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Record Nr. |
UNINA9910523786303321 |
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Autore |
Palani S |
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Titolo |
Signals and systems / / S. Palani |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Edizione |
[Second edition.] |
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Descrizione fisica |
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1 online resource (1093 pages) |
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Disciplina |
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Soggetti |
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Signal theory (Telecommunication) |
System analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface to Second Edition -- Preface to First Edition -- The notable features of this book includes the following: -- Contents -- About the Author -- 1 Representation of Signals -- 1.1 Introduction -- 1.2 Terminologies Related to Signals and Systems -- 1.2.1 Signal -- 1.2.2 System -- 1.3 Continuous and Discrete Time Signals -- 1.4 Basic Continuous Time Signals -- 1.4.1 Unit Impulse Function -- 1.4.2 Unit Step Function -- 1.4.3 Unit Ramp Function -- 1.4.4 Unit Parabolic Function -- 1.4.5 Unit Rectangular Pulse (or Gate) Function -- 1.4.6 Unit Area Triangular Function -- 1.4.7 Unit Signum Function -- 1.4.8 Unit Sinc Function -- 1.4.9 Sinusoidal Signal -- 1.4.10 Real Exponential Signal -- 1.4.11 Complex Exponential Signal -- 1.5 Basic Discrete Time Signals -- 1.5.1 The Unit Impulse Sequence -- 1.5.2 The Basic Unit Step Sequence -- 1.5.3 The Basic Unit Ramp Sequence -- 1.5.4 Unit Rectangular Sequence -- 1.5.5 Sinusoidal Sequence -- 1.5.6 Discrete Time Real Exponential Sequence -- 1.6 Basic Operations on Continuous Time Signals -- 1.6.1 Addition of CT Signals -- 1.6.2 Multiplications of CT Signals -- 1.6.3 Amplitude Scaling of CT Signals -- 1.6.4 Time Scaling of CT Signals -- 1.6.5 Time Shifting of CT Signals -- 1.6.6 Signal Reflection or Folding -- 1.6.7 Inverted CT Signal -- 1.6.8 Multiple Transformation -- 1.7 Basic Operations on Discrete Time Signals -- 1.7.1 Addition of Discrete Time Sequence -- 1.7.2 Multiplication of DT Signals -- 1.7.3 Amplitude Scaling of DT Signal -- |
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1.7.4 Time Scaling of DT Signal -- 1.7.5 Time Shifting of DT Signal -- 1.7.6 Multiple Transformation -- 1.8 Classification of Signals -- 1.8.1 Deterministic and Non-deterministic Continuous Signals -- 1.8.2 Periodic and Non-periodic Continuous Signals -- 1.8.3 Fundamental Period of Two Periodic Signals -- 1.8.4 Odd and Even Functions of Continuous Time Signals. |
1.8.5 Energy and Power of Continuous Time Signals -- 1.9 Classification of Discrete Time Signals -- 1.9.1 Periodic and Non-Periodic DT Signals -- 1.9.2 Odd and Even DT Signals -- 1.9.3 Energy and Power of DT Signals -- 2 Continuous and Discrete Time Systems -- 2.1 Introduction -- 2.2 Linear Time Invariant Continuous (LTIC) Time System -- 2.3 Linear Time Invariant Discrete (LTID) Time System -- 2.4 Properties (Classification) of Continuous Time System -- 2.4.1 Linear and Non-linear Systems -- 2.4.2 Time Invariant and Time Varying Systems -- 2.4.3 Static and Dynamic Systems (Memoryless and System with Memory) -- 2.4.4 Causal and Non-causal Systems -- 2.4.5 Stable and Unstable Systems -- 2.4.6 Invertibility and Inverse System -- 2.5 Discrete