Signal Processing for Neuroscientists, Second Edition provides an introduction to signal processing and modeling for those with a modest understanding of algebra, trigonometry and calculus. With a robust modeling component, this book describes modeling from the fundamental level of differential equations all the way up to practical applications in neuronal modeling. It features nine new chapters and an exercise section developed by the author. Since the modeling of systems and signal analysis are closely related, integrated presentation of these topics using identical or similar mathematics presents a didactic advantage and a significant resource for neuroscientists with quantitative interest.
Although each of the topics introduced could fill several volumes, this book provides a fundamental and uncluttered background for the non-specialist scientist or engineer to not only get applications started, but also evaluate more advanced literature on signal processing and modeling.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Data Acquisition - p. 17 3. Chapter 3. Noise - p. 37 4. Chapter 4. Signal Averaging - p. 59 5. Chapter 5. Real and Complex Fourier Series - p. 81 6. Chapter 6. Continuous, Discrete, and Fast Fourier Transform - p. 103 7. Chapter 7. 1-D and 2-D Fourier Transform Applications - p. 119 8. Chapter 8. Lomb's Algorithm and Multitaper Power Spectrum Estimation - p. 153 9. Chapter 9. Differential Equations: Introduction - p. 181 10. Chapter 10. Differential Equations: Phase Space and Numerical Solutions - p. 199 11. Chapter 11. Modeling - p. 211 12. Chapter 12. Laplace and z-Transform - p. 231 13. Chapter 13. LTI Systems: Convolution, Correlation, Coherence, and the Hilbert Transform - p. 251 14. Chapter 14. Causality - p. 289 15. Chapter 15. Introduction to Filters: The RC-Circuit - p. 307 16. Chapter 16. Filters: Analysis - p. 315 17. Chapter 17. Filters: Specification, Bode Plot, Nyquist Plot - p. 329 18. Chapter 18. Filters: Digital Filters - p. 345 19. Chapter 19. Kalman Filter - p. 361 20. Chapter 20. Spike Train Analysis - p. 375 21. Chapter 21. Wavelet Analysis: Time Domain Properties - p. 401 22. Chapter 22. Wavelet Analysis: Frequency Domain Properties - p. 425 23. Chapter 23. Low-Dimensional Nonlinear Dynamics: Fixed Points, Limit Cycles, and Bifurcations - p. 443 24. Chapter 24. Volterra Series - p. 467 25. Chapter 25. Wiener Series - p. 493 26. 25.1. Introduction - p. 493 27. 25.2. Wiener Kernels - p. 494 28. 25.3. Determination of the Zeroth-, First-, and Second-Order Wiener Kernels - p. 502 29. 25.4. Implementation of the Cross-Correlation Method - p. 507 30. 25.5. Relation Between Wiener and Volterra Kernels - p. 512 31. 25.6. Analyzing Spiking Neurons Stimulated With Noise - p. 513 32. 25.7. Nonwhite Gaussian Input - p. 519 33. 25.8. Summary - p. 521 34. Appendix 25.1 - p. 523 35. Appendix 25.2 - p. 525 36. Exercises - p. 526 37. Chapter 26. Poisson–Wiener Series - p. 529 38. 26.1. Introduction - p. 529 39. 26.2. Systems With Impulse Train Input - p. 529 40. 26.3. Determination of the Zeroth-, First-, and Second-Order Poisson–Wiener Kernels - p. 542 41. 26.4. Implementation of the Cross-Correlation Method - p. 549 42. 26.5. Spiking Output - p. 551 43. 26.6. Summary - p. 553 44. Appendix 26.1 - p. 553 45. Appendix 26.2 - p. 558 46. Exercises - p. 560 47. Chapter 27. Nonlinear Techniques - p. 561 48. Chapter 28. Decomposition of Multichannel Data - p. 579 49. Chapter 29. Modeling Neural Systems: Cellular Models - p. 619 50. Chapter 30. Modeling Neural Systems: Network Models - p. 647 51. 30.1. Introduction - p. 647 52. 30.2. Networks of Individual Cell Models - p. 649 53. 30.3. Mean Field Network Models - p. 657 54. 30.4. Spatiotemporal Model for the Electroencephalogram - p. 675 55. 30.5. A Field Equation for the Electroencephalogram - p. 678 56. 30.6. Models With a Stochastic Component - p. 686 57. 30.7. Concluding Remarks - p. 694 58. Appendix 30.1 Linearization of the Wilson–Cowan Equations - p. 696 59. Appendix 30.2 Adjusting Weights by Backpropagation of the Error - p. 698 60. Exercises - p. 701 61. Index - p. 707
Signal Processing for Neuroscientists, Second Edition provides an introduction to signal processing and modeling for those with a modest understanding of algebra, trigonometry and calculus. With a robust modeling component, this book describes modeling from the fundamental level of differential equations all the way up to practical applications in neuronal modeling. It features nine new chapters and an exercise section developed by the author. Since the modeling of systems and signal analysis are closely related, integrated presentation of these topics using identical or similar mathematics presents a didactic advantage and a significant resource for neuroscientists with quantitative interest.
