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Optimization of Flexible Filter Banks Based on Fast Convolution

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Abstract

Multirate filter banks can be implemented efficiently using fast-convolution (FC) processing. The main advantage of the FC filter banks (FC-FB) compared with the conventional polyphase implementations is their increased flexibility, that is, the number of channels, their bandwidths, and the center frequencies can be independently selected. In this paper, an approach to optimize the FC-FBs is proposed. First, a subband representation of the FC-FB is derived. Then, the optimization problems are formulated with the aid of the subband model. Finally, these problems are conveniently solved with the aid of a general nonlinear optimization algorithm. Several examples are included to demonstrate the proposed overall design scheme as well as to illustrate the efficiency and the flexibility of the resulting FC-FB.

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Notes

  1. 1.

    This contribution extends the work in [21] by generalizing the optimization method for the wider class of problems and by providing detailed descriptions of the overall FC-FB design scheme.

  2. 2.

    It should be noted that, in the case of conventional single-band interpolators, the frequency shift is typically equal to zero [ Θ k =c k =0 in Eq. 4] and the rightmost-hand term can be excluded from the numerator of Eq. 18a.

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Acknowledgments

The authors acknowledge the financial support by the European Union FP7-ICT project EMPhAtiC (http://www.ict-emphatic.eu) under grant agreement no. 318362.

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Correspondence to Juha Yli-Kaakinen.

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Yli-Kaakinen, J., Renfors, M. Optimization of Flexible Filter Banks Based on Fast Convolution. J Sign Process Syst 85, 101–111 (2016). https://doi.org/10.1007/s11265-015-1004-6

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Keywords

  • Digital filters
  • Multirate signal processing
  • Optimization
  • Filter banks
  • Sampling rate conversion