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Introduction to Biomedical Signals and Systems | |

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General Characteristics of Biomedical Signals | |

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Introduction | |

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Signals from physiological systems | |

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Signals from man-made instruments | |

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Discrete signals | |

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Some ways to describe signals | |

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Introduction to modulation and demodulation of physiological signals | |

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General Properties of Physiological Systems | |

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Introduction | |

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Analog systems | |

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Physiological systems | |

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Discrete systems | |

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Summary | |

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Review of Linear Systems Theory | |

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Linearity, Causality and Stationarity | |

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Analog Systems | |

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SISO and MIMO systems | |

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Introduction to ODEs and their solutions | |

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Systems Described by Sets of ODEs | |

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Introduction | |

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Introduction to matrix algebra | |

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Some matrix operations | |

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Introduction to state variables | |

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Linear System Characterization | |

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Introduction | |

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System impulse response | |

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Real convolution | |

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Transient response of systems | |

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Steady-state sinusoidal frequency response of LTI systems | |

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Bode plots | |

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Nyquist plots | |

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Discrete Signals and Systems | |

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Introduction | |

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Discrete convolution | |

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Discrete systems | |

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The z transform pair | |

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z Transform solutions of discrete state equations | |

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Discussion | |

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Stability of Systems | |

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Chapter Summary | |

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The Laplace Transform and Its Applications | |

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Introduction | |

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Properties of the Laplace Transform | |

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Some Examples of Finding Laplace Transforms | |

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The Inverse Laplace Transform | |

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Applications of the Laplace Transform | |

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Introduction | |

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Use of partial fraction expansions to find y(t) | |

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Application of the laplace transform to continuous state systems | |

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Use of signal flow graphs to find y(t) for continuous state systems | |

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Discussion | |

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Chapter Summary | |

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Fourier Series Analysis of Periodic Signals | |

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Introduction | |

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Properties of the Fourier Series | |

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Fourier Series Examples | |

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Chapter Summary | |

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The Continuous Fourier Transform | |

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Introduction | |

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Properties of the CFT | |

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Analog-to-Digital Conversion and the Sampling Theorem | |

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Introduction | |

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Impulse modulation and the poisson sum form of the sampled spectrum | |

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The sampling theorem | |

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The Analytical Signal and the Hilbert Transform | |

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Introduction | |

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The Hilbert transform and the analytical signal | |

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Properties of the Hilbert transform | |

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An application of the Hilbert transform | |

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The Modulation Transfer Function in Imaging | |

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Introduction | |

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The MTF | |

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The contrast transfer function | |

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Discussion | |

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Chapter Summary | |

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The Discrete Fourier Transform | |

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Introduction | |

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The CFT, ICFT, DFT and IDFT | |

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The CFT and ICFT | |

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Properties of the DFT and IDFT | |

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Applications of the DFT and IDFT | |

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Data Window Functions | |

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The FFT | |

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Introduction | |

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The fast Fourier transform | |

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Implementation of the FFT | |

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Discussion | |

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Chapter Summary | |

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Introduction to Time-Frequency Analysis of Biomedical Signals | |

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Introduction | |

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The Short-Term Fourier Transform | |

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Gabor and Adaptive Gabor Transform | |

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Wigner-Ville and Pseudo-Wigner Transforms | |

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Cohen's General Class of JTF Distributions | |

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Introduction to JTFA Using Wavelets | |

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Introduction | |

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Computation of the continuous wavelet transform | |

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Some wavelet basis functions, [psi] (t) | |

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Applications of JTF Analysis to Physiological Signals | |

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Introduction | |

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Heart sounds | |

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JTF analysis of EEG signals | |

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Other biomedical applications of JTF spectrograms | |

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JTFA Software | |

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Chapter Summary | |

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Introduction to the Analysis of Stationary Noise and Signals Contaminated with Noise | |

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Introduction | |

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Noise Descriptors and Noise in Systems | |

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Introduction | |

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Probability density functions | |

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Autocorrelation | |

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Cross-Correlation | |

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The continuous auto- and cross-power density spectrums | |

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Propagation of noise through stationary causal LTI continuous systems | |

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Propagation of noise through stationary causal LTI discrete systems | |

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Characteristic functions of random variables | |

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Price's theorem and applications | |

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Quantization Noise | |

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Introduction to "data scrubbing" by nonlinear discrete filtering | |

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Discussion | |

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Calculation of Noise Descriptors with Finite Discrete Data | |

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Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement | |

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Introduction | |

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Analysis of SNR improvement by averaging | |

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Introduction to signal-to-noise ratio improvement by linear filtering | |

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Discussion | |

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Introduction to the Application of Statistics and Information Theory to Genomics | |

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Introduction | |

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Review of DNA Biology | |

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RNAs and the basics of protein synthesis: transcription and translation | |

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Introduction to statistics applied to genomics | |

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Introduction to the application of information theory to genomics | |

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Introduction to hidden Markov models in genomics | |

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Discussion | |

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Chapter Summary | |

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Basic Mathematical Tools used in the Characterization of Physiological Systems | |

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Introduction | |

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Some General Properties of Physiological Systems | |

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Some Properties of Nonlinear Systems | |

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Physical Factors Determining the Dynamic Behavior of Physiological Systems | |

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Diffusion dynamics | |

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Biochemical systems and mass-action kinetics | |

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Means of Characterizing Physiological Systems | |

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Introduction | |

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The Nyquist stability criterion | |

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Describing functions and the stability of closed-loop nonlinear systems | |

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The use of Gaussian noise-based techniques to characterize physiological systems | |

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Discussion | |

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Chapter Summary | |

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The Mathematics of Tomographic Imaging | |

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Introduction | |

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Algebraic Reconstruction | |

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The Radon Transform | |

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The Fourier Slice Theorem | |

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The Filtered Back-Projection Algorithm | |

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Chapter Summary | |

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Appendices | |

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Cramer's Rule | |

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Signal Flow Graphs and Mason's Rule | |

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Bode (Frequency Response) Plots | |

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Computational Tools for Biomedical Signal Processing and Systems Analysis | |

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Introduction | |

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Simnon | |

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National Instruments' LabVIEW Signal Processing Tools | |

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Matlab, Simulink, and Toolkits | |

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Summary | |

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Bibliography and References | |

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Index | |