how to do implement difference equation in matlab

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moonman
moonman 2011-11-14
评论： Daniel 2024-3-27
Hi i am stuck with this question
Write a MATLAB program to simulate the following difference equation 8y[n] - 2y[n-1] - y[n-2] = x[n] + x[n-1] for an input, x[n] = 2n u[n] and initial conditions: y[-1] = 0 and y[0] = 1
(a) Find values of x[n], the input signal and y[n], the output signal and plot these signals over the range, -1 = n = 10.
The book has told to user filter command or filtic
my code is down kindly guide me about initial conditions
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Fangjun Jiang
Fangjun Jiang 2011-11-15
编辑：Walter Roberson 2021-3-5
My advice:
2. Use proper punctuation mark, e.g. comma, period, question mark.
3. Read your own question again after posting, e.g. what is x[n] = 2n u[n]?
4. Update your question with comments, not answers.

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回答（3 个）

Honglei Chen
Honglei Chen 2011-11-14
I think your b is incorrect, it should be [1 1] instead. To accommodate for the initial value of y and x, you need to translate them into the corresponding filter state. filter command is an implementation of direct form II transpose, so you can use filtic to convert y and x to the state.
Here is an example, where n runs from 1 to 10. Based on you example, x[0] is 1.
n = 1:10;
a = [8 -2 -1];
b = [1 1];
yi = [1 0];
xi = 1;
zi = filtic(b,a,yi,xi)
y = filter(b,a,2.^n,zi)
BTW, I doubt if the input is really 2.^n as this becomes unbounded very quickly. Are you sure it's not 2.^(-n)?
HTH
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Divya K M
Divya K M 2020-5-9
移动：DGM 2023-2-26
output of difference equation should be discrete but the output waveform is coming continuous
Aditya Kumar Singh
Aditya Kumar Singh 2020-11-17
移动：DGM 2023-2-26
use stem instead of plot... you should get the correct waveform after that

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Mohazam Awan
Mohazam Awan 2017-10-10
%%DSP LAb Task 4
% Difference equation implementation in matlab
%
clc
clear all
close all
% using filter function
n=-5:1:10;
index=find(n==0);
x=zeros(1,length(n));
x(index)=1;
subplot(2,2,1)
stem(n,x)
grid on
axis tight
b=[1 0];
a=[1 -2];
y=filter(b,a,x);
subplot(2,2,2)
stem(n,y,'filled','r')
grid on
axis tight
% Now without filter function
y1=zeros(1,length(n));
for i=1:length(n)
if(n(i)<0)
y1(i)=0;
end
if (n(i)>=0)
y1(i)=2*y1(i-1)+x(i);
end
end
subplot(2,2,3)
stem(n,y1,'filled','k')
grid on
axis tight
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Divya K M
Divya K M 2020-5-9

Is this code for given question if so means can I explain

Daniel
Daniel 2024-3-27
Why do you use negative samples in the n vector? I am trying to use only positve samples and it doesnt work

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Fangjun Jiang
Fangjun Jiang 2011-11-14
It might be a filter. But I thought all the assignment was asking you to do is to write a for-loop to generate the y series data based on the equation and the initial conditions.
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moonman
moonman 2011-11-14
移动：DGM 2023-2-26
no book has told to use filter is my code correct?? How to cater for initial conditions y[-1]=0 and y[0]=1

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