MATLAB: How i creat a code abaout fft without using fft comand

fft comand fft help edit

when i write "help fft" i get this formula

         X(k) =       sum  x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N

how to write this formula in matlab comand and get the result of this. where i have a variable fs = formula sampling, and x = data in time domain?

i need your help thankyou

What exactly is the problem? What have you tried so far?

for n = 1:N
  X_k = sum(x(n) * exp(-2j * pi * (k-1) * (n-1)/N);
end

I think that is covered in just about any textbook. The DFT is computationally intensive to implement as a matrix-vector multiplication.

The NxN DFT matrix times a Nx1 signal vector involves N^2 multiplications and N additions.

By exploiting certain symmetries the fft() reduces that significantly.

If you just read the wikipedia page, you'll find references:

Then you just do

 t = 0:0.001:1-0.001;
 I = cos(2*pi*100*t);
 Q = sin(2*pi*100*t);
 sig1 = I+1j*Q;
 dftsig1 = fft(sig1);

Do the same for I2 and Q2, etc.