Dealing with linearly variable magnitudes in fourier and wavelet packet transform frameworks

摘要

The paper deals with the analysis using Wavelet Packet Transform (WPT) and Fast Fourier Transform (FFT) of synthetically generated signals. The signals are initially sine waves of 10 periods with linearly decreasing/increasing magnitude M. M varies according to a constant slope G. The studied absolute difference between the final and initial values of M belongs to the set {2,5, 5, 7.5 and 10}% from the initial M. Harmonics whose magnitudes (HM) are proportional to M are also generated. Three RMS parameters (fundamental, distorting and total, symbolized by PQI) are calculated for two sampling rates (197 and 1576 samples per period). Firstly brief information about the algorithms and generated signals are given. Afterward details on the techniques used for the evaluation of PQI are provided. Results of the PQI evaluation for the generated signals by using both FFT and WPT are presented focusing on the maximum absolute values of percent relative errors (MAVPRE). Low levels of MAVPRE were obtained, proving that both FFT and WPT provide reliable results when applied in a proper manner. None of the methods can be declared superior to the other considering MAVPRE. Usually higher errors are yielded when M falls as compared to a raising M.