Signal processing of random physiological signals

Biomedical engineering signal analysis -- Introduction -- Generalized systems engineering approach -- System classification -- Order -- Causal vs noncausal -- Linear vs nonlinear -- Fixed vs time-varying -- Lumped parameter vs distributed parameter -- Continuous time vs discrete time -- Instantaneous vs dynamic -- Classification of signals -- How are signals classified -- Signal characterization (measurable parameters) -- Basis functions and signal representation -- Introduction to basis functions -- Desirable properties of basis functions --Evaluation of coefficients -- Signal representations -- Data acquisition process -- Data collection -- Data recording/transmission -- Data preparation -- Random data qualification -- Random data analysis -- Sampling theory and analog-to-digital conversion -- Basic concepts -- Sampling theory -- Quantization -- Digital format -- Signal reconstruction -- Digital-to-analog conversion (DAC) -- Stationarity and ergodic random processes -- Ensemble method to test for stationarity -- Extension-in-time method -- Review of basic parametric statistics and moment-generating functions -- Nonparametric statistic and the runs test for stationarity -- Review of nonparametric statistics used for testing stationarity -- Correlation functions -- The correlation process -- Properties of the Autocorrelation Function -- Steps in the autocorrelation process -- Numerical correlation: direct calculation -- Cross-Correlation Function -- Convolution -- Convolution evaluation -- Numerical convolution -- Convolution algebra -- Digital filters -- Classification of filters -- Digital filters -- Fourier series: trigonometric -- Fourier analysis -- Evaluation of the Fourier coefficients -- Equivalent form of the Fourier trigonometric series -- Symmetrical properties as related to Fourier -- Coefficients -- Euler expansion -- Limitations -- Limiting process -- Inverse Fourier transform -- Summary of symmetry tables -- Fast Fourier transform -- Continuous Fourier transform -- Discrete Fourier transform -- Definition of Sampling Rate (or Sampling Frequency) -- Cooley-Tukey FFT (Decimimation in Time) -- The FFT (3z(Bbutterfly(3y (Bsignal flow diagram -- Decimation-in-frequency -- Truncation of the infinite fourier transform -- Practical applications -- Spectral analysis -- Spectral density estimation -- Cross-spectral analysis -- Properties of Sspectral density functions -- Factors affecting the spectral density function estimation -- Advanced topic -- Window functions and spectral leakage -- Generalities about windows -- Performance measures -- Window functions and weighting equations -- Transfer function via spectral analysis -- Methods -- Autocorrelation -- The cross-correlation function -- Spectral density functions -- The coherence function -- Coherence function from spectral analysis -- Description of the coherence function -- Misapplication of the coherence function -- Examples of the use of coherence functions -- Problems that limit the application of coherence --Conclusion -- Error in random data estimate analysis (Information Is Paraphrased from Bendat & Piersol) -- Cross-spectral density function estimates.