Engineering Signal Analysis: From Fourier to filtering: Theory

Authors

Christian Tiberius
Department of Geoscience and Remote Sensing, Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands
https://orcid.org/0000-0002-2771-2978
Max Mulder
Department of Control and Operations, Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands
https://orcid.org/0000-0002-0932-3979

Keywords:

Fourier Series, Fourier transform, sampling, discrete Fourier transform, spectral estimation, linear systems, filtering

Synopsis

Engineering Signal Analysis - Theory, is an introductory textbook on the analysis of signals in time and frequency.  It takes an engineer’s perspective and discusses how to characterize, analyze and operate on signals. The basic theoretical concepts, Fourier series and transform, are explained in continuous time. It then introduces discrete-time signals, addressing how sampling and finite signal duration affect spectral analysis. It discusses the discrete Fourier transform and its use in spectral estimation. The book concludes with an introduction to linear systems and signal filtering.

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Author Biographies

Christian Tiberius, Department of Geoscience and Remote Sensing, Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands

Christian Tiberius is Associate Professor in the field of navigation and has over 20 years of experience in teaching the subject of signal analysis in the domains of applied earth science and civil engineering.

Max Mulder, Department of Control and Operations, Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands

Max Mulder is Full Professor Aerospace Human-Machine Systems and has over 30 years of experience in teaching signal analysis, systems, and control theory, mostly in the aerospace domain.

References

[1] Wikimedia Commons, (n.d.), media file repository, for public domain and freely licensed educational media content.

[2] T. Bořil, Fourier series 3d - interactive demonstration, (2016), website.

[3] J. G. Proakis and D. K. Manolakis, Digital signal processing, 4th ed. (Pearson Education Limited, 2014).

[4] M. T. Heideman, D. H. Johnson, and C. S. Burrus, Gauss and the history of the fast Fourier transform, Archive for History of Exact Sciences 34, 265 (1985).

[5] M. B. Priestley, Spectral analysis and time series (Academic Press, 1981).

[6] M. R. Spiegel, S. Lipschutz, and J. Liu, Mathematical handbook of formulas and tables, 3rd ed. (McGraw-Hill, 2009).

[7] R. E. Ziemer, W. H. Tranter, and D. R. Fannin, Signals and systems – continuous and discrete, 4th ed. (Prentice Hall, 1998).

[8] A. V. Oppenheim, A. S. Willsky, and I. T. Young, Signals and systems, 1st ed. (Prentice Hall International Editions, 1983).

[9] A. Papoulis, The Fourier integral and its applications, 2nd ed. (McGraw-Hill, 1962).

[10] J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation 19, 297 (1965).

[11] G. D. Bergland, A guided tour of the fast Fourier transform, IEEE Spectrum 6, 41 (1969).

[12] L. W. Couch, Digital and analog communication systems, seventh ed. (Pearson Prentice Hall, 2007).

[13] A. Papoulis, Probability, random variables, and stochastic processes, 2nd ed. (McGraw-Hill, 1984).

[14] A. Schuster, On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena, Terrestrial Magnetism 3, 13 (1898).

[15] P. Welch, The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms, IEEE Transactions on Audio and Electroacoustics 15, 70 (1967).

[16] M. Bartlett, Smoothing periodograms from time-series with continuous spectra, Nature 161, 686 (1948).

[17] J. S. Bendat and A. G. Piersol, Random data analysis and measurement procedures, 4th ed. (Wiley, 2010).

Cover image "Engineering Signal Analysis"

Published

February 5, 2026

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Details about the available publication format: View PDF

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ISBN-13 (15)

978-94-6518-235-3

Publication date (01)

2026-02-05

Details about the available publication format: Order hard copy

Order hard copy

ISBN-13 (15)

978-94-6384-901-2

How to Cite

Tiberius, C., & Mulder, M. (2026). Engineering Signal Analysis: From Fourier to filtering: Theory. TU Delft OPEN Books. https://doi.org/10.59490/mt.247