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Look-Ahead Sigma-Delta Modulation and Its Application to Super Audio CD

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Look-Ahead Sigma-Delta Modulation and Its Application to Super Audio CD Look-ahead sigma-delta modulation and its application to super audio CD Citation for published version (APA): Janssen, E. (2010). Look-ahead sigma-delta modulation and its application to super audio CD. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR691188 DOI: 10.6100/IR691188 Document status and date: Published: 01/01/2010 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 04. Oct. 2021 Look-ahead Sigma-Delta Modulation and its application to Super Audio CD Erwin Janssen The work described in this thesis has been carried out at the Philips Research Laboratories and NXP Semiconductors, Eindhoven, the Netherlands, as part of the Philips/NXP research program. Janssen, E. Look-ahead Sigma-Delta Modulation and its application to Super Audio CD Proefschrift Technische Universiteit Eindhoven, 2010 Trefwoorden: 1-bit audio, digital-to-digital conversion, linearization, look- ahead, noise shaping, sigma-delta modulation, signal processing A catalogue record is available from the Eindhoven University of Tech- nology Library ISBN: 978-90-386-2364-1 °c E. Janssen 2010 All rights reserved. Reproduction in whole or in part is prohibited without the written consent of the copyright owner. Look-ahead Sigma-Delta Modulation and its application to Super Audio CD PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magni¯cus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 1 december 2010 om 16.00 uur door Erwin Janssen geboren te Ede Dit proefschrift is goedgekeurd door promotor: prof.dr.ir. A.H.M. van Roermund Samenstelling promotiecommissie: prof.dr.ir. A.H.M. van Roermund Technische Universiteit Eindhoven prof.dr.ir. A.C.P.M. Backx Technische Universiteit Eindhoven dr.ir. J.A. Hegt Technische Universiteit Eindhoven dr.ir. P.C.W. Sommen Technische Universiteit Eindhoven prof.dr.ir. B. Nauta Universiteit Twente prof.dr.ir. G. Gielen Katholieke Universiteit Leuven dr. D. Reefman Philips Research dr.ir. L.J. Breems NXP Semiconductors Contents List of symbols and abbreviations vii 1 Introduction 1 1.1 Motivation . 2 1.2 Aim of the thesis . 3 1.3 Scope of the thesis . 4 1.4 Organization of the thesis . 4 2 Basics of sigma-delta modulation 7 2.1 AD, DD, and DA Sigma-Delta conversion . 11 2.1.1 AD conversion . 11 2.1.2 DD conversion . 12 2.1.3 DA conversion . 12 2.2 Sigma-Delta structures . 13 2.3 Linear modeling of an SDM . 16 2.4 SDM performance indicators . 22 2.4.1 Generic converter performance . 23 2.4.2 SDM speci¯c functional performance . 29 2.4.3 SDM speci¯c implementation costs . 34 2.4.4 Figure-Of-Merit of an SDM . 36 3 Transient SDM performance 39 3.1 Measuring signal conversion quality . 39 3.1.1 Steady-state . 39 3.1.2 Non-steady-state . 40 3.2 Time domain SINAD measurement . 41 3.3 Steady-state SINAD measurement analysis . 44 3.3.1 Obtaining the linearized STF . 45 3.3.2 Time domain SINAD measurement . 49 3.4 Non-steady-state SINAD measurement analysis . 50 3.5 Conclusions . 52 i Contents 4 Noise-shaping quantizer model 55 4.1 Generic quantizer . 55 4.2 Noise-shaping quantizer . 57 4.3 Noise-shaping quantizer with multiple cost functions . 59 4.4 Speci¯c realization structures . 60 5 Look-ahead sigma-delta modulation 63 5.1 Noise-shaping quantizer with look-ahead . 63 5.2 Look-ahead enabled SDM model . 65 5.3 Look-ahead principle . 67 5.3.1 Quantizer cost function . 69 5.4 Obtaining information about the future . 70 5.4.1 Approximated future input . 