Abstract
We provide a comprehensive analysis of the time-varying modified DFT (MDFT) filter bank based on the general time-varying filter bank theories (Wang, 2005, 2006, 2008, 2009) in both the time domain and frequency domain. We give firstly the description of the time-invariant MDFT filter bank including its perfect reconstruction (PR) condition, its mechanism of aliasing error cancellation and the relationship with the cosine-modulated filter bank in detail. Then, the time-varying MDFT filter bank is analyzed according to the time-domain description. Finally, the window switching method is introduced to design the prototype filter in the time-varying MDFT filter bank with examples. The error analysis shows that the introduced design approach is useful in practice.
Highlights
Modified DFT filter banks (MDFT) and their applications are intensively studied in [1,2,3,4,5]
All analyses are done in the frequency domain for the time-invariant modified DFT filter banks
We do not find any works for the time-varying MDFT filter bank
Summary
Modified DFT filter banks (MDFT) and their applications are intensively studied in [1,2,3,4,5]. The cosine-modulated filter bank was widely studied and applied due to its perfect reconstruction property and the easy prototype window design with the closed formulation [12]. Without the closed formulation of prototype windows, it is difficult to design an applicable prototype window for a cosinemodulated filter bank to keep the perfect reconstruction property In this case the cosine-modulated filter bank can only provide an almost perfect reconstruction similar with DFT polyphase filter bank. In comparison with cosine-modulated filter banks, the DFT polyphase filter bank has advantages such as linear phase, complex-valued signal processing, and better frequency characteristics in each subband. If we can find an approach to efficiently cancel the aliasing error in the DFT polyphase filter bank, the DFT polyphase filter bank has good application possibilities in digital signal processing like speech and image processing.
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