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Spectrum continuation analysis is a generalization of the concept of Fourier series to non-periodic functions of which only a fragment has been sampled in the time domain.
Recall that a Fourier series is only suitable to the analysis of periodic functions f with period 2π. It can be expressed as an infinite series of sinusoids:
where F n {\displaystyle F_{n}} is the amplitude of the individual harmonics.
In SCA however, one decomposes the spectrum into optimized discrete frequencies. As a consequence, and as the period of the sampled function is supposed to be infinite or not yet known, each of the discrete periodic functions that compose the sampled function fragment can not be considered to be a multiple of the fundamental frequency: