Digital Alias–free Signal Processing

As demand for applications working in extended frequency ranges increases, classical digital signal processing (DSP) techniques, not protected against aliasing, are becoming less effective. Digital alias–free signal processing (DASP) is a technique for overcoming the problems of aliasing at extended frequency ranges. Based on non–uniform or randomised sampling techniques and the development of novel algorithms, it creates the capacity to suppress potential aliasing crucial for high frequency applications and to reduce the complexity of designs.
This book provides practical and comprehensive coverage of the theory and techniques behind alias–free digital signal processing.
Digital Alias–free Signal Processing is ideal for practising engineers and researchers working on the development of digital signal processing applications at extended frequencies. It is also a valuable reference for electrical and computer engineering graduates taking courses in signal processing or digital signal processing.
Key features:Analyses issues of sampling, randomised and pseudo–randomised quantisation and direct and indirectly randomised sampling.Examines periodic and hybrid sampling, including information on processing algorithms and potential limitations imposed by signal dynamics.Sets out leading methods and techniques for complexity reduced designs, in particular designs of large aperture sensor arrays, massive data acquisition and compression from a number of signal sources, as well as complexity–reduced processing of non–uniform data.Presents examples of engineering applications using these techniques including spectrum analysis, waveform reconstruction and the estimation of various parameters, emphasising the importance of the technique for developing new technologies.Links DASP and traditional technologies by mapping them into embedded systems with standard inputs and outputs.

Spis treści:

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.
3.2.2 Spectra of Randomly Sampled Signals.
3.3 Aliasing Induced Errors at Seemingly Correct Sampling.< br>3.4 Overlapping of Sampled Signal Components.
3.5 Various Approaches to Randomization of Sampling.
Bibliography.
4 Randomized Quantization.
4.1 Randomized Versus Deterministic Quantization.
4.1.1 Basics.
4.1.2 Input–Output Characteristics.
4.1.3 Rationale of Randomizing.
4.2 Deliberate Introduction of Randomness.
4.2.1 Various Models.
4.3 Quantization Errors.
4.3.1 Probability Density Function of Errors.
4.3.2 Variance of Randomly Quantized Signals.
4.4 Quantization Noise.
4.4.1 Covariance between the Signal and Quantization Noise.
4.4.2 Spectrum.
Bibliography.
5 Pseudo–randomized Quantizing.
5.1 Pseudo–randomization Approach.
5.2 Optimal Quantizing.
5.2.1 Single–threshold Quantizing.
5.2.2 Multithreshold Quantizing.
5.2.3 Implementation Approaches.
5.3 Input–Output Relationships.
5.4 Quantization Errors.
5.5 Quantization Noise.
5.5.1 Covariance between Signal and Quantization Noise.
5.5.2 Spectrum of the Pseudo–randomized Quantization Noise.
5.5.3 Noise Reduction by Oversampling.
5.6 Some Properties of Quantized Signals.
5.7 Benefits.
Bibliography.
6 Direct Randomization of Sampling.
6.1 Periodic Sampling with Jitter.
6.2 Additive Random Sampling.
6.3 Sampling Function.
6.4 Elimination of Bias Errors.
Bibliography.
7 Threshold–crossing Sampling.
7.1 Sampling at Input and Reference Signal Crossings.
7.1.1 Level–crossing Sampling.
7.1.2 Time–variant Threshold Crossings.
7.2 Representing Signals Using Timing Information.
7.3 Sine–Wave Crossings.
7.3.1 Recovery of Signal Sample Values.
7.3.2 Various Realizations.
7.4 Remote Sampling Based on Sine–Wave Crossings.
7.5 Advantages and Disadvantages.
Bibliography .
8 Derivatives of Periodic Sampling.
8.1 Phase–shifted Periodic Sampling.
8.1.1 Dependence of Aliasing on the Sampling Phase.
8.1.2 Reconstruction of Sampled Signals.
8.2 Periodic Sampling with Random Skips.
8.2.1 General Model.
8.2.2 Typical Use.
8.3 Compensation Effect.
8.3.1 Display of Fourier Transforms.
8.3.2 Observing the Aliasing Processes.
8.4 Generation of Randomized Sampling Pulse Trains.
8.4.1 Basic Approach.
8.4.2 Practical Experience.
Bibliography.
9 Fuzzy Aliasing.
9.1 Meaning of the DFT of a Nonuniformly Sampled Signal.
9.2 Concept of Fuzzy Aliasing.
9.2.1 Generic Periodic Sampling with Random Skips.
9.2.2 Primary and Secondary Aliasing.
9.2.3 Decomposition of Sampling Point Processes.
9.3 Anatomy of Fuzzy Aliasing.
9.3.1 Tracking of Particular Contributions.
9.3.2 Incomplete Compensation of Aliases.
9.3.3 Aliasing at Multiple Frequencies.
9.4 Object Lesson.
Bibliography.
10 Hybrid Sampling.
10.1 Hybrids of Periodic and Random Sampling.
10.1.1 Basic Approach.
10.1.2 Arrangements for Sample Value Processing.
10.2 Hybrid Double Sampling.
10.2.1 Providing for Short Sampling Intervals.
10.2.2 Double Periodic Sampling with Jitter.
10.2.3 Double Additive Pseudo–random Sampling.
10.2.4 Periodic Additive Pseudo–random Sampling.
10.3 Mixing Hybrid Sampling with Periodic Sampling.
10.4 Comments in Conclusion.
Bibliography.
Part 2 Processing.
11 Data Acquisition.
11.1 Data Acquisition from Wideband Signal Sources.
11.1.1 Practical Results Confirming the Theory.
11.1.2 Sampling with Reduced Uncontrolled Jitter.
11.2 Application of Hybrid Double Sampling.
11.3 Pseudo–randomized Multiplexing.
11.4 Massive Data Acquisit