Precise interpolation for band‐limited digital signals based on sampling theorem incorporated with window functions

Abstract

AbstractThis paper proposes an interpolation method called the “window function method” in which the sampling theorem and the window functions are combined. The cause of the generation of the interpolation error is the folding distortion due to the multiplication of the time‐limited window to the input signal. The conditions to enable precise interpolation are that the functions are continuous, the windows with large spectral decays in the side lobes are normalized such that the window function values are unity at the interpolation points, and the main lobe width is set to an optimum. When the interpolation precision is compared with those by other interpolation methods, the present one is about the same as that in the “filter method” (the conventional method using the filter to eliminate the unwanted image components) but is somewhat poorer than that in the “least RMS error method” (theoretical limit) if Kaiser–Bessel windows are used. However, the number of input signal data to obtain the same interpolation precision is larger only by 10%. Hence, the operating time to obtain the required interpolation precision is close to optimum. The calculation of the coefficients needed for interpolation is basically a simple substitution and can avoid a design of higher‐order filters (in the filter method) and solution of the ill‐conditioned simulation equations (in the least RMS error method). © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 63–77, 2001