The discrete fourier transform :: theory, algorithms and applications /
This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Had...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large numbers of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book should be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. |
| Beschreibung: | 1 online resource (xiii, 374 pages :) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812810298 9812810293 9810245211 9789810245214 1281951803 9781281951809 |
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| 245 | 1 | 4 | |a The discrete fourier transform : |b theory, algorithms and applications / |c D. Sundararajan. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large numbers of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book should be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. | ||
| 505 | 0 | |a Ch. 1. Introduction. 1.1. The transform method. 1.2. The organization of this book -- ch. 2. The discrete sinusoid. 2.1. Signal representation. 2.2. The discrete sinusoid. 2.3. Summary and discussion -- ch. 3. The discrete Fourier transform. 3.1. The Fourier analysis and synthesis of waveforms. 3.2. The DFT and the IDFT. 3.3. DFT representation of some signals. 3.4. Direct computation of the DFT. 3.5. Advantages of sinusoidal representation of signals. 3.6. Summary -- ch. 4. Properties of the DFT. 4.1. Linearity. 4.2. Periodicity. 4.3. Circular shift of a time sequence. 4.4. Circular shift of a spectrum. 4.5. Time-reversal property. 4.6. Symmetry properties. 4.7. Transform of complex conjugates. 4.8. Circular convolution and correlation. 4.9. Sum and difference of sequences. 4.10. Padding the data with zeros. 4.11. Parseval's theorem. 4.12. Summary -- ch. 5. Fundamentals of the PM DFT algorithms. 5.1. Vector format of the DFT. 5.2. Direct computation of the DFT with vectors. 5.3. Vector format of the IDFT. 5.4. The computation of the IDFT. 5.5. Fundamentals of the PM DIT DFT algorithms. 5.6. Fundamentals of the PM DIF DFT algorithms. 5.7. The classification of the PM DFT algorithms. 5.8. Summary -- ch. 6. The u x 1 PM DFT algorithms. 6.1. The u x 1 PM DIT DFT algorithms. 6.2. The 2 x 1 PM DIT DFT algorithm. 6.3. Reordering of the input data. 6.4. Computation of a single DFT coefficient. 6.5. The u x 1 PM DIF DFT algorithms. 6.6. The 2 x 1 PM DIF DFT algorithm. 6.7. Computational complexity of the 2 x 1 PM DFT algorithms. 6.8. The 6 x 1 PM DIT DFT algorithm. 6.9. Flow chart description of the 2 x 1 PM DIT DFT algorithm. 6.10. Summary -- ch. 7. The 2 x 2 PM DFT algorithms. 7.1. The 2 x 2 PM DIT DFT algorithm. 7.2. The 2 x 2 PM DIF DFT algorithm. 7.3. Computational complexity of the 2 x 2 PM DFT algorithms. 7.4. Summary -- ch. 8. DFT algorithms for real data -- I. 8.1. The direct use of an algorithm for complex data. 8.2. Computation of the DFTs of two real data sets at a time. 8.3. Computation of the DFT of a single real data set. 8.4. Summary. | |
| 505 | 8 | |a Ch. 9. DFT algorithms for real data -- II. 9.1. The storage of data in PM RDFT and RIDFT algorithms. 9.2. The 2 x 1 PM DIT RDFT algorithm. 9.3. The 2 x 1 PM DIF RIDFT algorithm. 9.4. The 2 x 2 PM DIT RDFT algorithm. 9.5. The 2 x 2 PM DIF RIDFT algorithm. 9.6. Summary and discussion -- ch. 10. Two-dimensional discrete Fourier transform. 10.1. The 2-D DFT and IDFT. 10.2. DFT representation of some 2-D signals. 10.3. Computation of the 2-D DFT. 10.4. Properties of the 2-D DFT. 10.5. The 2-D PM DFT algorithms. 10.6. Summary -- ch. 11. Aliasing and other effects. 11.1. Aliasing effect. 11.2. Leakage effect. 11.3. Picket-fence effect. 11.4. Summary and discussion -- ch. 12. The continuous-time Fourier series. 