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The majority of the existing work on designing nonuniform filter banks (NUFBs) cannot achieve linear-phase (LP) property, because of the high complexity associated with phase distribution. This correspondence proposes an idea of partial cosine modulation to obtain the LP property of NUFBs with rational sampling factors. It makes the efficient modulation technique possible to be used to design LP NUFBs. Except the separately designed lowpass and highpass analysis/synthesis filters, we obtain the bandpass by cosine modulation of several prototypes, worth of the name ?partial cosine modulation.? By analyzing the phase issue of significant aliasing terms, we derive the matching conditions to make the required LP NUFB achievable. With these criteria being satisfied, the design problem becomes that of several prototypes as well as the lowpass and highpass filters, leading to a less design effort. By using the proposed method, near-perfect-reconstruction LP NUFBs can be obtained in a simple and efficient way as demonstrated by examples.

This correspondence proposes a novel method for designing directional filter banks (DFBs) with arbitrary number of subbands. Its key feature is the ability to decompose images into arbitrary directionally oriented subbands. The proposed approach is based on the pseudo-polar Fourier transform (PPFT) and one-dimensional (1-D) filter banks (FBs). We take some modifications on the PPFT and then employ 1-D FBs to the modified PPFT. With these operations, the two-dimensional (2-D) DFBs are obtained and the design of them is converted to that of 1-D FBs plus a modified PPFT. Since the number of channels of 1-D FBs can be arbitrary, the 2-D DFBs with arbitrary number of subbands can be achieved which is highly expected for directional representations of images. Two examples on directional feature extractions illustrate that the proposed non-2n channel DFBs can capture directional information more flexibly than the existing methods.

This correspondence proposes a novel method for designing a class of recombination nonuniform filter banks (RNFBs) with the linear-phase (LP) property. In the structure of the proposed nonuniform filter bank (FB), certain channels of an M-channel uniform FB are merged by synthesis filters of transmultiplexers (TMUXs), yielding nonuniform subbands. By a detailed analysis of the frequency characteristics of the RNFBs, we derive the existence and matching conditions that are necessary for constructing the proposed RNFBs having good frequency responses. With those conditions being satisfied, the design problem becomes that of a set of LP uniform FBs. By using the Parks-McClellan algorithm, we are able to design the near-perfect-reconstruction LP RNFBs in a very simple and efficient way as demonstrated by two examples