71 5.4.2 Actual future input . 71 5.5 Full look-ahead algorithm . 72 5.6 Linear modeling of a look-ahead SDM . 75 5.6.1 Boundary conditions and assumptions . 76 5.6.2 Feed-forward look-ahead SDM . 78 5.6.3 Feed-back look-ahead SDM . 80 5.7 Bene¯ts and disadvantages of look-ahead . 82 5.7.1 Bene¯ts . 82 5.7.2 Disadvantages . 86 5.8 Look-ahead AD conversion . 87 5.8.1 Potential bene¯ts and disadvantages of look-ahead in AD conversion . 87 5.8.2 Feasibility of a look-ahead ADC . 88 5.8.3 Hybrid look-ahead ADC . 90 5.8.4 Conclusion . 92 5.9 Look-ahead DD conversion . 92 5.10 Conclusions . 95 6 Reducing the complexity of LA DD conversion 97 6.1 Full look-ahead . 97 6.1.1 Complete response calculation with reuse of inter- mediate results . 98 6.1.2 Select and continue with half of the solutions . 98 6.1.3 Linear decomposition of the ¯lter response . 99 6.1.4 Conditional computation of the solutions . 101 6.1.5 Calculating multiple output symbols per step . 101 6.1.6 Summary . 103 6.2 Pruned look-ahead . 104 6.2.1 Motivation for pruning . 104 6.2.2 Basic pruned look-ahead modulation . 105 ii Contents 6.2.3 Pruned look-ahead modulation with reuse of results108 6.2.4 Summary . 120 6.3 Pruned look-ahead modulator realizations . 120 6.3.1 Trellis sigma-delta modulation . 121 6.3.2 E±cient Trellis sigma-delta modulation . 122 6.3.3 Pruned Tree sigma-delta modulation . 124 6.3.4 Pruned Tree sigma-delta modulation for SA-CD . 126 6.4 Conclusions . 127 7 Trellis sigma-delta modulation 129 7.1 Algorithm - Kato model . 130 7.1.1 Hidden Markov model . 131 7.1.2 Algorithm steps . 133 7.2 Algorithm - pruned look-ahead model . 137 7.3 Veri¯cation of the linearized NTF and STF . 139 7.3.1 NTF . 139 7.3.2 STF . 140 7.4 Relation Trellis order and Trellis depth . 142 7.4.1 Simulation setup . 143 7.4.2 Trellis depth as a function of the Trellis order and the signal amplitude . 144 7.4.3 Trellis depth as a function of the signal frequency . 146 7.4.4 Trellis depth as a function of the loop-¯lter con- ¯guration . 147 7.4.5 Summary . 148 7.5 Functional performance . 149 7.5.1 SNR, SINAD, THD and SFDR . 149 7.5.2 Converter stability . 155 7.5.3 Noise modulation . 160 7.5.4 Summary . 163 7.6 Implementation aspects . 164 7.6.1 Required computational resources . 164 7.6.2 Look-ahead ¯lter unit . 164 7.6.3 Output symbol selection . 168 7.7 Conclusions . 169 8 E±cient Trellis sigma-delta modulation 173 8.1 Reducing the number of parallel paths . 174 8.2 Algorithm . 176 8.3 Relation between N and M . 178 8.4 Required history length . 180 8.5 Functional performance . 183 8.5.1 SNR, SINAD, THD and SFDR . 183 iii Contents 8.5.2 Converter stability . 188 8.5.3 Noise modulation . 189 8.5.4 Summary . 192 8.6 Implementation aspects . 194 8.6.1 Selection step . 194 8.7 Conclusions . 196 9 Pruned Tree sigma-delta modulation 199 9.1 Removing the test for uniqueness . 199 9.2 Algorithm . 202 9.2.1 Initialization phase . 202 9.2.2 Operation phase . 203 9.3 Required history length . 204 9.4 Functional performance . 206 9.4.1 SNR, SINAD, THD and SFDR . 206 9.4.2 Converter stability . 210 9.4.3 Noise modulation . 213 9.4.4 Summary . 215 9.5 Implementation aspects . 217 9.6 Conclusions . 218 10 Pruned Tree sigma-delta modulation for SA-CD 223 10.1 Requirements of an SA-CD modulator . 224 10.2 SA-CD lossless data compression . 226 10.3 Dual optimization . 230 10.3.1 Predictor cost function . 231 10.3.2 Combining the cost functions . 232 10.3.3 Spectral shaping . 234 10.4 Algorithm . 237 10.5 Functional performance . 240 10.5.1 Lossless data compression . 240 10.5.2 SNR, SINAD, THD and SFDR .
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