12.1. The 1-D continuous-time Fourier series. 12.2. The 2-D continuous-time Fourier series. 12.3. Summary -- ch. 13. The continuous-time Fourier transform. 13.1. The 1-D continuous-time Fourier transform. 13.2. The 2-D continuous-time Fourier transform. 13.3. Summary -- ch. 14. Convolution and correlation. 14.1. The direct convolution. 14.2. The indirect convolution. 14.3. Overlap-save method. 14.4. Two-dimensional convolution. 14.5. Computation of correlation. 14.6. Summary -- ch. 15. Discrete cosine transform. 15.1. Orthogonality property revisited. 15.2. The 1-D discrete cosine transform. 15.3. The 2-D discrete cosine transform. 15.4. Summary -- ch. 16. Discrete Walsh-Hadamard transform. 16.1. The discrete Walsh transform. 16.2. The naturally ordered discrete Hadamard transform. 16.3. The sequency ordered discrete Hadamard transform. 16.4. Summary. | |
| 650 | 0 | |a Fourier transformations. |0 http://id.loc.gov/authorities/subjects/sh85051094 | |
| 650 | 7 | |a SCIENCE |x Physics |x Mathematical & Computational. |2 bisacsh | |
| 650 | 7 | |a Fourier transformations |2 fast | |
| 650 | 7 | |a FOURIER TRANSFORMATION. |2 nasat | |
| 650 | 7 | |a DISCRETE FUNCTIONS. |2 nasat | |
| 650 | 7 | |a FUNCTIONAL ANALYSIS. |2 nasat | |
| 650 | 7 | |a WALSH FUNCTION. |2 nasat | |
| 650 | 7 | |a DISCRETE COSINE TRANFORM. |2 nasat | |
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| author_GND | http://id.loc.gov/authorities/names/no2005104467 |
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| contents | Ch. 1. Introduction. 1.1. The transform method. 1.2. The organization of this book -- ch. 2. The discrete sinusoid. 2.1. Signal representation. 2.2. The discrete sinusoid. 2.3. Summary and discussion -- ch. 3. The discrete Fourier transform. 3.1. The Fourier analysis and synthesis of waveforms. 3.2. The DFT and the IDFT. 3.3. DFT representation of some signals. 3.4. Direct computation of the DFT. 3.5. Advantages of sinusoidal representation of signals. 3.6. Summary -- ch. 4. Properties of the DFT. 4.1. Linearity. 4.2. Periodicity. 4.3. Circular shift of a time sequence. 4.4. Circular shift of a spectrum. 4.5. Time-reversal property. 4.6. Symmetry properties. 4.7. Transform of complex conjugates. 4.8. Circular convolution and correlation. 4.9. Sum and difference of sequences. 4.10. Padding the data with zeros. 4.11. Parseval's theorem. 4.12. Summary -- ch. 5. Fundamentals of the PM DFT algorithms. 5.1. Vector format of the DFT. 5.2. Direct computation of the DFT with vectors. 5.3. Vector format of the IDFT. 5.4. The computation of the IDFT. 5.5. Fundamentals of the PM DIT DFT algorithms. 5.6. Fundamentals of the PM DIF DFT algorithms. 5.7. The classification of the PM DFT algorithms. 5.8. Summary -- ch. 6. The u x 1 PM DFT algorithms. 6.1. The u x 1 PM DIT DFT algorithms. 6.2. The 2 x 1 PM DIT DFT algorithm. 6.3. Reordering of the input data. 6.4. Computation of a single DFT coefficient. 6.5. The u x 1 PM DIF DFT algorithms. 6.6. The 2 x 1 PM DIF DFT algorithm. 6.7. Computational complexity of the 2 x 1 PM DFT algorithms. 6.8. The 6 x 1 PM DIT DFT algorithm. 6.9. Flow chart description of the 2 x 1 PM DIT DFT algorithm. 6.10. Summary -- ch. 7. The 2 x 2 PM DFT algorithms. 7.1. The 2 x 2 PM DIT DFT algorithm. 7.2. The 2 x 2 PM DIF DFT algorithm. 7.3. Computational complexity of the 2 x 2 PM DFT algorithms. 7.4. Summary -- ch. 8. DFT algorithms for real data -- I. 8.1. The direct use of an algorithm for complex data. 8.2. Computation of the DFTs of two real data sets at a time. 8.3. Computation of the DFT of a single real data set. 8.4. Summary. Ch. 9. DFT algorithms for real data -- II. 9.1. The storage of data in PM RDFT and RIDFT algorithms. 