Digital Alias-free Signal Processing

Contents

Preface

Frequently Used Symbols and Abbreviations

1 Introduction: Signal Digitizing and Digital Processing

1.1 Subject Matter

1.2 Digitizing Dictates Processing Preconditions

1.2.1 Connecting Computers to the Real-life World

1.2.2 Widening of the Digital Domain

1.2.3 Digital Signal Representation

1.2.4 Complexity Reduction of Systems

1.3 Approach to the Development of Signal Processing Systems

1.4 Alias-free Sampling Option

1.4.1 Anti-aliasing Irregularity of Sampling

1.4.2 Sparse Nonuniform Sampling

1.4.3 Nonuniform Sampling Events

1.5 Remarks in Conclusion

Bibliography

Part 1 Digitizing

2 Randomization as a Tool

2.1 Randomized Versus Statistical Signal Processing

2.2 Accumulation of Empirical Experience

2.2.1 Using Monte Carlo Methods for Signal Processing

2.2.2 Polarity Coincidence Methods

2.2.3 Stochastic–Ergodic Method

2.2.4 Stochastic Computing

2.2.5 Dithering

2.2.6 Generalized Scheme of Randomized Digitizing

2.3 Discovery of Alias-free Signal Processing

2.3.1 Early Academic Research in Randomized Temporal Sampling

2.3.2 Early Research in Randomized Spatial Signal Processing

2.3.3 Engineering Experience

2.4 Randomization Leading to DASP

2.4.1 DASP Mission

2.4.2 Demonstrator of DASP Advantages and Limitations

2.5 Some of the Typically Targeted Benefits

Bibliography

3 Periodic Versus Randomized Sampling

3.1 Periodic Sampling as a Particular Sampling Case

3.1.1 Generalized Sampling Model

3.2 Spectra of Sampled Signals

3.2.1 Spectra of Periodically Sampled Signals