Eliminating for loops in Matlab

Question

Here's a simple question. The following nested for loop creates an array of sine-wave values.

N = 2^16;
for m = 1:10;
    for i = 1:N
        sine(m,i) = sin(2*pi*i./(8*2^m));
    end
end

It seems like I should be able to create this array without the use of the for loops, but I've tried various syntaxes and always get an error message. Thanks in advance for any insights.

Answer 1

You could use bsxfun like this:

sine = sin(bsxfun(@times, 2*pi*(1:2^16), 1./(8*2.^(1:10))' ));

Answer 2

Try the following:

ii = 1:2^16;
m  = [1./(2.^(1:10))].'% transpose

prefactor = 2 * pi / 8;

sine = sin(prefactor * m * ii);

I perform a matrix multiplication A*B, in which a is a column vector size nrows, and B is a row vector size ncols, the resulting matrix will be of size nrows x ncols. Therefore m is a column vector and ii a row vector.