Advances in sampling theory and techniques:
"This book presents the current state of the art of digital engineering, as well as recent proposals for optimal methods of signal and image non-redundant sampling and interpolation-error-free resampling. Topics include classical sampling theory, conventional sampling, the peculiarities of samp...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Bellingham, Washington, USA
SPIE Press
[2020]
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| Online-Zugang: | FHD01 TUM01 Volltext |
| Zusammenfassung: | "This book presents the current state of the art of digital engineering, as well as recent proposals for optimal methods of signal and image non-redundant sampling and interpolation-error-free resampling. Topics include classical sampling theory, conventional sampling, the peculiarities of sampling 2D signals, artifacts, compressed sensing, fast algorithms, the discrete uncertainty principle, and sharply-band-limited discrete signals and basis functions with sharply limited support. Exercises based in MATLAB supplement the text throughout"-- |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781510633841 9781523133871 |
| DOI: | 10.1117/3.2554039 |
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| 100 | 1 | |a Jaroslavskij, Leonid P. |e Verfasser |0 (DE-588)110936582 |4 aut | |
| 245 | 1 | 0 | |a Advances in sampling theory and techniques |c Leonid P. Yaroslavsky |
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| 505 | 8 | |a Preface -- 1. Introduction: 1.1. A historical perspective of sampling: from ancient mosaics to computational imaging; 1.2. Book overview -- Part I: Signal sampling: 2. Sampling theorems: 2.1. Kotelnikov-Shannon sampling theorem: sampling band-limited 1D signals; 2.2. Sampling 1D band-pass signals; 2.3. Sampling band-limited 2D signals; optimal regular sampling lattices; 2.4. Sampling real signals; signal reconstruction distortions due to spectral aliasing; 2.5. The sampling theorem in a realistic reformulation; 2.6. Image sampling with a minimal sampling rate by means of image sub-band decomposition; 2.7. The discrete sampling theorem and its generalization to continuous signals; 2.8. Exercises -- 3. Compressed sensing demystified: 3.1. Redundancy of regular image sampling and image spectra sparsity; 3.2. Compressed sensing: why and how it is possible to precisely reconstruct signals sampled with aliasing; 3.3. Compressed sensing and the problem of minimizing the signal sampling rate; 3.4. Exercise -- 4. Image sampling and reconstruction with sampling rates close to the theoretical minimum: 4.1. The ASBSR method of image sampling and reconstruction; 4.2. Experimental verification of the method; 4.3. Some practical issues; 4.4. Other possible applications of the ASBSR method of image sampling and reconstruction; 4.5. Exercises | |
| 505 | 8 | |a 5. Signal and image resampling, and building their continuous models: 5.1. Signal/image resampling as an interpolation problem; convolutional interpolators; 5.2. Discrete sinc interpolation: a gold standard for signal resampling; 5.3. Fast algorithms of discrete sinc interpolation and their applications; 5.4. Discrete sinc interpolation versus other interpolation methods: performance comparison; 5.5. Exercises -- 6. Discrete sinc interpolation in other applications and implementations: 6.1. Precise numerical differentiation and integration of sampled signals; 6.2. Local ("elastic") image resampling: sliding-window discrete sinc interpolation algorithms; 6.3. Image data resampling for image reconstruction from projections; 6.4. Exercises -- 7. The discrete uncertainty principle, sinc-lets, and other peculiar properties of sampled signals: 7.1. The discrete uncertainty principle; 7.2. Sinc-lets: Sharply-band-limited basis functions with Sharply limited support; 7.3. Exercises -- Part II: Discrete representation of signal transformations: 8. Basic principles of discrete representation of signal transformations -- 9. Discrete representation of the convolution integral: 9.1. Discrete convolution; 9.2. Point spread functions and frequency responses of digital filters; 9.3. Treatment of signal borders in digital convolution | |
