Calculation of the frequency-shifted signal parameter based on the polynomial phase model

In this paper, a polynomial model was used to describe the phase of a frequency-shifted signal and the harmonic wavelet. The sine function was applied to the signal as a window function. The coefficient of the modified harmonic wavelet transform was used as a target function. We use the anneal-simulation arithmetic in finding the global maximum value of the target function. Then the parameter of the signal, including the initial phase and different orders of the phase changing rate, such as the frequency, the first order of the frequency-changing rate, and higher order of the frequency-changing rate, can be calculated. Even when noise exists, the main parts of the changing-rate of the signal phase can be got precisely. Applying this method on short signal, we can expect much better resolution than ordinary arithmetic based on FFT.