Signal Processing for Neuroscientists

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.

Includes an introduction to biomedical signals, noise characteristics, recording techniques, and the more advanced topics of linear, nonlinear and multi-channel systems analysis Features new chapters on the fundamentals of modeling, application to neuronal modeling, Kalman filter, multi-taper power spectrum estimation, and practice exercisesContains the basics and background for more advanced topics in extensive notes and appendicesIncludes practical examples of algorithm development and implementation in MATLABFeatures a companion website with MATLAB scripts, data files, figures and video lectures

1. Introduction
2. Data Acquisition
3. Noise
4. Signal Averaging
5. Real and Complex Fourier Series
6. Continuous, Discrete, and Fast Fourier Transform
7. 1D and 2D Fourier Transform Applications
8. Lomb’s Algorithm and Multi-Taper Power Spectrum Estimation
9. Differential Equations: Introduction
10. Differential Equations: Phase Space and Numerical Solutions
11. Modeling
12. Laplace and z-Transform
13. LTI Systems, Convolution, Correlation, Coherence, and the Hilbert Transform
14. Causality
15. Introduction to Filters: The RC-Circuit
16. Filters: Analysis
17. Filters: Specification, Bode Plot, and Nyquist Plot
18. Filters: Digital Filters
19. Kalman Filter
20. Spike Train Analyses
21. Wavelet Analysis: Time Domain Properties
22. Wavelet Analysis: Frequency Domain Properties
23. Low Dimensional Nonlinear Dynamics: Fixed Points, Limit Cycles and Bifurcations
24. Volterra Series
25. Wiener Series
26. Poisson-Wiener Series
27. Nonlinear Techniques
28. Decomposition of Multi-Channel Data
29. Modeling Neural Systems: Cellular Models
30. Modeling Neural Systems: Network Models