| 505 | 8 | |a 10. Discrete representation of the Fourier integral transform: 10.1. 1D discrete Fourier transforms; 10.2. 2D discrete Fourier transforms; 10.3. Discrete cosine transform; 10.4. Boundary-effect-free signal convolution in the DCT domain; 10.5. DFT and discrete frequency responses of digital filters; 10.6. Exercises -- Appendix 1. Fourier series, integral fourier transform, and delta function: A1.1. 1D Fourier series; A1.2. 2D Fourier series; A1.3. 1D integral Fourier transform; A1.4. 2D integral Fourier transform; A1.5. Delta function, sinc function, and the ideal low-pass filter; A1.6. Poisson summation formula -- Appendix 2. Discrete Fourier transforms and their properties: A2.1. Invertibility of discrete Fourier transforms and the discrete sinc function; A2.2. The Parseval's relation for the DFT; A2.3. Cyclicity of the DFT; A2.4. Shift theorem; A2.5. Convolution theorem; A2.6. Symmetry properties; A2.7. SDFT spectra of sinusoidal signals; A2.8. Mutual correspondence between the indices of ShDFT spectral coefficients and signal frequencies; A2.9. DFT spectra of sparse signals and spectral zero-padding; A2.10. Invertibility of the shifted DFT and signal resampling; A2.11. DFT as a spectrum analyzer; A2.12. Quasi-continuous spectral analysis; A2.13. Signal resizing and rotation capability of the rotated scaled DFT; A2.14. Rotated and scaled DFT as digital convolution -- References -- Index | |
| 520 | |a "This book presents the current state of the art of digital engineering, as well as recent proposals for optimal methods of signal and image non-redundant sampling and interpolation-error-free resampling. Topics include classical sampling theory, conventional sampling, the peculiarities of sampling 2D signals, artifacts, compressed sensing, fast algorithms, the discrete uncertainty principle, and sharply-band-limited discrete signals and basis functions with sharply limited support. Exercises based in MATLAB supplement the text throughout"-- | ||
| 650 | 4 | |a Signal processing / Digital techniques / Mathematics | |
| 650 | 4 | |a Image processing / Digital techniques / Mathematics | |
| 650 | 4 | |a Fourier transformations | |
| 650 | 7 | |a Fourier transformations |2 fast | |
| 650 | 7 | |a Image processing / Digital techniques / Mathematics |2 fast | |
| 650 | 7 | |a Signal processing / Digital techniques / Mathematics |2 fast | |
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Datensatz im Suchindex
| _version_ | 1804181415729823744 |
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| adam_txt | |
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| author | Jaroslavskij, Leonid P. |
| author_GND | (DE-588)110936582 |
| author_facet | Jaroslavskij, Leonid P. |
| author_role | aut |
| author_sort | Jaroslavskij, Leonid P. |
| author_variant | l p j lp lpj |
| building | Verbundindex |
| bvnumber | BV046693679 |
| collection | ZDB-10-ESC ZDB-50-SPI |
| contents | Preface -- 1. Introduction: 1.1. A historical perspective of sampling: from ancient mosaics to computational imaging; 1.2. Book overview -- Part I: Signal sampling: 2. Sampling theorems: 2.1. Kotelnikov-Shannon sampling theorem: sampling band-limited 1D signals; 2.2. Sampling 1D band-pass signals; 2.3. Sampling band-limited 2D signals; optimal regular sampling lattices; 2.4. Sampling real signals; signal reconstruction distortions due to spectral aliasing; 2.5. The sampling theorem in a realistic reformulation; 2.6. Image sampling with a minimal sampling rate by means of image sub-band decomposition; 2.7. The discrete sampling theorem and its generalization to continuous signals; 2.8. Exercises -- 3. Compressed sensing demystified: 3.1. Redundancy of regular image sampling and image spectra sparsity; 3.2. Compressed sensing: why and how it is possible to precisely reconstruct signals sampled with aliasing; 3.3. Compressed sensing and the problem of minimizing the signal sampling rate; 3.4. Exercise -- 4. Image sampling and reconstruction with sampling rates close to the theoretical minimum: 4.1. The ASBSR method of image sampling and reconstruction; 4.2. Experimental verification of the method; 4.3. Some practical issues; 4.4. Other possible applications of the ASBSR method of image sampling and reconstruction; 4.5. Exercises 5. Signal and image resampling, and building their continuous models: 5.1. Signal/image resampling as an interpolation problem; convolutional interpolators; 5.2. Discrete sinc interpolation: a gold standard for signal resampling; 5.3. Fast algorithms of discrete sinc interpolation and their applications; 5.4. Discrete sinc interpolation versus other interpolation methods: performance comparison; 5.5. Exercises -- 6. Discrete sinc interpolation in other applications and implementations: 6.1. Precise numerical differentiation and integration of sampled signals; 6.2. Local ("elastic") image resampling: sliding-window discrete sinc interpolation algorithms; 6.3. Image data resampling for image reconstruction