9.2. The 2 x 1 PM DIT RDFT algorithm. 9.3. The 2 x 1 PM DIF RIDFT algorithm. 9.4. The 2 x 2 PM DIT RDFT algorithm. 9.5. The 2 x 2 PM DIF RIDFT algorithm. 9.6. Summary and discussion -- ch. 10. Two-dimensional discrete Fourier transform. 10.1. The 2-D DFT and IDFT. 10.2. DFT representation of some 2-D signals. 10.3. Computation of the 2-D DFT. 10.4. Properties of the 2-D DFT. 10.5. The 2-D PM DFT algorithms. 10.6. Summary -- ch. 11. Aliasing and other effects. 11.1. Aliasing effect. 11.2. Leakage effect. 11.3. Picket-fence effect. 11.4. Summary and discussion -- ch. 12. The continuous-time Fourier series. 12.1. The 1-D continuous-time Fourier series. 12.2. The 2-D continuous-time Fourier series. 12.3. Summary -- ch. 13. The continuous-time Fourier transform. 13.1. The 1-D continuous-time Fourier transform. 13.2. The 2-D continuous-time Fourier transform. 13.3. Summary -- ch. 14. Convolution and correlation. 14.1. The direct convolution. 14.2. The indirect convolution. 14.3. Overlap-save method. 14.4. Two-dimensional convolution. 14.5. Computation of correlation. 14.6. Summary -- ch. 15. Discrete cosine transform. 15.1. Orthogonality property revisited. 15.2. The 1-D discrete cosine transform. 15.3. The 2-D discrete cosine transform. 15.4. Summary -- ch. 16. Discrete Walsh-Hadamard transform. 16.1. The discrete Walsh transform. 16.2. The naturally ordered discrete Hadamard transform. 16.3. The sequency ordered discrete Hadamard transform. 16.4. Summary. |
| ctrlnum | (OCoLC)271437141 |
| dewey-full | 530.15/5723 |
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It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large numbers of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book should be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Introduction. 1.1. The transform method. 1.2. The organization of this book -- ch. 2. The discrete sinusoid. 2.1. Signal representation. 2.2. The discrete sinusoid. 2.3. Summary and discussion -- ch. 3. The discrete Fourier transform. 3.1. The Fourier analysis and synthesis of waveforms. 3.2. The DFT and the IDFT. 3.3. DFT representation of some signals. 3.4. Direct computation of the DFT. 3.5. Advantages of sinusoidal representation of signals. 3.6. Summary -- ch. 4. Properties of the DFT. 4.1. Linearity. 4.2. Periodicity. 4.3. Circular shift of a time sequence. 4.4. Circular shift of a spectrum. 4.5. Time-reversal property. 4.6. Symmetry properties. 4.7. Transform of complex conjugates. 4.8. Circular convolution and correlation. 4.9. Sum and difference of sequences. 4.10. Padding the data with zeros. 4.11. Parseval's theorem. 4.12. Summary -- ch. 5. Fundamentals of the PM DFT algorithms. 5.1. Vector format of the DFT. 5.2. Direct computation of the DFT with vectors. 5.3. Vector format of the IDFT. 5.4. The computation of the IDFT. 5.5. Fundamentals of the PM DIT DFT algorithms. 5.6. Fundamentals of the PM DIF DFT algorithms. 5.7. The classification of the PM DFT algorithms. 5.8. Summary -- ch. 6. The u x 1 PM DFT algorithms. 6.1. The u x 1 PM DIT DFT algorithms. 6.2. The 2 x 1 PM DIT DFT algorithm. 6.3. Reordering of the input data. 6.4. Computation of a single DFT coefficient. 6.5. The u x 1 PM DIF DFT algorithms. 6.6. The 2 x 1 PM DIF DFT algorithm. 6.7. Computational complexity of the 2 x 1 PM DFT algorithms. 6.8. The 6 x 1 PM DIT DFT algorithm. 6.9. Flow chart description of the 2 x 1 PM DIT DFT algorithm. 6.10. Summary -- ch. 7. The 2 x 2 PM DFT algorithms. 7.1. The 2 x 2 PM DIT DFT algorithm. 7.2. The 2 x 2 PM DIF DFT algorithm. 7.3. Computational complexity of the 2 x 2 PM DFT algorithms. 