Abstract
In recent years, in the Fourier transform, the analytical method in which the length of the window for frequency can be arbitrarily determined was proposed by authors. Here, in the case that the length of a window is in inverse proportion to frequency, this becomes the same function as elasticity of the mother wavelet of Wavelet transform. In this analytical method, by using inner product between a sine wave or a cosine wave and a signal, the signal decomposes into many components which have each frequency. Furthermore calculating spectrum and reconstructing waveform from these decomposition waves were shown. Until now, a sine wave and a cosine wave have used independently as the cutting out wave. In this paper, In order to improve the approximation accuracy of the reconstruction wave, using the cutting out wave which combined a sine wave and a cosine wave is shown. In order to express the grade of approximation of a reconstruction wave and a signal waveform quantitatively, the degree of coincidence of both waveforms is introduced. In the example of numerical analysis, by using Japanese vocal sound /sa/, it is shown that the degree of approximation of the reconstruction wave to a signal waveform improves.
