I see when I increase number of samples, the imaginary error part of the FFT growth due to the error of sin(n*pi)!=0 where n is the index of the sample in Matlab or octave. Is there anyway to force Matlab/Octave to perform FFT without these type of errors? for example I know if you have sin (sym(pi)*n) =0 in Matlab or octave. Why default FFT in matlab/octave does not use sym(pi) instead of pi?
How could I perform FFT that take care of such PI approximation error? Thanks