On the performance of multirate filterbanks: Quantification of shift variance and cyclostationarity in the works of Til Aach

The paper discusses the issues of shift variance and cyclostationarity in multirate filterbanks as investigated in a series of articles by Til Aach. In its first part, the paper overviews the most important properties of multirate filterbanks such as perfect reconstruction, sampling rate conversion factors, number and type of subbands and subdivisions, orthogonality and bio-orthogonality, and frequency selectivity and preservation of polynomials. This part is intended introduce the reader to the topic and make a bridge to the properties of shift variance and cyclostationarity discussed next. Criteria for shift (in)variance and cyclostationarity as derived by Til Aach are presented and commented and conclusions about their importance are made.