Abstract
In this chapter some important FFT applications in DSP field are presented, mainly to spectral analysis. We learn how to exploit FFT for efficient and flexible calculations of the following DSP functions: discrete Fourier transform (DFT) and its zoomed as well as interpolated (IpDFT) version, discrete-time Fourier transform (DtFT), short-time Fourier transform function, signal correlation function and power spectral density (PSD), finally, signal convolution.
Having an F1 car or the X-Wing spacecraft it would be a big sin not to use it at full speed!
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Change history
14 January 2022
This book was inadvertently published with the incorrect copyright year.
References
F. Auger, P. Flandrin, Improving the readability of time-frequency and time-scale representations by the reassignment method. IEEE Trans. Signal Process. 43(5), 1068–1089 (1995)
F. Auger, P. Flandrin, P. Goncalves, O. Lemoine, Time-Frequency Toolbox. Online: http://tftb.nongnu.org/
S. Bagchi, S.K. Mitra, The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing (Kluwer, Boston, 1999)
J. Bendat, A. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980, 1993)
R.E. Blahut, Fast Algorithms for Digital Signal Processing (Addison-Wesley, Reading, 1985)
B. Boashash (ed.), Time-Frequency Signal Analysis and Processing. A Comprehensive Reference (Elsevier, Oxford, 2003)
C.S. Burrus, T.W. Parks, DFT/FFT and Convolution Algorithms. Theory and Implementation (Wiley, New York, 1985)
W.H. Chen, C.H. Smith, S. Fralick, A fast computational algorithm for the discrete cosine transform. IEEE Trans. Commun. 25, 1004–1009 (1977)
L. Cohen, Time-Frequency Analysis (Prentice Hall, Englewood Cliffs, 1995)
L. Cohen, P. Loughlin (eds.), Recent Developments in Time-Frequency Analysis (Kluwer, Boston, 1998)
K. Duda, T.P. Zieliński, Efficacy of the frequency and damping estimation of a real-value sinusoid. IEEE Mag. Instrum. Meas. 48–58 (2013)
D.F. Elliott, K.R. Rao, Fast Transforms. Algorithms, Analyses, Applications (Academic Press, New York, 1982)
P. Flandrin, Time-Frequency/Time-Scale Analysis (Academic Press, San Diego, 1999)
P. Flandrin, Explorations in Time-Frequency Analysis (Cambridge University Press, Cambridge, 2018)
G. Heinzel, A. Rudiger, R. Schilling, Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new flat-top windows, Technical Report, Max-Planck-Institut fur Gravitationsphysik (Albert-Einstein-Institut), Teilinstitut Hannover, 2002. Online: https://pure.mpg.de/rest/items/item_152164_1/component/file_152163/content
F. Hlawatsch, F. Auger (eds.), Time-Frequency Analysis: Concepts and Methods (Wiley, Chichester, 2008, 2013)
V.K. Ingle, J.G. Proakis, Digital Signal Processing Using Matlab (PWS Publishing, Boston, 1997; CL Engineering, 2011)
R.G. Lyons, Understanding Digital Signal Processing (Addison-Wesley Longman Publishing, Boston, 1996, 2005, 2010)
A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing (Pearson Education, Upper Saddle River, 2013)
J.G. Proakis, D.G. Manolakis, Digital Signal Processing. Principles, Algorithms, and Applications (Macmillan, New York, 1992; Pearson, Upper Saddle River, 2006)
D.S. Qian, D. Chen, Joint Time-Frequency Analysis (Prentice Hall, Upper Saddle River, 1996)
K. Shin, J.K. Hammond, Fundamentals of Signal Processing for Sound and Vibration Engineers (Wiley, Chichester, 2007)
S.W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, San Diego, 1997, 1999). Online: http://www.dspguide.com/
P. Stoica, R. Moses, Introduction to Spectral Analysis (Prentice Hall, Upper Saddle River, 1997)
P. Wigner, Quantum-mechanical distribution functions revisited, in Perspectives in Quantum Theory, ed. by W. Yowgram, A. van der Merwe (Dover, New York, 1979)
R.C. Wu, C.T. Chiang, Analysis of the exponential signal by the interpolated DFT algorithm. IEEE Trans. Instrum. Meas. 59(12), 3306–3317 (2010)
T.P. Zieliński, Cyfrowe Przetwarzanie Sygnalów. Od Teorii do Zastosowań (Digital Signal Processing. From Theory to Applications) (Wydawnictwa Komunikacji i Ł ączności (Transport and Communication Publishers), Warszawa, Poland, 2005, 2007, 2009, 2014)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zieliński, T.P. (2021). FFT Applications: Tips and Tricks. In: Starting Digital Signal Processing in Telecommunication Engineering. Textbooks in Telecommunication Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-49256-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-49256-4_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-49255-7
Online ISBN: 978-3-030-49256-4
eBook Packages: Computer ScienceComputer Science (R0)