The acquisition time of a real life signal limits the resolution of its spectrum, because it directly affects the orthogonality of its spectrum components. There is no spectral analysis yet to distinguish frequencies that are not orthogonal. A spectral analysis for distinguishing non orthogonal frequencies is proposed here. A system of linear equations is solved for the sampled points, producing a result equivalent to FFT of a longer acquisition time. There is an extra requirement for such an algorithm: to cover frequencies up to a value a couple of times higher than the maximum frequency of the signal. The simulations show it is possible to distinguish between non orthogonal frequencies. The spectral analysis consists of only a matrix multiplication, once it is computed, but building that matrix requires a high computational cost. Beside spectral analysis, the proposed approach can be used for extrapolation.