Errors of Constant Rotation Angle Fast Orthogonal Transforms Used for Fixed-Point Arithmetic DSP Applications: Preliminary Results

Abstract

A brief description of the constant rotation angle fast orthogonal transform (CRAFOT) is presented. The main goal of the present work is the investigation of the errors of CRAFOT algorithm caused by the quantization and the size of operands (the input signal vector and the transform matrix). The obtained results show significant error oscillations that depend on the rotation angle. The paper presents the upper limit of the normalized to the quantization step the maximal mean-squared error (MSE) of restoration of signal (after the subsequent direct and inverse transform). The restoration error is approximately constant depending on the wordlength of CRAFOT operands and practically linear (in the logarithmic scale) versus the size of operands. Ill. 5, bibl. 8 (in English, summaries in Lithuanian, English, Russian).