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Part 2: Processing
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Part 2: Processing
by Ivars Bilinskis
Digital Alias-free Signal Processing
Cover Page
Title Page
Copyright
Contents
Preface
Frequently Used Symbols and Abbreviations
1: Introduction: Signal Digitizing and Digital Processing
1.1 Subject Matter
1.2 Digitizing Dictates Processing Preconditions
1.3 Approach to the Development of Signal Processing Systems
1.4 Alias-free Sampling Option
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
2.3 Discovery of Alias-free Signal Processing
2.4 Randomization Leading to DASP
2.5 Some of the Typically Targeted Benefits
Bibliography
3: Periodic Versus Randomized Sampling
3.1 Periodic Sampling as a Particular Sampling Case
3.2 Spectra of Sampled Signals
3.3 Aliasing Induced Errors at Seemingly Correct Sampling
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
4.2 Deliberate Introduction of Randomness
4.3 Quantization Errors
4.4 Quantization Noise
Bibliography
5: Pseudo-randomized Quantizing
5.1 Pseudo-randomization Approach
5.2 Optimal Quantizing
5.3 Input–Output Relationships
5.4 Quantization Errors
5.5 Quantization Noise
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
7.2 Representing Signals Using Timing Information
7.3 Sine-Wave Crossings
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
8.2 Periodic Sampling with Random Skips
8.3 Compensation Effect
8.4 Generation of Randomized Sampling Pulse Trains
Bibliography
9: Fuzzy Aliasing
9.1 Meaning of the DFT of a Nonuniformly Sampled Signal
9.2 Concept of Fuzzy Aliasing
9.3 Anatomy of Fuzzy Aliasing
9.4 Object Lesson
Bibliography
10: Hybrid Sampling
10.1 Hybrids of Periodic and Random Sampling
10.2 Hybrid Double 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
11.2 Application of Hybrid Double Sampling
11.3 Pseudo-randomized Multiplexing
11.4 Massive Data Acquisition
Bibliography
12: Quantizing-specific Signal Parameter Estimation
12.1 Theoretical Limits
12.2 Optimal Estimation
12.3 Specifics Related to Pseudo-randomized Quantizing
12.4 Estimation of the Absolute Mean Value
12.5 Estimation of the Mean Power
12.6 Errors Due to Randomized Sampling
Bibliography
13: Estimation of Correlation Functions
13.1 Multiplication of Quantized Signals
13.2 Correlation Analysis of Pseudo-randomly Quantized Signals
13.3 Correlation Analysis of Pseudo-randomly Sampled Signals
13.4 Comments
Bibliography
14: Signal Transforms
14.1 Problem of Matching Signal Processing to Sampling
14.2 Bases of Signal Transforms
14.3 Orthogonal Transforms
14.4 Discrete Unorthogonal Transforms
14.5 Conversion of Unorthogonal Transforms
Bibliography
15: DFT of Nonuniformly Sampled Signals
15.1 Problems Related to Sampling Irregularities
15.2 Cross-interference Corrupting DFT
15.3 Exploitation of FFT
15.4 Revealing the Essence of the Fourier Coefficient Estimation
Bibliography
16: Complexity-reduced DFT
16.1 Potential Gains from Application of Rectangular Function Sets
16.2 Complexity-reduced DFT Exploiting Rectangular Functions
16.3 Computer Simulations of the Rectangular Function-based DFT
16.4 Fast DFT of Sine-Wave Crossings
Bibliography
17: Spatial Data Acquisition and Processing
17.1 Sensor Array Model
17.2 Temporal and Spatial Spectra of Array Signals
17.3 Beamforming
17.4 Signal Direction of Arrival Estimation
17.5 Pseudo-randomization of Sensor Arrays
Bibliography
18: Adapting Signal Processing to Sampling Nonuniformities
18.1 Cross-interference Coefficients
18.2 Taking the Cross-interference into Account
18.3 Achievable Improvement and Typical Problems
18.4 Parallel Computing Approach
18.5 Mapping of the Cross-interference Coefficients
19: Estimation of Object Parameters
19.1 Measuring the Frequency Response of Objects
19.2 Test Signal Synthesis from a Sparsely Periodically Sampled Basis Function
19.3 Test Signal Synthesis from a Nonuniformly Sampled Basis Function
19.4 Synthesis of Narrowband and Wideband Signals
19.5 Measuring Small Delays and Switching Times
19.6 Bioimpedance Signal Demodulation in Real-time
Bibliography
20: Encapsulating DASP Technology
20.1 Linking Digital Alias-free Signal Processing with Traditional Methods
20.2 Algorithm Options in the Development of Firmware
20.3 Dedicated Services of the Embedded DASP Systems
20.4 Dedicated Services Related to Processing of Digital Inputs
20.5 Reducing the Quantity of Sensors in Large-aperture Arrays
Bibliography
Index
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10: Hybrid Sampling
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11: Data Acquisition
Part 2
Processing
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