Essentials of Signals and Systems

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This textbook offers a novel approach to the challenging subject of signals and systems, aiming to make it more accessible for students. It argues that traditional methods are often overly complex and proposes a clearer connection between the theory of signals and systems and linear algebra. The author begins with a review of linear algebra, highlighting how vectors change with different bases, particularly focusing on the significance of eigenvector bases in diagonalizing operators. This analogy helps students grasp that signals correspond to vectors, systems to matrices, and Fourier transforms serve as a basis change that diagonalizes linear time-invariant (LTI) operators. Key concepts in analyzing linear and time-invariant systems are emphasized, revealing both the algebraic and physical meanings of Fourier transforms. The text connects essential transforms—Fourier series, Discrete Time Fourier Transform, Discrete Fourier Transform, Laplace, and z-transforms—while illustrating their relationships. It also bridges continuous and discrete time domains and guides students through using the FFT function with straightforward examples. Incorporating learning objectives and problems, along with simple MATLAB codes, the book lays a solid foundation for students to explore advanced topics in future courses. Developed from successful lecture notes tested with over 600 students, it covers vital topics relevant to undergraduate stud