Although each of the topics introduced could fill several volumes, this book provides a fundamental and uncluttered background for the non-specialist scientist or engineer to not only get applications started, but also evaluate more advanced literature on signal processing and modeling.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Data Acquisition - p. 17 3. Chapter 3. Noise - p. 37 4. Chapter 4. Signal Averaging - p. 59 5. Chapter 5. Real and Complex Fourier Series - p. 81 6. Chapter 6. Continuous, Discrete, and Fast Fourier Transform - p. 103 7. Chapter 7. 1-D and 2-D Fourier Transform Applications - p. 119 8. Chapter 8. Lomb's Algorithm and Multitaper Power Spectrum Estimation - p. 153 9. Chapter 9. Differential Equations: Introduction - p. 181 10. Chapter 10. Differential Equations: Phase Space and Numerical Solutions - p. 199 11. Chapter 11. Modeling - p. 211 12. Chapter 12. Laplace and z-Transform - p. 231 13. Chapter 13. LTI Systems: Convolution, Correlation, Coherence, and the Hilbert Transform - p. 251 14. Chapter 14. Causality - p. 289 15. Chapter 15. Introduction to Filters: The RC-Circuit - p. 307 16. Chapter 16. Filters: Analysis - p. 315 17. Chapter 17. Filters: Specification, Bode Plot, Nyquist Plot - p. 329 18. Chapter 18. Filters: Digital Filters - p. 345 19. Chapter 19. Kalman Filter - p. 361 20. Chapter 20. Spike Train Analysis - p. 375 21. Chapter 21. Wavelet Analysis: Time Domain Properties - p. 401 22. Chapter 22. Wavelet Analysis: Frequency Domain Properties - p. 425 23. Chapter 23. Low-Dimensional Nonlinear Dynamics: Fixed Points, Limit Cycles, and Bifurcations - p. 443 24. Chapter 24. Volterra Series - p. 467 25. Chapter 25. Wiener Series - p. 493 26. 25.1. Introduction - p. 493 27. 25.2. Wiener Kernels - p. 494 28. 25.3. Determination of the Zeroth-, First-, and Second-Order Wiener Kernels - p. 502 29. 25.4. Implementation of the Cross-Correlation Method - p. 507 30. 25.5. Relation Between Wiener and Volterra Kernels - p. 512 31. 25.6. Analyzing Spiking Neurons Stimulated With Noise - p. 513 32. 25.7. Nonwhite Gaussian Input - p. 519 33. 25.8. Summary - p. 521 34. Appendix 25.1 - p. 523 35. Appendix 25.2 - p. 525 36. Exercises - p. 526 37. Chapter 26. Poisson–Wiener Series - p. 529 38. 26.1. Introduction - p. 529 39. 26.2. Systems With Impulse Train Input - p. 529 40. 26.3. Determination of the Zeroth-, First-, and Second-Order Poisson–Wiener Kernels - p. 542 41. 26.4. Implementation of the Cross-Correlation Method - p. 549 42. 26.5. Spiking Output - p. 551 43. 26.6. Summary - p. 553 44. Appendix 26.1 - p. 553 45. Appendix 26.2 - p. 558 46. Exercises - p. 560 47. Chapter 27. Nonlinear Techniques - p. 561 48. Chapter 28. Decomposition of Multichannel Data - p. 579 49. Chapter 29. Modeling Neural Systems: Cellular Models - p. 619 50. Chapter 30. Modeling Neural Systems: Network Models - p. 647 51. 30.1. Introduction - p. 647 52. 30.2. Networks of Individual Cell Models - p. 649 53. 30.3. Mean Field Network Models - p. 657 54. 30.4. Spatiotemporal Model for the Electroencephalogram - p. 675 55. 30.5. A Field Equation for the Electroencephalogram - p. 678 56. 30.6. Models With a Stochastic Component - p. 686 57. 30.7. Concluding Remarks - p. 694 58. Appendix 30.1 Linearization of the Wilson–Cowan Equations - p. 696 59. Appendix 30.2 Adjusting Weights by Backpropagation of the Error - p. 698 60. Exercises - p. 701 61. Index - p. 707
