## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

## Book Description

Signals and Systems provides comprehensive coverage of all topics within the signals and systems' paper offered to undergraduates of electrical and electronics engineering.

1. Cover
2. Title Page
3. Contents
4. Dedication
5. Preface
6. Mathematical Preliminaries
1. Matrices
2. Trigonometry Formulae
3. Calculus
7. 1. Fundamentals of Signals and Systems
1. 1.1 Signals and Systems
2. 1.2 Classification of Signals
3. 1.3 Continuous Time Signals
4. 1.4 Basic Continuous Time Signals
5. 1.5 Classification of Continuous Time Systems
6. 1.6 Discrete Time Signals
7. 1.7 Concept of Frequency in Discrete Time Signals
8. 1.8 Standard Discrete Time Signals
9. 1.9 Classification of Discrete Time Signals
10. 1.10 Discrete Time Systems
11. 1.11 Representation of Discrete Time Systems
12. 1.12 Classifications of Discrete Time Systems
13. 1.13 Nyquist Rate
14. 1.14 Sampling Theorem
15. 1.15 Aliasing
16. 1.16 Convolution
17. 1.17 Correlation
19. Significant Points
21. Exercises
22. Multiple Choice Questions
8. 2. Fourier Series
1. 2.1 Fourier Series
2. 2.2 Dirichlet Conditions
3. 2.3 Determination of Fourier Co-efficients
4. 2.4 Wave Symmetry
5. 2.5 Exponential Form of Fourier Series
7. Significant Points
9. Exercises
10. Multiple Choice Questions
9. 3. Fourier Transform
1. 3.1 Fourier Transform
2. 3.2 Condition for the Existence of Fourier Integral
3. 3.3 Fourier Transform of Some Functions
4. 3.4 Fourier Transformation Theorem
5. 3.5 Fourier Transform of Periodic Signals
6. 3.6 Energy Density and Power Spectral Density
7. 3.7 Nyquist Theorem
8. 3.8 System Analysis Using Fourier Transform
9. 3.9 Relation between Differential Equation and System Function
11. Significant Points
13. Exercises
14. Multiple Choice Questions
10. 4. Laplace Transform
1. 4.1 Laplace Transform
2. 4.2 Region of Convergence (ROC)
3. 4.3 Inverse Laplace Transformation
4. 4.4 Basic Properties of Laplace Transforms
5. 4.5 Laplace Transform of a Derivative
6. 4.6 Laplace Transform of an Integral ∫ f (t) dt
7. 4.7 Laplace Transform of Some Common Time Function
8. 4.8 Laplace Transform of Two-Sided Functions (BLT)
9. 4.9 Initial Value Theorem
10. 4.10 Final Value Theorem
11. 4.11 Partial Fraction Expansions
12. 4.12 Relation between Step Response and Impulse Response
13. 4.13 Application of Laplace Transforms in Circuit
14. 4.14 Pure Resistive Element
15. 4.15 Pure Inductive Element
16. 4.16 Pure Capacitive Element
17. 4.17 Step Response of Series R-L Circuit
18. 4.18 Step Response of Series R-C Circuit
19. 4.19 Step Response of Series R-L-C Circuit
20. 4.20 Impulse Response of Series R-L Circuit
21. 4.21 Impulse Response of Series R-C Circuit
22. 4.22 Pulse Response of Series R-L Circuit
23. 4.23 Pulse Response of Series R-C Circuit
25. Significant Points
27. Exercises
28. Multiple Choice Questions
11. 5. System Modelling
1. 5.1 Transfer Function
2. 5.2 Impulse Response and Transfer Function
3. 5.3 Properties of Transfer Function (TF)
4. 5.4 Definition of Basic Elements of Block Diagram
5. 5.5 Basic Definition of Signal Flow Graph (SFG)
6. 5.6 Mason’s Gain Formula
7. 5.7 Modelling of Mechanical Systems
8. 5.8 Modelling of Electrical Systems
9. 5.9 Analogous Systems
10. 5.10 Representation by Nodal Method
