Digital Signal Processing

Part I Mathematical Methods for Signal Analysis Introduction to complex analysis; the delta function and the Green's function; Fourmet series; the Fourier transform, convolution and correlation, the sampling theorem, the Laplace transform; the Hilbert transform and quadrature detection, modulation and demodulation, the wavelet transform, the z-transform, the Wigner transform. Part II Computational Techniques in Linear Algebra Basic linear algebra, types of linear systems, formal methods of solution; direct methods of solution; iterative improvement; vector and matrix norms, conditioning and the condition number, the least squares method; iterative methods of solution; the conjugate gradient method; the computation of eigen values and eigen vectors. Part III Programming and Software Engineering Number systems and numerical error, programming languages, software design methods, structured and modular programming; software engineering for DSP in C. Part IV Digital Signal Processing; Methods Algorithms and Building a Library Digital frequency filtering, the DFT and FFT, computing with the FFT, spectral leakage and windowing; inverse filters, the Wiener filter, the matched filter, constrained deconvolution, homomorphic filtering; noise and chaos; Bayesian estimation methods, the maximum entropy method, spectral extrapolation; FIR and IIR filters, non-stationary signal processing; random fractal and multi-random-fractal signals.