Abstract
This chapter is focused on methods of signal re-sampling. Such task occurs very frequently in systems working with signals acquired with many sampling rates, for example, in acoustical digital mixers or digital multi-rate telecommunication transceivers (during frequency up/down conversion). We learn about signal up-sampling (interpolation) and down-sampling (decimation). Designing special low-pass filters for digital interpolators (sample expanders) and decimators (sample reducers) is discussed. For high-order re-sampling usage of one long interpolation/decimation filter is not optimal: in this case a cascade of shorter filters is preferred, what is presented. Finally, fast polyphase filter structures for signal up/down-sampling are introduced. They omit filter weights multiplications by signal samples equal to zero during signal interpolation and calculation of samples to be removed during signal decimation. The chapter ends with explanation of Farrow filter technique of Lagrange signal interpolation and with description of dyadic wavelet filter banks (discrete wavelet transform).
Who would not like to have a perfect micro-macro-scope for seeing a single electron and the whole solar system? This is an introduction to our dream of multi-resolution signal processing.
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Zieliński, T.P. (2021). FIR Filters in Signal Interpolation, Re-sampling, and Multi-Rate Processing. In: Starting Digital Signal Processing in Telecommunication Engineering. Textbooks in Telecommunication Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-49256-4_10
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DOI: https://doi.org/10.1007/978-3-030-49256-4_10
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