Linear systems and signal sampling, Fourier transforms and frequency analysis, Laplace transforms, FFT and inverse FFT algorithms, convolution/de-convolution, impulse response, random signals, noise characterization, auto- and cross-correlation, power spectra, adaptive filters, detection and clustering. These topics will be covered with extensive coverage on their applications to various topics in mechanical or biomedical engineering. In mechanical engineering such topics include vibrations, signal timing, spectral/phase analysis, signature analysis, thermal waves, acoustic emission, engine performance analysis, resonant acoustic spectroscopy (RAS), crack detection and location with ultrasound, flow measurements, condition-based monitoring and maintenance, fracture mechanics, etc. In biomedical engineering these topics include modeling of biomedical control systems, analysis of evoked potentials, analysis of electroencephalograms and electrocardiograms.