Bridged micromechanical filters

The M channel maximally decimated filter bank shown in Fig. 1.1 has been studied extensively, (see references in [l]). When the system in Fig. 1.1 is alias free, it is an LTI system with transfer function T ( z) , as indicated in Fig. 1.1. T ( z) will be called the overall response. A maximally decimated filter bank is well-known for its application in subband coding. Another application of maximally decimated filter banks is in block filtering, [a]. Convolution through block filtering has the advantages that parallelism is increased and data is processed at a lower rate. However, the computational complexity is comparable to that in direct convolution. In [3], filter banks are used to map long convolutions into smaller ones in the subbands. Computations are then performed in parallel at a lower rate. More recently 641, another type of filter bank convolver has been developed. In this scheme the convolution is performed in the subbands and for a fixed rate the re-sult of convolution is more accurate than direct convolu-tion. This type of filter bank convolver also enjoys the advantages of block filtering, parallelism and lower work-ing rate. Nevertheless, like block filtering, there is no computational saving. In this paper, we introduce the new under-decimated system. A filter bank is said to be under-decimated if the number of channels is more than the decimation ratio in the subbands. Two types of low-complexity filter banks can be used for the new system, the DFT filter bank and cosine modulated filter bank [5]. Fig. 1.2 shows the setup of the under-decimated sys-tem; it has 2M channels but is decimated only by M. In both DFT filter bank case and cosine modulated fil-ter bank case, the system is approximately alias free and overall response is equivalent to a tunable multilevel fil-ter. Properties of the DFT filter banks and the cosine modulated filter banks can be exploited to simultane-ously achieve parallelism, computational saving and lower working rate. Furthermore, in both filter banks the im-plementation cost of the analysis bank is comparable t