Time System -- 2.6 Properties of Discrete Time System -- 2.6.1 Linear and Non-linear Systems -- 2.6.2 Time Invariant and Time Varying DT Systems -- 2.6.3 Causal and Non-causal DT Systems -- 2.6.4 Stable and Unstable Systems -- 2.6.5 Static and Dynamic Systems -- 2.6.6 Invertible and Inverse Discrete Time Systems -- 3 Time Domain Analysis of Continuous and Discrete Time Systems -- 3.1 Introduction -- 3.2 Time Response of Continuous Time System -- 3.3 The Unit Impulse Response -- 3.4 Unit Impulse Response and the Convolution Integral -- 3.5 Step by Step Procedure to Solve Convolution -- 3.6 Properties of Convolution -- 3.6.1 The Commutative Property -- 3.6.2 The Distributive Property -- 3.6.3 The Associative Property -- 3.6.4 The Shift Property -- 3.6.5 The Width Property -- 3.7 Analytical Method of Convolution Operation -- 3.7.1 Convolution Operation of Non-causal Signals -- 3.8 Causality of an Linear Time Invariant Continuous Time System -- 3.9 Stability of a Linear Time Invariant System -- 3.10 Step Response from Impulse Response -- 3.11 Representation of Discrete Time Signals in Terms of Impulses. |
3.12 The Discrete Time Unit Impulse Response -- 3.13 The Convolution Sum -- 3.14 Properties of Convolution Sum -- 3.14.1 Distributive Property -- 3.14.2 Associative Property of Convolution -- 3.14.3 Commutative Property of Convolution -- 3.14.4 Shifting Property of Convolution -- 3.14.5 The Width Property of Convolution -- 3.14.6 Convolution with an Impulse -- 3.14.7 Convolution with Delayed Impulse -- 3.14.8 Convolution with Unit Step -- 3.14.9 Convolution with Delayed Step -- 3.14.10 System Causality from Convolution -- 3.14.11 BIBO Stability from Convolution -- 3.14.12 Step Response in Terms of Impulse Response of a LTDT System -- 3.15 Response Using Convolution Sum -- 3.15.1 Analytical Method Using Convolution Sum -- 3.15.2 Convolution Sum of Two Sequences by Multiplication Method -- 3.15.3 Convolution Sum by Tabulation Method -- 3.15.4 Convolution Sum of Two Sequences by Matrix Method -- 3.16 Convolution Sum by Graphical Method -- 3.17 Deconvolution -- 3.18 Step Response of the System -- 3.19 Stability from Impulse Response -- 3.20 System Causality -- 4 Fourier Series Analysis of Continuous Time Signals -- 4.1 Introduction -- 4.2 Periodic Signal Representation by Fourier Series -- 4.3 Different Forms of Fourier Series Representation -- 4.3.1 Trigonometric Fourier Series -- 4.3.2 Complex Exponential Fourier Series -- 4.3.3 Polar or Harmonic Form Fourier Series -- 4.4 Properties of Fourier Series -- 4.4.1 Linearity -- 4.4.2 Time Shifting Property -- 4.4.3 Time Reversal |
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Property -- 4.4.4 Time Scaling Property -- 4.4.5 Multiplication Property -- 4.4.6 Conjugation Property -- 4.4.7 Differentiation Property -- 4.4.8 Integration Property -- 4.4.9 Parseval's Theorem -- 4.5 Existence of Fourier Series-the Dirichlet Conditions -- 4.6 Convergence of Continuous Time Fourier Series -- 4.7 Fourier Series Spectrum. |
