Signal waveform reconstruction from noisy bispectrum estimations pre-processed by vector filters

Abstract

The reconstruction of I-D signal waveform from noisy bispectrum estimations in case of a limited ensemble realization number and low input SNRS leads to considerable output errors. In order to improve the signal bispectrum estimations we propose to smooth the obtained bispect" estimations. The methods based on vector filter application to 2-D complex valued hispectrum processing are considered in this paper. The influence of input SNR, the filter type and the used norm selection on signal reconstruction system performance is analyzed using computer simulations. It is shown that the proposed methods can decrease both fluctuation error and bias ofreconstmcted signal.

Performance Study of Adaptive Filtering in Bispectrum Signal Reconstruction

“…One way to improve the reconstructed signal estimate is to process the magnitude and phase estimates, respectively given by (3) and (4), by 1D filters [20] or to smoothB( p, q) by 2D filters [11], [21]. These methods have been called combined bispectrum filtering.…”

“…Although, most papers on bispectrum analysis consider the high-SNR case [6], [18], the results presented in [11], [20], [21] have demonstrated that the bispectrum methods can be effectively used in the low-SNR case also.…”

“…One of the recently proposed approaches to solve this problem for data corrupted with heavy noise is the combined bispectrum filtering developed in [11], [20], [21], including the filtering of a two-dimensional (2D) bispectrum using scalar [21] and vector [11] filters, and filtering of one-dimensional (1D) phase and magnitude Fourier spectra recovered from the bispectrum [20]. Despite promising results that have been demonstrated in [11], [20], [21], some important questions have not been studied yet.…”

“…Despite promising results that have been demonstrated in [11], [20], [21], some important questions have not been studied yet.…”

“…This study is the first topic of this paper, and is described in Section 2. The several well-known non-adaptive filtering techniques studied in [11], [20], [21] are considered in Section 3. However, as is the case in many different applications of digital filtering [1], the problem of a proper filter choice arises.…”