This paper presents a new decomposition for exact representation of a signal in terms of sinusoids with arbitrary frequencies. It is shown that the choice of N/2 distinct frequencies can provide a set of N linearly independent sine and cosine vectors in the N-dimensional space which in turn enable the exact decomposition of any N samples signal. A dramatic improvement of the spectral resolution is achieved which does not depend on the number of available samples. The frequencies of this decomposition are not predetermined and may be selected according to the needs of the problem. Based on this decomposition, a new algorithm is presented for measuring the frequency of a sinusoid. [References: 7]
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