Orthogonal Transforms for Digital Signal ProcessingThis book is intended for those wishing to acquire a working knowledge of orthogonal transforms in the area of digital signal processing. The authors hope that their introduction will enhance the opportunities for interdiscipli nary work in this field. The book consists of ten chapters. The first seven chapters are devoted to the study of the background, motivation and development of orthogonal transforms, the prerequisites for which are a basic knowledge of Fourier series transform (e.g., via a course in differential equations) and matrix al gebra. The last three chapters are relatively specialized in that they are di rected toward certain applications of orthogonal transforms in digital signal processing. As such, a knowlegde of discrete probability theory is an essential additional prerequisite. A basic knowledge of communication theory would be helpful, although not essential. Much of the material presented here has evolved from graduate level courses offered by the Departments of Electrical Engineering at Kansas State University and the University of Texas at Arlington, during the past five years. With advanced graduate students, all the material was covered in one semester. In the case of first year graduate students, the material in the first seven chapters was covered in one semester. This was followed by a prob lems project-oriented course directed toward specific applications, using the material in the last three chapters as a basis. |
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2-dimensional DFT Ahmed algorithm to compute amplitude Applications of Walsh b₁ binary bit-reversal C₁ C₂ C₂(k Chapter classifier consider convolution corresponding covariance matrices covariance matrix Cx(k cyclic data compression data sequence X(m decision boundary defined denotes developed diagonal digital signal discrete Fourier discriminant functions dyadic einwot equations example Fast Fourier Transform feature selection feature space follows Fourier series FWHT given Gray code Haar functions Hadamard IEEE IEEE Trans illustrated inverse iteration k₁ k₂ m₁ m₂ matrix factors mean-square error MWHT N₁ N₂ obtain orthogonal transforms phase spectra power and phase power spectrum Prob Proc Rademacher functions representation respectively sampling shown in Fig signal flow graph signal x(t slant spectral point Substitution of Eq t₁ theorem training set transform matrix vector Walsh Functions Walsh-Hadamard Transform WHT)n Wiener filtering X(m₁ X₁ Xp(t yields Z₁