You are previewing Digital Alias-free Signal Processing.
O'Reilly logo
Digital Alias-free Signal Processing

Book Description

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.

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 and 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.

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.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface
  6. Frequently Used Symbols and Abbreviations
  7. 1: Introduction: Signal Digitizing and Digital Processing
    1. 1.1 Subject Matter
    2. 1.2 Digitizing Dictates Processing Preconditions
    3. 1.3 Approach to the Development of Signal Processing Systems
    4. 1.4 Alias-free Sampling Option
    5. 1.5 Remarks in Conclusion
    6. Bibliography
  8. Part 1: Digitizing
    1. 2: Randomization as a Tool
      1. 2.1 Randomized Versus Statistical Signal Processing
      2. 2.2 Accumulation of Empirical Experience
      3. 2.3 Discovery of Alias-free Signal Processing
      4. 2.4 Randomization Leading to DASP
      5. 2.5 Some of the Typically Targeted Benefits
      6. Bibliography
    2. 3: Periodic Versus Randomized Sampling
      1. 3.1 Periodic Sampling as a Particular Sampling Case
      2. 3.2 Spectra of Sampled Signals
      3. 3.3 Aliasing Induced Errors at Seemingly Correct Sampling
      4. 3.4 Overlapping of Sampled Signal Components
      5. 3.5 Various Approaches to Randomization of Sampling
      6. Bibliography
    3. 4: Randomized Quantization
      1. 4.1 Randomized Versus Deterministic Quantization
      2. 4.2 Deliberate Introduction of Randomness
      3. 4.3 Quantization Errors
      4. 4.4 Quantization Noise
      5. Bibliography
    4. 5: Pseudo-randomized Quantizing
      1. 5.1 Pseudo-randomization Approach
      2. 5.2 Optimal Quantizing
      3. 5.3 Input–Output Relationships
      4. 5.4 Quantization Errors
      5. 5.5 Quantization Noise
      6. 5.6 Some Properties of Quantized Signals
      7. 5.7 Benefits
      8. Bibliography
    5. 6: Direct Randomization of Sampling
      1. 6.1 Periodic Sampling with Jitter
      2. 6.2 Additive Random Sampling
      3. 6.3 Sampling Function
      4. 6.4 Elimination of Bias Errors
      5. Bibliography
    6. 7: Threshold-crossing Sampling
      1. 7.1 Sampling at Input and Reference Signal Crossings
      2. 7.2 Representing Signals Using Timing Information
      3. 7.3 Sine-Wave Crossings
      4. 7.4 Remote Sampling Based on Sine-Wave Crossings
      5. 7.5 Advantages and Disadvantages
      6. Bibliography
    7. 8: Derivatives of Periodic Sampling
      1. 8.1 Phase-shifted Periodic Sampling
      2. 8.2 Periodic Sampling with Random Skips
      3. 8.3 Compensation Effect
      4. 8.4 Generation of Randomized Sampling Pulse Trains
      5. Bibliography
    8. 9: Fuzzy Aliasing
      1. 9.1 Meaning of the DFT of a Nonuniformly Sampled Signal
      2. 9.2 Concept of Fuzzy Aliasing
      3. 9.3 Anatomy of Fuzzy Aliasing
      4. 9.4 Object Lesson
      5. Bibliography
    9. 10: Hybrid Sampling
      1. 10.1 Hybrids of Periodic and Random Sampling
      2. 10.2 Hybrid Double Sampling
      3. 10.3 Mixing Hybrid Sampling with Periodic Sampling
      4. 10.4 Comments in Conclusion
      5. Bibliography
  9. Part 2: Processing
    1. 11: Data Acquisition
      1. 11.1 Data Acquisition from Wideband Signal Sources
      2. 11.2 Application of Hybrid Double Sampling
      3. 11.3 Pseudo-randomized Multiplexing
      4. 11.4 Massive Data Acquisition
      5. Bibliography
    2. 12: Quantizing-specific Signal Parameter Estimation
      1. 12.1 Theoretical Limits
      2. 12.2 Optimal Estimation
      3. 12.3 Specifics Related to Pseudo-randomized Quantizing
      4. 12.4 Estimation of the Absolute Mean Value
      5. 12.5 Estimation of the Mean Power
      6. 12.6 Errors Due to Randomized Sampling
      7. Bibliography
    3. 13: Estimation of Correlation Functions
      1. 13.1 Multiplication of Quantized Signals
      2. 13.2 Correlation Analysis of Pseudo-randomly Quantized Signals
      3. 13.3 Correlation Analysis of Pseudo-randomly Sampled Signals
      4. 13.4 Comments
      5. Bibliography
    4. 14: Signal Transforms
      1. 14.1 Problem of Matching Signal Processing to Sampling
      2. 14.2 Bases of Signal Transforms
      3. 14.3 Orthogonal Transforms
      4. 14.4 Discrete Unorthogonal Transforms
      5. 14.5 Conversion of Unorthogonal Transforms
      6. Bibliography
    5. 15: DFT of Nonuniformly Sampled Signals
      1. 15.1 Problems Related to Sampling Irregularities
      2. 15.2 Cross-interference Corrupting DFT
      3. 15.3 Exploitation of FFT
      4. 15.4 Revealing the Essence of the Fourier Coefficient Estimation
      5. Bibliography
    6. 16: Complexity-reduced DFT
      1. 16.1 Potential Gains from Application of Rectangular Function Sets
      2. 16.2 Complexity-reduced DFT Exploiting Rectangular Functions
      3. 16.3 Computer Simulations of the Rectangular Function-based DFT
      4. 16.4 Fast DFT of Sine-Wave Crossings
      5. Bibliography
    7. 17: Spatial Data Acquisition and Processing
      1. 17.1 Sensor Array Model
      2. 17.2 Temporal and Spatial Spectra of Array Signals
      3. 17.3 Beamforming
      4. 17.4 Signal Direction of Arrival Estimation
      5. 17.5 Pseudo-randomization of Sensor Arrays
      6. Bibliography
    8. 18: Adapting Signal Processing to Sampling Nonuniformities
      1. 18.1 Cross-interference Coefficients
      2. 18.2 Taking the Cross-interference into Account
      3. 18.3 Achievable Improvement and Typical Problems
      4. 18.4 Parallel Computing Approach
      5. 18.5 Mapping of the Cross-interference Coefficients
    9. 19: Estimation of Object Parameters
      1. 19.1 Measuring the Frequency Response of Objects
      2. 19.2 Test Signal Synthesis from a Sparsely Periodically Sampled Basis Function
      3. 19.3 Test Signal Synthesis from a Nonuniformly Sampled Basis Function
      4. 19.4 Synthesis of Narrowband and Wideband Signals
      5. 19.5 Measuring Small Delays and Switching Times
      6. 19.6 Bioimpedance Signal Demodulation in Real-time
      7. Bibliography
    10. 20: Encapsulating DASP Technology
      1. 20.1 Linking Digital Alias-free Signal Processing with Traditional Methods
      2. 20.2 Algorithm Options in the Development of Firmware
      3. 20.3 Dedicated Services of the Embedded DASP Systems
      4. 20.4 Dedicated Services Related to Processing of Digital Inputs
      5. 20.5 Reducing the Quantity of Sensors in Large-aperture Arrays
      6. Bibliography
  10. Index