Nonlinear Digital Filtering

In digital signal processing for separation of convolved signals the complex cepstrum appear to be an excellent tool. The complex cepstrum has been efficiently used to transform linear-phase FIR-filters into minimum-phase FIR-filters. Using the complex cepstrum for this transformation introduces two problems:
1. The final filter has double zeros inside the unit circle.
2. The final filter is only an approximation due to aliasing errors.
In this project a procedure is developed which avoid the double zeros inside the unit circle. A second goal is investigating the effect of aliasing in the complex cepstrum and development of a
procedure which minimize the problem.
In higher order statistics the complex cepstrum (bicepstrum and tricepstrum)
is widely used for design of equalizers. Like in the conventional complex cepstrum the problem is the transformation to the the bi- and tricepstrum which can not be done without introducing errors. It is investigated how this transformation error can be minimized.