The generation of phase noise based on wavelet transform

Phase noise presents a treatment of the problem of charactering, analyzing and measuring short-term frequency instabilities of ultrastable oscillation as well as of loop-controlled oscillation. As yet no entirely satisfactory framework has been described for such noise, wavelet bases are used to provide a construction for phase noise. In general, the most widely used model for oscillators phase noise is power law noise model. This paper first addresses the conception of phase noise and introduces several general methods to generate phase noise. Then, the theory of orthonormal wavelet expansion is presented. We develop the wavelet expansion as a Karhunen-Loeve expansion for power law noise. After that, the generation of power law noise which is based on the orthonormal wavelet expansion is introduced specifically. Finally, the simulated phase noise both in time domain and frequency domain are obtained.