Discrete-time Fourier transform (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Discrete-time Fourier transform" in English language version.

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Oppenheim, Alan V.; Schafer, Ronald W.; Buck, John R. (1999). "4.2, 8.4". Discrete-time signal processing (2nd ed.). Upper Saddle River, N.J.: Prentice Hall. ISBN 0-13-754920-2. samples of the Fourier transform of an aperiodic sequence x[n] can be thought of as DFS coefficients of a periodic sequence obtained through summing periodic replicas of x[n].
Proakis, John G.; Manolakis, Dimitri G. (1996). Digital Signal Processing: Principles, Algorithms and Applications (3 ed.). New Jersey: Prentice-Hall International. Bibcode:1996dspp.book.....P. ISBN 9780133942897. sAcfAQAAIAAJ.
Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, NJ: Prentice-Hall, Inc. p. 59 (2.163). ISBN 978-0139141010.

armms.org

Lillington, John. "A Review of Filter Bank Techniques - RF and Digital" (PDF). armms.org. Isle of Wight, UK: Libra Design Associates Ltd. p. 11. Retrieved 2020-09-06. Fortunately, there is a much more elegant solution, as shown in Figure 20 below, known as the Polyphase or WOLA (Weight, Overlap and Add) FFT.

berkeley.edu

casper.berkeley.edu

Chennamangalam, Jayanth (2016-10-18). "The Polyphase Filter Bank Technique". CASPER Group. Retrieved 2016-10-30.

books.google.com

Rao, R. (2008). Signals and Systems. Prentice-Hall Of India Pvt. Limited. ISBN 9788120338593.

byu.edu

scholarsarchive.byu.edu

Dahl, Jason F. (2003-02-06). Time Aliasing Methods of Spectrum Estimation (Ph.D.). Brigham Young University. Retrieved 2016-10-31.

caltech.edu

authors.library.caltech.edu

Lin, Yuan-Pei; Vaidyanathan, P.P. (June 1998). "A Kaiser Window Approach for the Design of Prototype Filters of Cosine Modulated Filterbanks" (PDF). IEEE Signal Processing Letters. 5 (6): 132–134. Bibcode:1998ISPL....5..132L. doi:10.1109/97.681427. S2CID 18159105. Retrieved 2017-03-16.

doi.org

Wang, Hong; Lu, Youxin; Wang, Xuegang (16 October 2006). "Channelized Receiver with WOLA Filterbank". 2006 CIE International Conference on Radar. Shanghai, China: IEEE. pp. 1–3. doi:10.1109/ICR.2006.343463. ISBN 0-7803-9582-4. S2CID 42688070.
Lin, Yuan-Pei; Vaidyanathan, P.P. (June 1998). "A Kaiser Window Approach for the Design of Prototype Filters of Cosine Modulated Filterbanks" (PDF). IEEE Signal Processing Letters. 5 (6): 132–134. Bibcode:1998ISPL....5..132L. doi:10.1109/97.681427. S2CID 18159105. Retrieved 2017-03-16.
Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform" (PDF). Proceedings of the IEEE. 66 (1): 51–83. Bibcode:1978IEEEP..66...51H. CiteSeerX 10.1.1.649.9880. doi:10.1109/PROC.1978.10837. S2CID 426548.

embedded.com

Lyons, Richard G. (June 2008). "DSP Tricks: Building a practical spectrum analyzer". EE Times. Retrieved 2024-09-19. Note however, that it contains a link labeled weighted overlap-add structure which incorrectly goes to Overlap-add method.

harvard.edu

ui.adsabs.harvard.edu

Lin, Yuan-Pei; Vaidyanathan, P.P. (June 1998). "A Kaiser Window Approach for the Design of Prototype Filters of Cosine Modulated Filterbanks" (PDF). IEEE Signal Processing Letters. 5 (6): 132–134. Bibcode:1998ISPL....5..132L. doi:10.1109/97.681427. S2CID 18159105. Retrieved 2017-03-16.
Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform" (PDF). Proceedings of the IEEE. 66 (1): 51–83. Bibcode:1978IEEEP..66...51H. CiteSeerX 10.1.1.649.9880. doi:10.1109/PROC.1978.10837. S2CID 426548.
Proakis, John G.; Manolakis, Dimitri G. (1996). Digital Signal Processing: Principles, Algorithms and Applications (3 ed.). New Jersey: Prentice-Hall International. Bibcode:1996dspp.book.....P. ISBN 9780133942897. sAcfAQAAIAAJ.

