Extraction of nonstationary sinusoids

A novel method of extraction of nonstationary sinusoids and estimation of their parameters is presented. The proposed algorithm has a nonlinear structure which renders it fully adaptive in tracking time-variations in the parameters of the targeted sinusoid including its phase and frequency. Mathematical properties of the differential equations governing the proposed algorithm are presented and the performance of the proposed algorithm is demonstrated with the aid of computer simulations. The proposed algorithm has been digitally implemented on a digital signal processor (DSP) platform and the laboratory verification of its performance is presented. Superiority of the proposed algorithm over conventional Fourier analysis and linear adaptive methods is demonstrated by its successful application to a number of real problems. Elimination of sinusoidal disturbances under time-varying conditions is a challenging problem of current research. The proposed algorithm is entployed to construct an adaptive notch filter for the rejection of quasi-periodic interferences. Its performance is exemplified by its application to the problem of elimination of power line noise potentially present on electrocardiogram and telephone cables. Application of the proposed algorithm in the estimation of low-level biomedical signals polluted by noise constitutes another example of its superior performance over conventional methods. Refinement and analysis of ultrasonic waves used in non-destructive testing (NDT) of materials is presented as another useful application of the proposed algorithm. Finally, estimation of instantaneous frequency in noise, exemplified by Doppler frequency shift estimation, is demonstrated. The proposed algorithm exhibits a high degree of immunity with regard to both external noise and internal parameter settings while offering structural simplicity crucial for real-time applications.