# Is it possible exctract sinusoids from non periodic signal?

Digital signal UT1-UTC is not periodic but is including many sinusoids (periodic elements in IERS nomenclature) that are not multiples of some fundamental. For example tidal sinusoids are not multiples of yearly seasonal sinusoid because lunar month is not submultiple of the year. Then, is it possible these sinusoids be extracted from UT1-UTC by Discrete Fourier Transform?

• My question is related to UTC (or leap second) problem, 13 years long debate between USA and UK. Root of problem is just the noise (random element or irregularities) in UT1-UTC digital signal. – George Theodosiou Feb 2 '16 at 12:41
• For get it (noise in UT1-UTC signal) one should detect every sinusoid and remove them by moving average as long I understand. – George Theodosiou Feb 2 '16 at 12:49

DFT is always finitely long. So yes, that's what it does: deconstruct a finite sequence of $N$ samples into a representation based on the orthogonal $N$ sinusoidals. That works for every sample vector $\in \mathbb C^N$, the DFT mathematically just being a multiplication with a Matrix $\in \mathbb C^{N\times N}$, and being bijective.