Circuits, Systems and Signal Processing

This book is a collection of tutorial-like chapters on all core topics of signals and systems and the electronic circuits. All the topics dealt with in the book are parts of the core syllabi of standard programs in Electrical Engineering, Electrical and Computer Engineering, and Electronics and Telecommunication Engineering domains. This book is intended to serve as a secondary reader or supplementary text for core courses in the area of signals and systems, electronic circuits, and analog and digital signal processing. When studying or teaching a particular topic, the students and instructors of such courses would find it interesting and worthwhile to study the related tutorial chapter in this book in order to enhance their understanding of the fundamentals, simplification of procedures, alternative approaches and relation to other associated topics. In addition, the book can also be used as a primary or secondary text in short-term or refresher courses, and as a self-study guide for professionals wishing to gain a comprehensive review of the signals and systems domain.

Section I: Signals and Systems.- 1. Basic Concepts in Signals and Systems.- 2. The Mysterious Impulse Function and Its Mysteries.- 3. State Variables - Part I.- 4. State Variables - Part II.- 5. Carry Out Partial Fraction Expansion of Functions with Repeated Poles.- 6. A Very Simple Method of Finding the Residues at Repeated Poles of a Rational Function in z-1.- Section II: Passive Circuits.- 7. Circuit Analysis without Transforms.- 8. Transient Response of RLC Networks Revisited.- 9. Appearances can be Deceptive: A Circuit Paradox.- 10. Appearances can be Deceptive- An Initial Value Problem.- 11. Resonance.- 12. The Many Faces of the Single Tuned Circuit.- 13. Analyzing the Parallel-T RC Network.- 14. Design of Parallel-T Resistance Capacitance Networks for Maximum Selectivity.- 15. Perfect Transformer, Current Discontinuity and Degeneracy.- 16. Analytical Solution to the Problem of Charging a Capacitor through a Lamp.- 17. Difference Equations, z-Transforms and Resistive Ladders.- 18. A Third Order Driving Point Synthesis Problem.- 19. Interference Rejection in a UWB System: An Example of LC Driving Point Synthesis.- 20. Low Order Butterworth Filters: From Magnitude to Transfer Function.- 21. Band-Pass/Band-Stop Filter Design by Frequency Transformation.- 22. Optimum Passive Differentiators.- Section III: Active Circuits.- 23. Amplifier Fundamentals.- 24. Appearances can be Deceptive: The Case of a BJT Biasing Circuit.- 25. BJT Biasing Revisited.- 26. Analysis of a High Frequency Transistor Stage.- 27. Transistor Wien Bridge Oscillator.- 28. Analyzing Sinusoidal Oscillator Circuits: A Different Approach.- 29. Triangular to Sine Wave Converter.- 30. Dynamic Output Resistance of the Wilson Current Mirror.- Section IV: Digital Signal Processing.- 31. The ABCD's of Digital Signal Processing (Part 1).- 32. The ABCD's of Digital Signal Processing (Part 2).- 33. On Second Order Digital Band-Pass and Band-Stop Filters.- 34. Derivation of Second Order Canonic All-Pass Digital Filter Realizations.- 35. Derivation of the FIR Lattice Structure.- 36. Solution to a Problem in FIR Lattice Synthesis.- 37. FIR Lattice Structures with Single Multiplier Sections.- 38. A Note on the FFT.- Appendix : Some Mathematical Topics Simplified.- A.1. A Semi-Analytical Method for Finding the Roots of a Polynomial.- A.2. A Fresh Look at the Euler's Relation.- A.3. Approximating the Square Root of the Sum of Two Squares .- A.4. On the Solution of Quartic and Cubic Equations.- A.5. Many Ways of Solving an Ordinary Linear Second Order Differential Equation with Constant Coefficients.- A.6. Proofs of Two Chebyshev Polynomial Identities Useful in Digital Filter Design.- A.7. Computation of the Coefficients of Chebyshev Polynomials .- Sources.