Decision method of expansion coefficients for finite fourier series by partial sampling values
Taizo Iijima · Electronics and Communications in Japan (Part I Communications) · 1981
Abstract According to the well‐known sampling theorem, expansion coefficients of a finite Fourier series can be determined from a properly selected finite linear sum of all sampling values which correspond to equally spaced division points in the entire interval of the period. In this paper, the sampling theorem is extended to the case where sampling points under consideration do not necessarily spread out on the entire interval. The first half of this paper considers the case where the sampling point interval is equal to an inverse of integer multiple of the period. The second half considers the more general case and general solutions for the successive extrapolation method are derived in a linear recursive form. This method enables one to calculate frequency components from the waveform which was observed successively at constant pitch.