7.4. Summary -- ch. 8. DFT algorithms for real data -- I. 8.1. The direct use of an algorithm for complex data. 8.2. Computation of the DFTs of two real data sets at a time. 8.3. Computation of the DFT of a single real data set. 8.4. Summary.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Ch. 9. DFT algorithms for real data -- II. 9.1. The storage of data in PM RDFT and RIDFT algorithms. 9.2. The 2 x 1 PM DIT RDFT algorithm. 9.3. The 2 x 1 PM DIF RIDFT algorithm. 9.4. The 2 x 2 PM DIT RDFT algorithm. 9.5. The 2 x 2 PM DIF RIDFT algorithm. 9.6. Summary and discussion -- ch. 10. Two-dimensional discrete Fourier transform. 10.1. The 2-D DFT and IDFT. 10.2. DFT representation of some 2-D signals. 10.3. Computation of the 2-D DFT. 10.4. Properties of the 2-D DFT. 10.5. The 2-D PM DFT algorithms. 10.6. Summary -- ch. 11. Aliasing and other effects. 11.1. Aliasing effect. 11.2. Leakage effect. 11.3. Picket-fence effect. 11.4. Summary and discussion -- ch. 12. The continuous-time Fourier series. 12.1. The 1-D continuous-time Fourier series. 12.2. The 2-D continuous-time Fourier series. 12.3. Summary -- ch. 13. The continuous-time Fourier transform. 13.1. The 1-D continuous-time Fourier transform. 13.2. The 2-D continuous-time Fourier transform. 13.3. Summary -- ch. 14. Convolution and correlation. 14.1. The direct convolution. 14.2. The indirect convolution. 14.3. Overlap-save method. 14.4. Two-dimensional convolution. 14.5. Computation of correlation. 14.6. Summary -- ch. 15. Discrete cosine transform. 15.1. Orthogonality property revisited. 15.2. The 1-D discrete cosine transform. 15.3. The 2-D discrete cosine transform. 15.4. Summary -- ch. 16. Discrete Walsh-Hadamard transform. 16.1. The discrete Walsh transform. 16.2. The naturally ordered discrete Hadamard transform. 16.3. The sequency ordered discrete Hadamard transform. 16.4. Summary.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Fourier transformations.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85051094</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Physics</subfield><subfield code="x">Mathematical & Computational.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fourier transformations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">FOURIER TRANSFORMATION.</subfield><subfield code="2">nasat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">DISCRETE FUNCTIONS.</subfield><subfield code="2">nasat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">FUNCTIONAL ANALYSIS.</subfield><subfield code="2">nasat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">WALSH FUNCTION.</subfield><subfield code="2">nasat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">DISCRETE COSINE TRANFORM.</subfield><subfield code="2">nasat</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">The discrete fourier transform (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFwQf9ffg6K93HTkPbXR4y</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Sundararajan, D.</subfield><subfield code="t">Discrete fourier transform.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, ©2001</subfield><subfield code="z">9810245211</subfield><subfield code="z">9789810245214</subfield><subfield code="w">(DLC) 2001275221</subfield><subfield code="w">(OCoLC)47718203</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235873</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235873</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24685537</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1681469</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255910</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235873</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">195180</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2901925</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn271437141 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:16:56Z |