kupdf.net

Crochiere, R.E.; Rabiner, L.R. (1983). "7.2". Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall. pp. 313–326. ISBN 0136051626.

mathworks.com

"Periodogram power spectral density estimate - MATLAB periodogram".

mit.edu

web.mit.edu

Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform" (PDF). Proceedings of the IEEE. 66 (1): 51–83. Bibcode:1978IEEEP..66...51H. CiteSeerX 10.1.1.649.9880. doi:10.1109/PROC.1978.10837. S2CID 426548.

psu.edu

citeseerx.ist.psu.edu

Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform" (PDF). Proceedings of the IEEE. 66 (1): 51–83. Bibcode:1978IEEEP..66...51H. CiteSeerX 10.1.1.649.9880. doi:10.1109/PROC.1978.10837. S2CID 426548.

semanticscholar.org

api.semanticscholar.org

Wang, Hong; Lu, Youxin; Wang, Xuegang (16 October 2006). "Channelized Receiver with WOLA Filterbank". 2006 CIE International Conference on Radar. Shanghai, China: IEEE. pp. 1–3. doi:10.1109/ICR.2006.343463. ISBN 0-7803-9582-4. S2CID 42688070.
Lillington, John (March 2003). "Comparison of Wideband Channelisation Architectures" (PDF). Dallas: International Signal Processing Conference. p. 4 (fig 7). S2CID 31525301. Archived from the original (PDF) on 2019-03-08. Retrieved 2020-09-06. The "Weight Overlap and Add" or WOLA or its subset the "Polyphase DFT", is becoming more established and is certainly very efficient where large, high quality filter banks are required.
Lin, Yuan-Pei; Vaidyanathan, P.P. (June 1998). "A Kaiser Window Approach for the Design of Prototype Filters of Cosine Modulated Filterbanks" (PDF). IEEE Signal Processing Letters. 5 (6): 132–134. Bibcode:1998ISPL....5..132L. doi:10.1109/97.681427. S2CID 18159105. Retrieved 2017-03-16.
Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform" (PDF). Proceedings of the IEEE. 66 (1): 51–83. Bibcode:1978IEEEP..66...51H. CiteSeerX 10.1.1.649.9880. doi:10.1109/PROC.1978.10837. S2CID 426548.

pdfs.semanticscholar.org

Lillington, John (March 2003). "Comparison of Wideband Channelisation Architectures" (PDF). Dallas: International Signal Processing Conference. p. 4 (fig 7). S2CID 31525301. Archived from the original (PDF) on 2019-03-08. Retrieved 2020-09-06. The "Weight Overlap and Add" or WOLA or its subset the "Polyphase DFT", is becoming more established and is certainly very efficient where large, high quality filter banks are required.

sp4comm.org

Prandoni, Paolo; Vetterli, Martin (2008). Signal Processing for Communications (PDF) (1 ed.). Boca Raton, FL: CRC Press. pp. 72, 76. ISBN 978-1-4200-7046-0. Retrieved 4 October 2020. the DFS coefficients for the periodized signal are a discrete set of values for its DTFT

uni-bonn.de

bonndoc.ulb.uni-bonn.de

Hochgürtel, Stefan (2013), "2.5", Efficient implementations of high-resolution wideband FFT-spectrometers and their application to an APEX Galactic Center line survey (PDF), Bonn: Rhenish Friedrich Wilhelms University of Bonn, pp. 26–31, retrieved 2024-09-19, To perform M-fold WOLA for an N-point DFT, M·N real input samples a_j first multiplied by a window function w_j of same size

web.archive.org

Gumas, Charles Constantine (July 1997). "Window-presum FFT achieves high-dynamic range, resolution". Personal Engineering & Instrumentation News: 58–64. Archived from the original on 2001-02-10.{{cite journal}}: CS1 maint: bot: original URL status unknown (link)
Lillington, John (March 2003). "Comparison of Wideband Channelisation Architectures" (PDF). Dallas: International Signal Processing Conference. p. 4 (fig 7). S2CID 31525301. Archived from the original (PDF) on 2019-03-08. Retrieved 2020-09-06. The "Weight Overlap and Add" or WOLA or its subset the "Polyphase DFT", is becoming more established and is certainly very efficient where large, high quality filter banks are required.