Abstract
In this chapter we investigate a big family of Fourier transforms: continuous Fourier transform (CFT), Fourier series (FS), discrete-time Fourier transform (DtFT), and discrete Fourier transform (DFT). The DFT, in its fast form (FFT), is probably one of the most frequently used orthogonal transforms in the world apart from the discrete cosine transform (DCT). We learn that DtFT originates from continuous Fourier transform, while DFT from Fourier series. We become familiar with transform features and understand their strong and weak points. We learn the fundamentals of frequency analysis of discrete-time signals by DtFT and DFT. We see the significance of special signal shaping functions called windows in spectral analysis of signals.
Always there are many runners but typically the winner is the same: DFT in the form of FFT!
This is a preview of subscription content, log in via an institution to check access.
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
L.F. Chaparro, Signals and Systems Using Matlab (Academic Press, Burlington MA, 2011)
F.J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978)
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)
A.V. Oppenheim, A.S. Willsky, S.H. Nawab, Signals & Systems (Prentice Hall, Upper Saddle River, 1997, 2006)
A. Papoulis, Signal Analysis (McGraw Hill, New York, 1977)
J.G. Proakis, D.G. Manolakis, Digital Signal Processing. Principles, Algorithms, and Applications (Macmillan, New York, 1992; Pearson, Upper Saddle River, 2006)
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/
M. Vetterli, J. Kovacevic, V.K. Goyal, Foundations of Signal Processing (Cambridge University Press, Cambridge, 2014)
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). Discrete Fourier Transforms: DtFT and DFT. In: Starting Digital Signal Processing in Telecommunication Engineering. Textbooks in Telecommunication Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-49256-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-49256-4_4
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)