| institution | BVB |
| isbn | 9789812810298 9812810293 9810245211 9789810245214 1281951803 9781281951809 |
| language | English |
| oclc_num | 271437141 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xiii, 374 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Sundararajan, D. https://id.oclc.org/worldcat/entity/E39PCjwTQH4QFMRDGhKjDvtf9C http://id.loc.gov/authorities/names/no2005104467 The discrete fourier transform : theory, algorithms and applications / D. Sundararajan. Singapore ; River Edge, NJ : World Scientific, ©2001. 1 online resource (xiii, 374 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references and index. Print version record. This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large numbers of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book should be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Ch. 1. Introduction. 1.1. The transform method. 1.2. The organization of this book -- ch. 2. The discrete sinusoid. 2.1. Signal representation. 2.2. The discrete sinusoid. 2.3. Summary and discussion -- ch. 3. The discrete Fourier transform. 3.1. The Fourier analysis and synthesis of waveforms. 3.2. The DFT and the IDFT. 3.3. DFT representation of some signals. 3.4. Direct computation of the DFT. 3.5. Advantages of sinusoidal representation of signals. 3.6. Summary -- ch. 4. Properties of the DFT. 4.1. Linearity. 4.2. Periodicity. 4.3. Circular shift of a time sequence. 4.4. Circular shift of a spectrum. 4.5. Time-reversal property. 4.6. Symmetry properties. 4.7. Transform of complex conjugates. 4.8. Circular convolution and correlation. 4.9. Sum and difference of sequences. 4.10. Padding the data with zeros. 4.11. Parseval's theorem. 4.12. Summary -- ch. 5. Fundamentals of the PM DFT algorithms. 5.1. Vector format of the DFT. 5.2. Direct computation of the DFT with vectors. 5.3. Vector format of the IDFT. 5.4. The computation of the IDFT. 5.5. Fundamentals of the PM DIT DFT algorithms. 5.6. Fundamentals of the PM DIF DFT algorithms. 5.7. The classification of the PM DFT algorithms. 5.8. Summary -- ch. 6. The u x 1 PM DFT algorithms. 6.1. The u x 1 PM DIT DFT algorithms. 6.2. The 2 x 1 PM DIT DFT algorithm. 6.3. Reordering of the input data. 6.4. Computation of a single DFT coefficient. 6.5. The u x 1 PM DIF DFT algorithms. 6.6. The 2 x 1 PM DIF DFT algorithm. 6.7. Computational complexity of the 2 x 1 PM DFT algorithms. 6.8. The 6 x 1 PM DIT DFT algorithm. 6.9. Flow chart description of the 2 x 1 PM DIT DFT algorithm. 6.10. Summary -- ch. 7. The 2 x 2 PM DFT algorithms. 7.1. The 2 x 2 PM DIT DFT algorithm. 7.2. The 2 x 2 PM DIF DFT algorithm. 7.3. Computational complexity of the 2 x 2 PM DFT algorithms. 7.4. Summary -- ch. 8. DFT algorithms for real data -- I. 8.1. The direct use of an algorithm for complex data. 8.2. Computation of the DFTs of two real data sets at a time. 8.3. Computation of the DFT of a single real data set. 8.4. Summary. Ch. 9. DFT algorithms for real data -- II. 9.1. The storage of data in PM RDFT and RIDFT algorithms. 9.2. The 2 x 1 PM DIT RDFT algorithm. 9.3. The 2 x 1 PM DIF RIDFT algorithm. 9.4. The 2 x 2 PM DIT RDFT algorithm. 9.5. The 2 x 2 PM DIF RIDFT algorithm. 9.6. Summary and discussion -- ch. 10. Two-dimensional discrete Fourier transform. 10.1. The 2-D DFT and IDFT. 10.2. DFT representation of some 2-D signals. 10.3. Computation of the 2-D DFT. 10.4. Properties of the 2-D DFT. 10.5. The 2-D PM DFT algorithms. 