sum of a series

Hi,

Can someone please help me to write the following code using a summation

for i = 1:1000
v(i) =y(i) - a0- a1*y(i-1)-a2*y(i-2);
end

Thanks.

Answer 1

[Azzi Abdelmalek]

a0=1;
a1=2;
a2=1;
y=rand(1,1000) % your data
coeff=[-a2 -a1 1];
for ii = 3:1000
  v(ii) =sum(y(ii-2:ii).* coeff)-a0;
end

Answer 2

[Youssef Khmou]

hi, what is Y[nT]? random variable?

N=1000;
a0=2.36;
a1=4.56;
a2=5.57;
y=randn(N,1);
v=zeros(N,1);
v(1:2)=y(1:2); % Optional, take is as initial condition 

 % Using Loops
 for n=3:N
          v(n)=y(n)-a0-(a1*y(n-1))-(a2*y(n-2));
 end
 figure, plot(y), hold on, plot(v,'r'), hold off

 % Vectorization
 Y1=zeros(size(y));
 Y1(2:end)=y(1:end-1);

 Y2=zeros(size(y));
 Y2(3:end)=y(1:end-2);

 V=y-a0-a1*Y1-a2*Y2;

 % Comparaison

 figure, plot(v), hold , plot(V,'r'), hold off

[dav]

thank for your reply. However, I need to write this using "sum( .. ) " in matlab. and I call y(i), y(i-1).... from a data set.

[Youssef Khmou]

sorry, i was completing the code....look at the second part..... it is translation of the loop you posted

[dav]

I am sorry, may be my question wasn't clear...

my ys could grow like

v(i) =y(i) - a0- a1*y(i-1)-a2*y(i-2)-a3*y(i-3)-...-ap*y(i-p)

so I need to write it like when you use a summation notation in math.

Thanks

[dav]

I figured it out. Thanks for your time.

[Youssef Khmou]

ok