from projections; 6.4. Exercises -- 7. The discrete uncertainty principle, sinc-lets, and other peculiar properties of sampled signals: 7.1. The discrete uncertainty principle; 7.2. Sinc-lets: Sharply-band-limited basis functions with Sharply limited support; 7.3. Exercises -- Part II: Discrete representation of signal transformations: 8. Basic principles of discrete representation of signal transformations -- 9. Discrete representation of the convolution integral: 9.1. Discrete convolution; 9.2. Point spread functions and frequency responses of digital filters; 9.3. Treatment of signal borders in digital convolution 10. Discrete representation of the Fourier integral transform: 10.1. 1D discrete Fourier transforms; 10.2. 2D discrete Fourier transforms; 10.3. Discrete cosine transform; 10.4. Boundary-effect-free signal convolution in the DCT domain; 10.5. DFT and discrete frequency responses of digital filters; 10.6. Exercises -- Appendix 1. Fourier series, integral fourier transform, and delta function: A1.1. 1D Fourier series; A1.2. 2D Fourier series; A1.3. 1D integral Fourier transform; A1.4. 2D integral Fourier transform; A1.5. Delta function, sinc function, and the ideal low-pass filter; A1.6. Poisson summation formula -- Appendix 2. Discrete Fourier transforms and their properties: A2.1. Invertibility of discrete Fourier transforms and the discrete sinc function; A2.2. The Parseval's relation for the DFT; A2.3. Cyclicity of the DFT; A2.4. Shift theorem; A2.5. Convolution theorem; A2.6. Symmetry properties; A2.7. SDFT spectra of sinusoidal signals; A2.8. Mutual correspondence between the indices of ShDFT spectral coefficients and signal frequencies; A2.9. DFT spectra of sparse signals and spectral zero-padding; A2.10. Invertibility of the shifted DFT and signal resampling; A2.11. DFT as a spectrum analyzer; A2.12. Quasi-continuous spectral analysis; A2.13. Signal resizing and rotation capability of the rotated scaled DFT; A2.14. Rotated and scaled DFT as digital convolution -- References -- Index |
| ctrlnum | (OCoLC)1152204135 (DE-599)BVBBV046693679 |
| doi_str_mv | 10.1117/3.2554039 |
| format | Electronic eBook |
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| id | DE-604.BV046693679 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:25:57Z |
| indexdate | 2024-07-10T08:51:18Z |
| institution | BVB |
| isbn | 9781510633841 9781523133871 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032104387 |
| oclc_num | 1152204135 |
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| owner_facet | DE-1050 DE-91G DE-BY-TUM |
| physical | 1 Online-Ressource |
| psigel | ZDB-10-ESC ZDB-50-SPI ZDB-10-ESC TUM_Lizenz |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | SPIE Press |
| record_format | marc |
| spelling | Jaroslavskij, Leonid P. Verfasser (DE-588)110936582 aut Advances in sampling theory and techniques Leonid P. Yaroslavsky Bellingham, Washington, USA SPIE Press [2020] 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Preface -- 1. Introduction: 1.1. A historical perspective of sampling: from ancient mosaics to computational imaging; 1.2. Book overview -- Part I: Signal sampling: 2. Sampling theorems: 2.1. Kotelnikov-Shannon sampling theorem: sampling band-limited 1D signals; 2.2. Sampling 1D band-pass signals; 2.3. Sampling band-limited 2D signals; optimal regular sampling lattices; 2.4. Sampling real signals; signal reconstruction distortions due to spectral aliasing; 2.5. The sampling theorem in a realistic reformulation; 2.6. Image sampling with a minimal sampling rate by means of image sub-band decomposition; 2.7. The discrete sampling theorem and its generalization to continuous signals; 2.8. Exercises -- 3. Compressed sensing demystified: 3.1. Redundancy of regular image sampling and image spectra sparsity; 3.2. Compressed sensing: why and how it is possible to precisely reconstruct signals sampled with aliasing; 3.3. Compressed sensing and the problem of minimizing the signal sampling rate; 3.4. Exercise -- 4. Image sampling and reconstruction with sampling rates close to the theoretical minimum: 4.1. The ASBSR method of image sampling and reconstruction; 4.2. Experimental verification of the method; 4.3. Some practical issues; 4.4. Other possible applications of the ASBSR method of image sampling and reconstruction; 4.5. Exercises 5. Signal and image resampling, and building their continuous models: 5.1. Signal/image resampling as an interpolation problem; convolutional interpolators; 5.2. Discrete sinc interpolation: a gold standard for signal resampling; 5.3. Fast algorithms of discrete