Use of smoothing in class 1 frequency domain estimation matrix filters

It is observed that the performance of the frequency-domain Wiener estimation filters relies heavily on the type of smoothing algorithm and the characteristics of the signal. Thus, the designer or engineer must carefully select the optimum system regarding the implementation domain, smoothing algorithm, and computation complexity. Simulations showed that a frequency-domain Wiener estimation filter using diagonal smoothing perfectly estimates a narrowband signal. On the other hand, circulant smoothing is proved to be superior when estimating wideband signals. Both Toeplitz and circulant smoothing perform well for time-limited signals, thus necessitating a tradeoff between vector sparseness and MSE. It was found that diagonal smoothing yields the most computationally efficient structure. Therefore, advantage must be taken of this fact; for example, if the Fourier transformation is used, filters performing well under frequency-domain circulant smoothing can be replaced with time-domain filters using diagonal smoothing techniques