are constants and t is the time, which are measured in discrete periods. The question is how...

Homework Statement Find a closed-form expression for c_n. c_{n+1} = \frac{c_0 (3c_n + c_0)}{2c_n + c_0} Homework Equations The Attempt at a Solution Besides finding c_1, c_2, c_3, \ldots and looking for a pattern, I have absolutely no idea.

This is some math from "Discrete-Time Signal Processing" by Oppenheim: We have the homogeneous difference equation: \sum_{k=0}^N a_k y_h [n-k] = 0 "The sequence y_h[n] is in fact a member of a family of solutions of the form: y_h[n] = \sum_{m=1}^ N A_m z^n_m " So what is Oppenheim...

please help me to implement this difference equation in MATLAB? y[n]=x[n]-x[n-1]; matlab is not supportin -ve index...

I have been having a difficult time understanding how to determine the input/output difference equations of a circuit. I believe I am good on series circuits but would like some feedback on Series/parallel determinations. Please look at included file and see if I am on the correct path.

Let be the equation: A(2n)-A(2n-1)=3 i,m a bit stuck..i don,t know how to solve it :frown: :frown: it it weren't for the 3 term i would try A(n)=r^n where r is an unknown number..however the 3 factor spoils all..also we could try the identity...

This is not quite a homework question, but I hope close enough that it can be posted here. I'm going through a signal processing book on my free time, doing all the problems and so on, and I've come across a problem which I'm not too sure about how to solve. Here it is-- Consider the...

I am currently struggling to solve Difference equations (especially the first order ones). Here is a 'simple' one which I cannot get the correct answer to despite trying many times. Here is what I think is my most decent attempt. 2y_{n + 1} = y_n + 2 Rearranging gives y_{n + 1} =...

Hi, I've been working on a difference equation and I just can't get the answer. Can someone checking my working? w_{n + 1} = 2w_n + 1 w_1 = 2w_0 + 1 w_2 = 2w_1 + 1 = 2(2w_0 + 1) + 1 = 2^2w_0 + 1 + 2^1 \Rightarrow w_n = 2^n w_0 + \sum\limits_{i = 0}^{n - 1} {2^i } = 2^n w_0 +...

Ok, I am not sure if this is the right section, but seeing that difference equations are the discrete version... Now the question is : Into how many regions do n simple ovals divide the plane, given that every oval meets every other oval in two points and no point in the plane is common to...

I'm posting this under analysis because of the method I'm thinking about using to solve it. Here is the equation: \varepsilon \left( x\right) =e^{\varepsilon \left( x-1\right) } and the initial condition is \varepsilon \left( 0\right) =1. My main goal is to consider x as a number in...

I'm attempting to solve a difference equation y(k+1) = -0.5*y(k) + x(k) where y(0) = 0 and x(k) is in my case a unit step function ie = 1 well, I'm trying to solve this using a for loop, but am having some trouble. The code I've generated gets an error, "Index into matrix is negative or...

I was never taught how to do this I was just given problems with no solutions so I don't know what to do can someone please help me I have two questions which are similar maybe if I get help with one I can solve the other one on my own. It says simplify the following \cos(\pi+x) + \cos...

an+1=2an where n is a natural number and a0 is some fixed real number. (in case it's not clear, what's on the right hand side is 2 to the an power.) thanks! i'm wondering if it will be possible to let n=1/2 and have the half iterate to 2^x i was looking for earlier, where by that i mean a...

Hi i posted here before and got great help, and I ran into another problem maybe you can help me this is the question. Two loud speakers are placed on a wall 2.00 m apart. A listener stands 3.00m from the wall direclty infront of one of the speakers. A single ocillator is driving the speakers...