Sampling and recovery formula in finite HANKEL transform based on the minimum‐norm principle
Kiyomichi Araki · Electronics and Communications in Japan (Part I Communications) · 1986
Abstract It is known that the sampling theorem applies to the waveform after band‐limited transformation. It frequently happens as in the case of the far visual field of an image where only a finite number of sampling points are available, in the waveform after Hankel transform, for which the spectrum is limited to a finite region. Yen introduced a restoration formula based on the minimum‐norm principle for the finite Fourier transform waveform to restore the original waveform from such a finite number of sampled points. The method was discussed in detail by Kishi and Sakaniwa. This paper applies the idea of Hankel transform and presents several theorems indicating that the interpolation ability of the formula is better than that of the past formula by Dini's expansion. The effectiveness of the method is demonstrated by a numerical example. The proposed restoration formula requires a little more complex numerical calculation but the realized interpolation accuracy is far better both in waveform and in norm.