Analysis of the quantization noise of linear time-invariant filters for image processing

Abstract

The problem of quantization of the coefficients of arbitrary linear time-invariant filters in order to minimize the noise of this phenomenon is investigated in this paper. The implementation of the method of linear time-invariant filtration is proposed, which makes it possible to reduce the bit-width of the filter coefficients and simplify the performance of rounding operations. The analysis of the effect of the bit-width of the filter coefficients on the magnitude of the quantization noise and the resulting error of the filtration method being investigated is carried out. The formulas for determining the minimum bit-width of the filter coefficients, providing high quality of image processing, are derived, depending on the filter used. It is concluded that when using these formulas, the quantization noise that occurs when the filter coefficients are rounded off does not have a significant effect on the image processing result