FREQUENCY ESTIMATE BASED ON WAVELET TRANSFORM AND FOURIER TRANSFORM

In this paper, we will investigate the consistency of a frequency estimate of real-valued signal with varying amplitude. The wavelet based estimation procedure has already been investigated by Shibata and Takagiwa (1997) for the case of complex-valued signals. Whether the signal is complex-valued or real-valued does not seem to make any significant difference, but in fact it does. We will propose a new wavelet based estimation procedure which is different from the procedure previously proposed for complex-valued signals. The sampling scheme employed in this paper is that of a dense observation on a fixed time interval or on the neighborhood of a specified time point. We will demonstrate that our estimation procedure is consistent under the smoothness condition of the amplitude, but that the conventional Fourier based estimation procedure is rarely consistent.