sinc interpolation and their applications; 5.4. Discrete sinc interpolation versus other interpolation methods: performance comparison; 5.5. Exercises -- 6. Discrete sinc interpolation in other applications and implementations: 6.1. Precise numerical differentiation and integration of sampled signals; 6.2. Local ("elastic") image resampling: sliding-window discrete sinc interpolation algorithms; 6.3. Image data resampling for image reconstruction from projections; 6.4. Exercises -- 7. The discrete uncertainty principle, sinc-lets, and other peculiar properties of sampled signals: 7.1. The discrete uncertainty principle; 7.2. Sinc-lets: Sharply-band-limited basis functions with Sharply limited support; 7.3. Exercises -- Part II: Discrete representation of signal transformations: 8. Basic principles of discrete representation of signal transformations -- 9. Discrete representation of the convolution integral: 9.1. Discrete convolution; 9.2. Point spread functions and frequency responses of digital filters; 9.3. Treatment of signal borders in digital convolution 10. Discrete representation of the Fourier integral transform: 10.1. 1D discrete Fourier transforms; 10.2. 2D discrete Fourier transforms; 10.3. Discrete cosine transform; 10.4. Boundary-effect-free signal convolution in the DCT domain; 10.5. DFT and discrete frequency responses of digital filters; 10.6. Exercises -- Appendix 1. Fourier series, integral fourier transform, and delta function: A1.1. 1D Fourier series; A1.2. 2D Fourier series; A1.3. 1D integral Fourier transform; A1.4. 2D integral Fourier transform; A1.5. Delta function, sinc function, and the ideal low-pass filter; A1.6. Poisson summation formula -- Appendix 2. Discrete Fourier transforms and their properties: A2.1. Invertibility of discrete Fourier transforms and the discrete sinc function; A2.2. The Parseval's relation for the DFT; A2.3. Cyclicity of the DFT; A2.4. Shift theorem; A2.5. Convolution theorem; A2.6. Symmetry properties; A2.7. SDFT spectra of sinusoidal signals; A2.8. Mutual correspondence between the indices of ShDFT spectral coefficients and signal frequencies; A2.9. DFT spectra of sparse signals and spectral zero-padding; A2.10. Invertibility of the shifted DFT and signal resampling; A2.11. DFT as a spectrum analyzer; A2.12. Quasi-continuous spectral analysis; A2.13. Signal resizing and rotation capability of the rotated scaled DFT; A2.14. Rotated and scaled DFT as digital convolution -- References -- Index "This book presents the current state of the art of digital engineering, as well as recent proposals for optimal methods of signal and image non-redundant sampling and interpolation-error-free resampling. Topics include classical sampling theory, conventional sampling, the peculiarities of sampling 2D signals, artifacts, compressed sensing, fast algorithms, the discrete uncertainty principle, and sharply-band-limited discrete signals and basis functions with sharply limited support. Exercises based in MATLAB supplement the text throughout"-- Signal processing / Digital techniques / Mathematics Image processing / Digital techniques / Mathematics Fourier transformations Fourier transformations fast Image processing / Digital techniques / Mathematics fast Signal processing / Digital techniques / Mathematics fast Erscheint auch als Online-Ausgabe, epub 978-1-5106-3385-8 Erscheint auch als Online-Ausgabe, kindle edition 978-1-5106-3386-5 Erscheint auch als Druck-Ausgabe, paperback 978-1-5106-3383-4 https://doi.org/10.1117/3.2554039 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Jaroslavskij, Leonid P. Advances in sampling theory and techniques Preface -- 1. Introduction: 1.1. A historical perspective of sampling: from ancient mosaics to computational imaging; 1.2. Book overview -- Part I: Signal sampling: 2. Sampling theorems: 2.1. Kotelnikov-Shannon sampling theorem: sampling band-limited 1D signals; 2.2. Sampling 1D band-pass signals; 2.3. Sampling band-limited 2D signals; optimal regular sampling lattices; 2.4. Sampling real signals; signal reconstruction distortions due to spectral aliasing; 2.5. The sampling theorem in a realistic reformulation; 2.6. Image sampling with a minimal sampling rate by means of image sub-band decomposition; 2.7. The discrete sampling theorem and its generalization to continuous signals; 2.8. Exercises -- 3. Compressed sensing demystified: 3.1. Redundancy of regular image sampling and image spectra sparsity; 3.2. Compressed sensing: why and how it is possible to precisely reconstruct signals sampled with aliasing; 3.3. Compressed sensing and the problem