5 Fourier Series Analysis of Discrete Time Signals -- 5.1 Introduction -- 5.2 Periodicity of Discrete Time Signal -- 5.3 DT Signal Representation by Fourier Series -- 5.4 Fourier Spectra of x[n] -- 5.5 Properties of Discrete Time Fourier Series -- 5.5.1 Linearity Property -- 5.5.2 Time Shifting Property -- 5.5.3 Time Reversal Property -- 5.5.4 Multiplication Property -- 5.5.5 Conjugation Property -- 5.5.6 Difference Property -- 5.5.7 Parseval's Theorem -- 6 Fourier Transform Analysis of Continuous Time Signals -- 6.1 Introduction -- 6.2 Representation of Aperiodic Signal by Fourier Integral-The Fourier Transform -- 6.3 Convergence of Fourier Transforms-The Dirichlet Conditions -- 6.4 Fourier Spectra -- 6.5 Connection Between the Fourier Transform and Laplace Transform -- 6.6 Properties of Fourier Transform -- 6.6.1 Linearity -- 6.6.2 Time Shifting -- 6.6.3 Conjugation and Conjugation Symmetry -- 6.6.4 Differentiation in Time -- 6.6.5 Differentiation in Frequency -- 6.6.6 Time Integration -- 6.6.7 Time Scaling -- 6.6.8 Frequency Shifting -- 6.6.9 Duality -- 6.6.10 The Convolution -- 6.6.11 Parseval's Theorem (Relation) -- 6.7 Fourier Transform of Periodic Signal -- 6.7.1 Fourier Transform Using Differentiation and Integration Properties -- 7 Fourier Transform Analysis of Discrete Time Signals and Systems-DTFT, DFT and FFT -- 7.1 Introduction -- 7.2 Representation of Discrete Time Aperiodic Signals -- 7.3 Connection Between the Fourier Transform and the z-Transform -- 7.4 Properties of Discrete Time Fourier Transform -- 7.4.1 Linearity -- 7.4.2 Time Shifting Property -- 7.4.3 Frequency Shifting -- 7.4.4 Time Reversal -- 7.4.5 Time Scaling -- 7.4.6 Multiplication by n -- 7.4.7 Conjugation -- 7.4.8 Time Convolution -- 7.4.9 Parseval's Theorem -- 7.4.10 Modulation Property -- 7.5 Inverse Discrete Time Fourier Transform (IDTFT). |
7.6 LTI System Characterized by Difference Equation -- 7.7 Discrete Fourier Transform (DFT) -- 7.7.1 The Discrete Fourier Transform Pairs -- 7.7.2 Four Point, Six Point and Eight Point Twiddle Factors -- 7.7.3 Zero Padding -- 7.8 Properties of DFT -- 7.8.1 Periodicity -- 7.8.2 Linearity -- 7.8.3 Complex Conjugate Symmetry -- 7.8.4 Circular Time Shifting -- 7.8.5 Circular Frequency Shifting -- 7.8.6 Circular Correlation -- 7.8.7 Multiplication of Two DFTs -- 7.8.8 Parseval's Theorem -- 7.9 Circular Convolution -- 7.9.1 Circular Convolution-Circle Method -- 7.9.2 Circular Convolution-Matrix Multiplication Method -- 7.9.3 Circular Convolution-DFT-IDFT Method -- 7.10 Fast Fourier Transform -- 7.10.1 FFT Algorithm-Decimation in Time -- 7.10.2 FFT Algorithm-Decimation in Frequency -- 8 The Laplace Transform Method for the Analysis of Continuous Time Signals and Systems -- 8.1 Introduction -- 8.2 Definition and Derivations of the LT -- 8.2.1 LT of Causal and Non-causal Systems -- 8.3 The Existence of LT -- 8.4 The Region of Convergence -- 8.4.1 Properties of ROCs for LT -- 8.5 The Unilateral Laplace Transform -- 8.6 Properties of Laplace Transform -- 8.6.1 Linearity -- 8.6.2 Time Shifting -- 8.6.3 Frequency Shifting -- 8.6.4 Time Scaling -- 8.6.5 Frequency Scaling -- 8.6.6 Time Differentiation -- 8.6.7 Time Integration -- 8.6.8 Time Convolution -- 8.6.9 Complex Frequency Differentiation -- 8.6.10 Complex Frequency Shifting -- 8.6.11 Conjugation Property -- 8.6.12 Initial Value Theorem -- 8.6.13 Final Value Theorem -- 8.7 Laplace Transform of Periodic Signal -- 8.8 Inverse Laplace Transform -- 8.8.1 Graphical Method of Determining the Residues -- 8.9 Solving Differential Equation -- 8.9.1 |
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Solving Differential Equation without Initial Conditions -- 8.9.2 Solving Differential Equation with the Initial Conditions -- 8.9.3 Zero Input and Zero State Response. |
8.9.4 Natural and Forced Response Using LT. |
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