Abstract
The frequency-response masking (FRM) technique was introduced as a means of generating linear-phase FIR filters with narrow transition band and low arithmetic complexity. This paper proposes an approach for synthesizing modulated maximally decimated FIR filter banks (FBs) utilizing the FRM technique. A new tailored class of FRM filters is introduced and used for synthesizing nonlinear-phase analysis and synthesis filters. Each of the analysis and synthesis FBs is realized with the aid of only three subfilters, one cosine-modulation block, and one sine-modulation block. The overall FB is a near-perfect reconstruction (NPR) FB which in this case means that the distortion function has a linear-phase response but small magnitude errors. Small aliasing errors are also introduced by the FB. However, by allowing these small errors (that can be made arbitrarily small), the arithmetic complexity can be reduced. Compared to conventional cosine-modulated FBs, the proposed ones lower significantly the overall arithmetic complexity at the expense of a slightly increased overall FB delay in applications requiring narrow transition bands. Compared to other proposals that also combine cosine-modulated FBs with the FRM technique, the arithmetic complexity can typically be reduced by 40% in specifications with narrow transition bands. Finally, a general design procedure is given for the proposed FBs and examples are included to illustrate their benefits.
Highlights
Decimated filter banks (FBs) find applications in numerous areas [1,2,3]
Imposing perfect reconstruction (PR) on the FB is an unnecessarily severe restriction which may lead to a higher arithmetic complexity than is required to meet the specification at hand
This paper proposes a new class of FBs with nearly perfect reconstruction
Summary
Decimated FBs (see Figure 1) find applications in numerous areas [1,2,3]. Over the past two decades, a vast number of papers on the theory and design of such FBs have been published. Compared to conventional cosine modulated FBs as well as similar approaches, the proposed ones lower the overall arithmetic complexity significantly, in applications requiring narrow transition bands. An example of such an application is frequency-band decomposition for parallel sigmadelta systems [7] (what is gained using parallelism, is lost with a wide transition band). The efficiency of this technique is exploited in the article after appropriate modifications Both cosine and sine modulations are utilized together with a modified class of FRM filters (see below), which generates efficient overall FBs. When the transition bands of the filters are narrow, the overall complexity may be high.
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