How to use summation in MATLAB?

Question

I have a randomly generated vector, say A of length M.

Say:

A = rand(M,1)

And I also have a function, X(k) = sin(2*pi*k).

How would I find Y(k) which is summation of A(l)*X(k-l) as l goes from 0 to M?

Assume any value of k... But the answer should be summation of all M+1 terms.

Answer 1

Given M and k, this is how you can perform your summation:

A = rand(M+1,1);            %# Create M+1 random values
Y = sin(2*pi*(k-(0:M)))*A;  %# Use a matrix multiply to perform the summation

EDIT: You could even create a function for Y that takes k and A as arguments:

Y = @(k,A) sin(2*pi*(k+1-(1:numel(A))))*A;  %# An anonymous function
result = Y(k,A);                            %# Call the function Y

Answer 2

A = rand(1, M + 1);
X = sin(2 * pi * (k - (0 : M)));
total = sum(A .* X);

Answer 3

This should almost certainly be tagged homework. But if you're trying to do a fourier transform, you should also look at fft.

Answer 4

You may be looking for the convolution of the vectors A and X:

Y = conv(A, X);