10.6. Summary -- ch. 11. Aliasing and other effects. 11.1. Aliasing effect. 11.2. Leakage effect. 11.3. Picket-fence effect. 11.4. Summary and discussion -- ch. 12. The continuous-time Fourier series. 12.1. The 1-D continuous-time Fourier series. 12.2. The 2-D continuous-time Fourier series. 12.3. Summary -- ch. 13. The continuous-time Fourier transform. 13.1. The 1-D continuous-time Fourier transform. 13.2. The 2-D continuous-time Fourier transform. 13.3. Summary -- ch. 14. Convolution and correlation. 14.1. The direct convolution. 14.2. The indirect convolution. 14.3. Overlap-save method. 14.4. Two-dimensional convolution. 14.5. Computation of correlation. 14.6. Summary -- ch. 15. Discrete cosine transform. 15.1. Orthogonality property revisited. 15.2. The 1-D discrete cosine transform. 15.3. The 2-D discrete cosine transform. 15.4. Summary -- ch. 16. Discrete Walsh-Hadamard transform. 16.1. The discrete Walsh transform. 16.2. The naturally ordered discrete Hadamard transform. 16.3. The sequency ordered discrete Hadamard transform. 16.4. Summary. Fourier transformations. http://id.loc.gov/authorities/subjects/sh85051094 SCIENCE Physics Mathematical & Computational. bisacsh Fourier transformations fast FOURIER TRANSFORMATION. nasat DISCRETE FUNCTIONS. nasat FUNCTIONAL ANALYSIS. nasat WALSH FUNCTION. nasat DISCRETE COSINE TRANFORM. nasat has work: The discrete fourier transform (Text) https://id.oclc.org/worldcat/entity/E39PCFwQf9ffg6K93HTkPbXR4y https://id.oclc.org/worldcat/ontology/hasWork Print version: Sundararajan, D. Discrete fourier transform. Singapore ; River Edge, NJ : World Scientific, ©2001 9810245211 9789810245214 (DLC) 2001275221 (OCoLC)47718203 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235873 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235873 Volltext |
| spellingShingle | Sundararajan, D. The discrete fourier transform : theory, algorithms and applications / Ch. 1. Introduction. 1.1. The transform method. 1.2. The organization of this book -- ch. 2. The discrete sinusoid. 2.1. Signal representation. 2.2. The discrete sinusoid. 2.3. Summary and discussion -- ch. 3. The discrete Fourier transform. 3.1. The Fourier analysis and synthesis of waveforms. 3.2. The DFT and the IDFT. 3.3. DFT representation of some signals. 3.4. Direct computation of the DFT. 3.5. Advantages of sinusoidal representation of signals. 3.6. Summary -- ch. 4. Properties of the DFT. 4.1. Linearity. 4.2. Periodicity. 4.3. Circular shift of a time sequence. 4.4. Circular shift of a spectrum. 4.5. Time-reversal property. 4.6. Symmetry properties. 4.7. Transform of complex conjugates. 4.8. Circular convolution and correlation. 4.9. Sum and difference of sequences. 4.10. Padding the data with zeros. 4.11. Parseval's theorem. 4.12. Summary -- ch. 5. Fundamentals of the PM DFT algorithms. 5.1. Vector format of the DFT. 5.2. Direct computation of the DFT with vectors. 5.3. Vector format of the IDFT. 5.4. The computation of the IDFT. 5.5. Fundamentals of the PM DIT DFT algorithms. 5.6. Fundamentals of the PM DIF DFT algorithms. 5.7. The classification of the PM DFT algorithms. 5.8. Summary -- ch. 6. The u x 1 PM DFT algorithms. 6.1. The u x 1 PM DIT DFT algorithms. 6.2. The 2 x 1 PM DIT DFT algorithm. 6.3. Reordering of the input data. 6.4. Computation of a single DFT coefficient. 6.5. The u x 1 PM DIF DFT algorithms. 6.6. The 2 x 1 PM DIF DFT algorithm. 6.7. Computational complexity of the 2 x 1 PM DFT algorithms. 6.8. The 6 x 1 PM DIT DFT algorithm. 6.9. Flow chart description of the 2 x 1 PM DIT DFT algorithm. 6.10. Summary -- ch. 7. The 2 x 2 PM DFT algorithms. 