Algorithm for Identifi cation of Parameters Sinusoidal Signal with the Exponentially Damping Amplitude

Abstract

The paper proposes a new method for estimating the parameters of an unbiased sinusoidal signal with the exponentially damping amplitude: frequency, damping coefficient. A sinusoidal signal with exponentially damping amplitude is an important class that can be observed in a wide range of natural phenomena, such as the propagation of acoustic waves, and can also characterize the behavior of artificial systems, arising, for example, as a result of complex interactions between the components of power systems, therefore the task of estimating parameters is sinusoidal. signal with exponentially decaying amplitude is relevant at the present time. It is assumed that the phase, frequency, damping factor and amplitude of a sinusoidal signal with exponentially decaying amplitude are unknown functions of time. In the present work, a new method is proposed for parameterizing a sinusoidal signal with exponentially decaying amplitude. First, a sinusoidal signal with exponentially decaying amplitude is presented as the output of a linear generator, the parameters of the decaying sinusoidal signal (amplitude, phase, damping factor and frequency) are unknown. Then the Jordan form of the matrix and the delay are applied to transform the measured signal, then a linear regression model is obtained, which depends on the frequency and the attenuation coefficient. At the last stage, unknown parameters (frequency, attenuation coefficient) are calculated from the obtained linear regression model. Numerical modeling demonstrates the effectiveness of the proposed methodology.