Non-linear Down-sampling and Signal Reconstruction, without Folding

Abstract

This paper presents a theory of 1.5 factor nonlinear down-sampling, reconstruction and noise elimination. For linear down sampling of two or three factor, one sample is taken and next one or two samples are not taken/discarded. Here in non-linear down sampling two or three samples are taken and the next one is not taken. The purpose of this nonlinear down sampling is to send less data samples in voice communication. Though one sample is discarded after taking two samples value of this sample can be reconstructed from values of other samples. Here, two samples are at original sampling period, T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> interval and next two samples are at 2T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> interval. High-frequency sharp changes were extracted when sampled at T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> interval. From received signal, discarded sample can be reconstructed from nearby four samples (Previous two and next two). When original signal contains higher frequency some error signal is introduced, after reconstruction. This error signal depends on original signal. Error signal is eliminated using original signal. Down-sampling is performed after sampling and signal reconstruction is performed just before hearing the sound.