Estimation of generalized transfer function.

摘要

In this research, we present a procedure to recover the generalized transfer function as defined by Priestley's evolutionary spectral analysis from the evolutionary periodogram (EP) transfer function expression. In order to accomplish this objective we employ a multiple iterative deconvolution approach to remove the blurring effects of the time and frequency kernels and obtain the desired transfer function. A step by step presentation for this approach is outlined. We analyze the conditions of convergence for this iterative technique with regard to our application. We also discuss regularization for the deconvolution algorithm including necessary constraints to obtain the desired answer.; The proposed method recovers the generalized transfer function in contrast to the time-frequency representation by deconvolving Cohen's class bilinear distribution as in Emresoy et al. approach. Our method also differs from that of Shah et al. in recovering the generalized transfer function from the evolutionary periodogram transfer function expression by first calculating the blurring kernels then applying the deconvolution algorithm rather than using the relationship between Cohen's class distribution and the generalized transfer function. In our approach, the evolutionary periodogram transfer function expression is represented as a one dimensional convolution with a frequency blurring function then the result is convolved again in time with another blurring kernel. This type of representation justifies the use of the deconvolution technique in a clear notation. Unlike the previous methods, we did not have to make any assumption or approximations to calculate the generalized transfer function.