Spectrum interpolation method, spectrum interpolation apparatus, and spectrum interpolation program storage medium

摘要

A spectrum interpolation method obtains a spectrum value at an arbitrary frequency by interpolating discrete spectra obtained through sampling one period of a periodic function at N sampling points to perform a Fourier transform. The spectrum value F_P(omega) at the arbitrary frequency f=omega/2pi is obtained in accordance with the following formula or any of formulae equivalent to the following formula $\begin{array}{cc}\left[\mathrm{Formula}1\right]& \\ F_p\left(\mathrm{omega}\right)=\sum _{k=0}^{N-1}F_p\left({\mathrm{omega}}_0+k.\mathrm{Delta}\mathrm{omega}\right).\mathrm{Psi}\left(\mathrm{omega}-\left({\mathrm{omega}}_0+k.\mathrm{Delta}\mathrm{omega}\right)\right)& \end{array}$ where $\begin{array}{cc}\left[\mathrm{Formula}2\right]& \\ \mathrm{Psi}\left(\mathrm{omega}\right)=\frac{1}{N}.\exp \left(-j\frac{\left(N-1\right)\mathrm{pi}.\mathrm{omega}}{N\mathrm{Delta}\mathrm{omega}}\right).\frac{\sin \left(\frac{\mathrm{pi}.\mathrm{omega}}{\mathrm{Delta}\mathrm{omega}}\right)}{\sin \left(\frac{\mathrm{pi}.\mathrm{omega}}{N.\mathrm{Deltaomega}}\right)}& \end{array}$ (where omega is an angular frequency of interest, F_P(omega) is the spectrum value at the angular frequency omega, Deltaomega is the distance between discrete spectra, omegao is an arbitrary reference angular frequency, including omegao=0, and Psi(omega) is an interpolation function).