7.1. The 2 x 2 PM DIT DFT algorithm. 7.2. The 2 x 2 PM DIF DFT algorithm. 7.3. Computational complexity of the 2 x 2 PM DFT algorithms. 7.4. Summary -- ch. 8. DFT algorithms for real data -- I. 8.1. The direct use of an algorithm for complex data. 8.2. Computation of the DFTs of two real data sets at a time. 8.3. Computation of the DFT of a single real data set. 8.4. Summary. Ch. 9. DFT algorithms for real data -- II. 9.1. The storage of data in PM RDFT and RIDFT algorithms. 9.2. The 2 x 1 PM DIT RDFT algorithm. 9.3. The 2 x 1 PM DIF RIDFT algorithm. 9.4. The 2 x 2 PM DIT RDFT algorithm. 9.5. The 2 x 2 PM DIF RIDFT algorithm. 9.6. Summary and discussion -- ch. 10. Two-dimensional discrete Fourier transform. 10.1. The 2-D DFT and IDFT. 10.2. DFT representation of some 2-D signals. 10.3. Computation of the 2-D DFT. 10.4. Properties of the 2-D DFT. 10.5. The 2-D PM DFT algorithms. 10.6. Summary -- ch. 11. Aliasing and other effects. 11.1. Aliasing effect. 11.2. Leakage effect. 11.3. Picket-fence effect. 11.4. Summary and discussion -- ch. 12. The continuous-time Fourier series. 12.1. The 1-D continuous-time Fourier series. 12.2. The 2-D continuous-time Fourier series. 12.3. Summary -- ch. 13. The continuous-time Fourier transform. 13.1. The 1-D continuous-time Fourier transform. 13.2. The 2-D continuous-time Fourier transform. 13.3. Summary -- ch. 14. Convolution and correlation. 14.1. The direct convolution. 14.2. The indirect convolution. 14.3. Overlap-save method. 14.4. Two-dimensional convolution. 14.5. Computation of correlation. 14.6. Summary -- ch. 15. Discrete cosine transform. 15.1. Orthogonality property revisited. 15.2. The 1-D discrete cosine transform. 15.3. The 2-D discrete cosine transform. 15.4. Summary -- ch. 16. Discrete Walsh-Hadamard transform. 16.1. The discrete Walsh transform. 16.2. The naturally ordered discrete Hadamard transform. 16.3. The sequency ordered discrete Hadamard transform. 16.4. Summary. Fourier transformations. http://id.loc.gov/authorities/subjects/sh85051094 SCIENCE Physics Mathematical & Computational. bisacsh Fourier transformations fast FOURIER TRANSFORMATION. nasat DISCRETE FUNCTIONS. nasat FUNCTIONAL ANALYSIS. nasat WALSH FUNCTION. nasat DISCRETE COSINE TRANFORM. nasat |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85051094 |
| title | The discrete fourier transform : theory, algorithms and applications / |
| title_auth | The discrete fourier transform : theory, algorithms and applications / |
| title_exact_search | The discrete fourier transform : theory, algorithms and applications / |
| title_full | The discrete fourier transform : theory, algorithms and applications / D. Sundararajan. |
| title_fullStr | The discrete fourier transform : theory, algorithms and applications / D. Sundararajan. |
| title_full_unstemmed | The discrete fourier transform : theory, algorithms and applications / D. Sundararajan. |
| title_short | The discrete fourier transform : |
| title_sort | discrete fourier transform theory algorithms and applications |
| title_sub | theory, algorithms and applications / |
| topic | Fourier transformations. http://id.loc.gov/authorities/subjects/sh85051094 SCIENCE Physics Mathematical & Computational. bisacsh Fourier transformations fast FOURIER TRANSFORMATION. nasat DISCRETE FUNCTIONS. nasat FUNCTIONAL ANALYSIS. nasat WALSH FUNCTION. nasat DISCRETE COSINE TRANFORM. nasat |
| topic_facet | Fourier transformations. SCIENCE Physics Mathematical & Computational. Fourier transformations FOURIER TRANSFORMATION. DISCRETE FUNCTIONS. FUNCTIONAL ANALYSIS. WALSH FUNCTION. DISCRETE COSINE TRANFORM. |
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