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Polyphase FIR Networks Based on Frequency Sampling for Multirate DSP Applications

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Abstract

It is well known that the frequency sampling approach to the design of Finite Impulse Response digital filters allows recursive implementations which are computationally efficient when most of the frequency samples are integers, powers of 2 or null. The design and implementation of decimation (or interpolation) filters using this approach is studied herein. Firstly, a procedure is described which optimizes the tradeoff between the stopband energy and the deviation of the passband from the ideal filter. The search space is limited to a small number of samples (in the transition band), imposing the condition that the resulting filter have a large number of zeros in the stopband. Secondly, three different structures to implement the decimation (or interpolation) filter are proposed. The implementation complexity, i.e., the number of multiplications and additions per input sample, are derived for each structure. The results show that, without taking into account finite word-length effects, the most efficient implementation depends on the filter length to decimation (or interpolation) ratio.

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Authors and Affiliations

  1. Department of Teoría de la Señal y Comunicaciones, Escuela Politécnica Superior de la Universidad de Alcalá, 28871, Alcalá de Henares, (Madrid), Spain

    Fernando Cruz-Roldán

  2. Department of Ingeniería de Circuitos y Sistemas, Escuela Universitaria de Ingeniería Técnica de Telecomunicación, Universidad Politécnica de Madrid, 28031, Madrid, Spain

    José David Osés del Campo & Juan Ignacio Godino-Llorente

  3. Department of Electrónica, Escuela Politécnica Superior de la Universidad de Alcalá, 28871, Alcalá de Henares, (Madrid), Spain

    Luciano Boquete-Vázquez

  4. School of Computer Science and Informatics, University College Dublin, Belfield, Dublin 4, Ireland

    C. J. Bleakley

Authors
  1. Fernando Cruz-Roldán
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  2. José David Osés del Campo
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  3. Juan Ignacio Godino-Llorente
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  4. Luciano Boquete-Vázquez
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  5. C. J. Bleakley
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Corresponding author

Correspondence to Fernando Cruz-Roldán.

Additional information

This work was partially supported by the Spanish Ministry of Education and Science under grant PR2007-0218, and by Comunidad Autónoma de Madrid and Universidad de Alcalá through projects CCG07-UAH/TIC-1740, CCG08-UAH/TIC-3941, and CCG08-UAH/TIC-4054.

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Cruz-Roldán, F., Osés del Campo, J.D., Godino-Llorente, J.I. et al. Polyphase FIR Networks Based on Frequency Sampling for Multirate DSP Applications. Circuits Syst Signal Process 29, 169–181 (2010). https://doi.org/10.1007/s00034-009-9140-5

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  • DOI: https://doi.org/10.1007/s00034-009-9140-5

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