VERSATILITY OF TIME-VARYING AMPLITUDE METHOD IN HARMONIC ANALYSIS OF DISCRETE DATA

This paper proposes a method that overcomes the problem of the amplitude not being zero at the starting time .when the Cosine waveform is used in Harmonic analysis. The paper employs the method of time-varying amplitude method to get a satisfactory answer to this nagging issue of the amplitude having a value different than zero when the motion has not started for discrete data. Models obtained using the time-varying amplitude method have shown to produce better results than those from the constant amplitude model when the traditional time-invariant Fourier method is employed in Fourier analysis. The method is also flexible in the sense that it can be used to convert a decaying amplitude to a growing one and vice versa and at the same time produces amplitudes that will match oscillations whose amplitudes change with time. Using the time-varying amplitude method reduced the Sum of squares of errors of the constant amplitude model by about 56% and increased the amplitude by over 91 %, and more weights are giving to the recent data like in the smoothing methods .Besides, the method has reduced the effect of spurious correlation in time series.