12. Significant Points
14. Exercises
15. Multiple Choice Questions
12. 6. z-Transform
1. 6.1 z-Transform
2. 6.2 Region of Convergence (ROC)
3. 6.3 Properties of z-transform
4. 6.4 z-Transform of Right-Sided Exponential Sequences
5. 6.5 z-Transform of Left-Sided Exponential Sequences
6. 6.6 Finite Length Sequence
7. 6.7 z-Transform of Unit Sample Sequence
8. 6.8 z-Transform of Delayed Unit Sample Sequence
9. 6.9 z-Transform of Unit Step Sequence
10. 6.10 z-Transform of Folded Unit Step Sequence
11. 6.11 z-Transform of the Signal x(n)=Nanu(n)
12. 6.12 z-Transform of Unit Ramp Sequence
13. 6.13 z-Transform of Causal cosine Sequence
14. 6.14 z-Transform of Causal sine Sequence
15. 6.15 z-Transform of ancos(nω)u(n)
16. 6.16 z-Transform of ansin (nω) u(n)
17. 6.17 Inverse z-transform
18. 6.18 Inverse z-transform Using Partial Fraction Expansion
19. 6.19 Inverse z-transform Using Power Series Expansion
20. 6.20 System Function and Pole-Zero Plots from z-transform
21. 6.21 Pole-Zero Plot
22. 6.22 System Function of the LTI System
23. 6.23 Causality and Stability in Terms of z-transform
25. Significant Points
27. Exercises
28. Multiple Choice Questions
13. 7. Convolution
14. 8. Stability
1. 8.1 Effect of Location of Poles on Stability
2. 8.2 Routh-Hurwitz Criterion
3. Significant Points
5. Exercises
6. Multiple Choice Questions
15. 9. State Variable Approach (Continuous Systems)
2. 9.2 Concepts of State, State Variables and State Model
3. 9.3 State Model
4. 9.4 Non-Uniqueness of the State Model
5. 9.5 Different Representations of a State Model
6. 9.6 Eigen Value
7. 9.7 Transfer Function Derivation from the State Model
8. 9.8 Solution of the State Equation
9. 9.8.1 Solution of Homogeneous State Equation
10. 9.8.2 State Transition Matrix
11. 9.8.3 Properties of STM, φ (t)
12. 9.8.4 Solution of Non-homogeneous State Equation
13. 9.9 Controllability
14. 9.10 Observability
16. Significant Points
18. Exercises
19. Multiple Choice Questions
16. 10. State Variable Methods (Discrete Case)
17. 11. Discrete Fourier Transform and Fast Fourier Transform
1. 11.1 Fourier Transform of Discrete Time Signals
2. 11.2 Properties of Fourier Transform
3. 11.3 Inverse Fourier Transform
4. 11.4 Magnitude/Phase Transfer Functions Using Fourier Transform
5. 11.5 Discrete Fourier Transform
6. 11.6 Properties of Discrete Fourier Transform
7. 11.7 Relationship Between DFT and z-Transform
8. 11.8 Fast Fourier Transform (FFT)
9. 11.8.1 Properties of FFT
12. 11.11 Computational Complexity Compared to Direct Computation
13. 11.12 Memory Requirement and In Place Computations
14. 11.13 Bit Reversal
15. 11.14 Radix-2 DIF FFT Algorithm
16. Significant Points
18. Exercises
19. Multiple Choice Questions
18. 12. Structures and design of digital filters
1. 12.1 Classification of Filters
2. 12.2 Review of Analog Filters
3. 12.3 Specification of the Frequency Response Characteristics of the Filters
4. 12.4 Specifications of Phase Response
5. 12.5 Structure of Digital Filter
6. 12.6 Describing Equation
7. 12.7 Structure of FIR Filter
8. 12.8 Structure for IIR Filter
9. 12.9 Realization Procedure for Digital Filter
10. 12.10 Notch Filter
11. 12.11 Comb Filter
12. 12.12 All-pass Filter
13. 12.13 Design of an IIR Filter
14. 12.14 Design of FIR Filters
15. Significant Points