Nonlinear C-filters for nonstationary signals and deconvolution in impulsive noise

The combination filter or C-filter incorporates both temporal and rank-order information of the input sequence to produce its outputs. It can be used as an equalization filter to restore an original waveform which has been dispersed by a channel, in the presence of additive white Gaussian and impulsive noise. The filter coefficients can be designed by using the LMS (least mean squares) algorithm. This approach is examined and an example is given demonstrating the usefulness of the C-filter. The authors consider a technique which combines both rank-order statistics and FIR (finite impulse response) filtering schemes to deconvolve noisy channel characteristics, and to simultaneously reject the impulse noise. The problem of gain normalization at frequencies other than zero is also addressed; this arises during filtering of nonstationary signals in impulsive noise. It is concluded that the C-filter provides a useful alternative to the FIR filter for applications in inverse filtering and frequency-selective nonstationary signal restoration when the additive noise contains impulsive components and step nonstationarity in signal level