How to fsum on only one variable?

Hi, I want to find the following Z(i)s but inside the sum is only for j. How can I write following script with sum on only j? Sorry if my question is very basic stuff

for i=1:n
for j=1:m
Z(i)=Z(i)-sum(S(j).*Z(i-j))
end
end

Answer 1

[Fred]

 H=filter([1,-S],0 , Z);

Answer 2

[Image Analyst]

I have no idea what you're trying to do. First of all, Z(1) will depend on Z(1) which hasn't been defined yet so that will bomb. Next, i-j will equal zero when both i and j are 1, so that will bomb also. Beyond that I have no idea whatsoever what you're trying to do. And what is S?

[Fred]

Sorry for confusion; I have two vectors Z and S (Z is my data and S are coefficients from another formula) and I want to adjust Z values by some type of differencing. So old Z values are replaced by new ones (I used the same name as Z but I can use a new name too like Z2). about i-j I think that I should think of a condition It is some think like this:

      Z(i)=Z(i)-0.3*Z(i-1)-0.105*Z(i-2)-0.059*Z(i-3)-...
or

    Z2(i)=Z(i)-0.3*Z(i-1)-0.105*Z(i-2)-0.059*Z(i-3)-...

where S=[0.3 0.105 0.059 ...]