I can´t get the matrix dimension right

I am doing a work where it asks me to use the variables zred(matrix 82x1) and d18red(82x1) on a frequencie f 1:0.2:20. for each value of f, i have to calculate the value of t truth this equation

t=(1./(4*f*pi))*atan(sum(sin(4*ti*f*pi))/(sum(cos(4*pi*f*ti)));

and ti with i=1,...,m. i think i have to make a matrix that includes zred and d180red (82x2) to solve the equation above after calculating the t i have to calculate p(f) with this equation

 p=(((sum(d18ored*sin(2*pi*f*(ti-t)))).^2)/(sum(d18red*sin(2*pi*f*(ti-t)).^2)))+((sum(d18red*cos(2*pi*f*(ti-t)))).^2)/(sum(d18red*cos(2*pi*f*(ti-t).^2)));

my problem is in this last equation because it gives me a error saying inner matrix dimensions must agree.

Answer 1

[Ced]

That's a typical matlab error. In your case, you are asking for a matrix multiplication (, /) where in fact you want an element-wise multiplication (., ./). See here in case you are not familiar with these operations: Array vs. Matrix Multiplication

Two examples from your equation:

t and f are 1x96 row vectors
d18red is a 82x1 column vector

so

f*(ti-t)

does not make sense, because you are trying to make a matrix multiplication between two vectors with dimensions (96x1).

e.g.

d18ored*sin(2*pi*f.*(ti-t))

This (note that I changed * to .*) would therefore be a (82x1) vector times a (1x96) vector, which would give you a (82x96) matrix.

etc. etc.