Abstract
In this chapter we briefly outline some well-known facts about Discrete-time periodic signals, their transforms and periodic digital filters and filter banks. For details we refer to the classical textbook A. V. Oppenheim and R. W. Schafer (Discrete-Time Signal Processing, Prentice Hall, New York, 2010, [3]) and Volume I of our book (Averbuch, Neittaanmäki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Periodic Splines, vol. 1 (Springer, Berlin, 2014)) [1] Throughout the volume, unless other indicated, \(N=2^{j}, \;j\in \mathbb {N}\).
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References
A.Z. Averbuch, P. Neittaanmäki, V.A. Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Periodic Splines, vol. 1 (Springer, Berlin, 2014)
J.W. Cooley, J.W. Tukey, An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19(90), 297–301 (1965)
A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing, 3rd edn. (Prentice Hall, New York, 2010)
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Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2019). Introduction: Periodic Signals and Filters. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-92123-5_1
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DOI: https://doi.org/10.1007/978-3-319-92123-5_1
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