Reduced-rank noise reduction: A filter-bank interpretation

The key step in reduced-rank noise reduction algorithms is to approximate a matrix by another one with lower rank, typically by truncating a singular value decomposition (SVD). We give an explicit and closed-form derivation of the filter properties of the rank reduction operation and interpret this operation in the frequency domain by showing that the reduced-rank output signal is identical to that from a filter-bank whose analysis and synthesis filters are determined by the SVD. Our analysis includes the important general case in which pre-and dewhitening is used.