Non-Maximally Decimated Analysis/Synthesis Filter Banks: Applications in Wideband Digital Filtering

We present a new class of highly effective and low complexity digital filters for processing very wideband signals. Digital filtering for wideband signals is often limited by the number of arithmetic operations that has to be performed per input sampling interval. We will show the new architecture permits filtering to be performed on partitioned spectral segments of the input signal at significantly reduced sample rate. The digital filtering will be shown to include various tasks such as linear/non-linear phase finite impulse response (FIR) filtering, fractional delay filter among others. The proposed technique utilizes the framework of non-maximally decimated filter banks (NMDFBs) with perfect reconstruction (PR) property, which makes the filter bank design simpler and more flexible. Compact representation for the generalized DFT based NMDFBs as well as its efficient polyphase implementation will be provided. The digital filtering is made possible by incorporating the desired intermediate processing elements in between the analysis and synthesis filter banks. We will show this embedded intermediate processing elements can achieve spectral shaping/signal manipulation task, which is a generalization of the concept of manipulating a digital filter in the frequency domain. We also analyze both analytically and experimentally, the spectral shaping accuracy based on different design strategies.