System Identification Using Discrete Wavelet Transforms
Edward N. Bachelder · 2002
A technique for extracting the impulse response characteristics of a linear, time-varying system has been developed and evaluated. It is shown that the discrete wavelet transform (DWT) can be used in conjunction with state-space methods to estimate the impulse response function of a system over short intervals of time. The order of the system is assumed, an estimate of the free response is subtracted from the observed total response, and the residual forced response is used in the convolution integral to compute the impulse response using wavelet analysis. The Fourier transform of the impulse response is computed to produce a bode plot of the observed system. A least-squares fit of the model to the observed bode plot (by iterating on the model poles and zeros) is performed using a non-linear regression method. Results are presented for a simulation that was conducted using a sum-of-sines input forcing function on a second-order linear system whose poles were changed over time.