of minimizing the signal sampling rate; 3.4. Exercise -- 4. Image sampling and reconstruction with sampling rates close to the theoretical minimum: 4.1. The ASBSR method of image sampling and reconstruction; 4.2. Experimental verification of the method; 4.3. Some practical issues; 4.4. Other possible applications of the ASBSR method of image sampling and reconstruction; 4.5. Exercises 5. Signal and image resampling, and building their continuous models: 5.1. Signal/image resampling as an interpolation problem; convolutional interpolators; 5.2. Discrete sinc interpolation: a gold standard for signal resampling; 5.3. Fast algorithms of discrete sinc interpolation and their applications; 5.4. Discrete sinc interpolation versus other interpolation methods: performance comparison; 5.5. Exercises -- 6. Discrete sinc interpolation in other applications and implementations: 6.1. Precise numerical differentiation and integration of sampled signals; 6.2. Local ("elastic") image resampling: sliding-window discrete sinc interpolation algorithms; 6.3. Image data resampling for image reconstruction from projections; 6.4. Exercises -- 7. The discrete uncertainty principle, sinc-lets, and other peculiar properties of sampled signals: 7.1. The discrete uncertainty principle; 7.2. Sinc-lets: Sharply-band-limited basis functions with Sharply limited support; 7.3. Exercises -- Part II: Discrete representation of signal transformations: 8. Basic principles of discrete representation of signal transformations -- 9. Discrete representation of the convolution integral: 9.1. Discrete convolution; 9.2. Point spread functions and frequency responses of digital filters; 9.3. Treatment of signal borders in digital convolution 10. Discrete representation of the Fourier integral transform: 10.1. 1D discrete Fourier transforms; 10.2. 2D discrete Fourier transforms; 10.3. Discrete cosine transform; 10.4. Boundary-effect-free signal convolution in the DCT domain; 10.5. DFT and discrete frequency responses of digital filters; 10.6. Exercises -- Appendix 1. Fourier series, integral fourier transform, and delta function: A1.1. 1D Fourier series; A1.2. 2D Fourier series; A1.3. 1D integral Fourier transform; A1.4. 2D integral Fourier transform; A1.5. Delta function, sinc function, and the ideal low-pass filter; A1.6. Poisson summation formula -- Appendix 2. Discrete Fourier transforms and their properties: A2.1. Invertibility of discrete Fourier transforms and the discrete sinc function; A2.2. The Parseval's relation for the DFT; A2.3. Cyclicity of the DFT; A2.4. Shift theorem; A2.5. Convolution theorem; A2.6. Symmetry properties; A2.7. SDFT spectra of sinusoidal signals; A2.8. Mutual correspondence between the indices of ShDFT spectral coefficients and signal frequencies; A2.9. DFT spectra of sparse signals and spectral zero-padding; A2.10. Invertibility of the shifted DFT and signal resampling; A2.11. DFT as a spectrum analyzer; A2.12. Quasi-continuous spectral analysis; A2.13. Signal resizing and rotation capability of the rotated scaled DFT; A2.14. Rotated and scaled DFT as digital convolution -- References -- Index Signal processing / Digital techniques / Mathematics Image processing / Digital techniques / Mathematics Fourier transformations Fourier transformations fast Image processing / Digital techniques / Mathematics fast Signal processing / Digital techniques / Mathematics fast |
| title | Advances in sampling theory and techniques |
| title_auth | Advances in sampling theory and techniques |
| title_exact_search | Advances in sampling theory and techniques |
| title_exact_search_txtP | Advances in sampling theory and techniques |
| title_full | Advances in sampling theory and techniques Leonid P. Yaroslavsky |
| title_fullStr | Advances in sampling theory and techniques Leonid P. Yaroslavsky |
| title_full_unstemmed | Advances in sampling theory and techniques Leonid P. Yaroslavsky |
| title_short | Advances in sampling theory and techniques |
| title_sort | advances in sampling theory and techniques |
| topic | Signal processing / Digital techniques / Mathematics Image processing / Digital techniques / Mathematics Fourier transformations Fourier transformations fast Image processing / Digital techniques / Mathematics fast Signal processing / Digital techniques / Mathematics fast |
| topic_facet | Signal processing / Digital techniques / Mathematics Image processing / Digital techniques / Mathematics Fourier transformations |
| url | https://doi.org/10.1117/3.2554039 |
| work_keys_str_mv | AT jaroslavskijleonidp advancesinsamplingtheoryandtechniques |