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Record Nr. |
UNINA9910634054003321 |
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Autore |
Sundararajan D. |
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Titolo |
Signals and systems : a practical approach / / D. Sundararajan |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2023] |
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©2023 |
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ISBN |
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9783031193774 |
9783031193767 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (479 pages) |
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Disciplina |
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Soggetti |
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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 the Second Edition -- Preface to the First Edition -- Contents -- Abbreviations -- 1 Discrete Signals -- 1.1 Introduction -- 1.2 Basic Signals -- 1.2.1 Unit-Impulse Signal -- 1.2.2 Unit-Step Signal -- 1.2.3 Unit-Ramp Signal -- 1.2.4 Sinusoids and Exponentials -- 1.2.4.1 The Polar Form of Sinusoids -- 1.2.4.2 The Rectangular Form of Sinusoids -- 1.2.4.3 The Sum of Sinusoids of the Same Frequency -- 1.2.4.4 Exponentials -- 1.2.4.5 The Complex Sinusoids -- 1.2.4.6 Exponentially Varying Amplitude Sinusoids -- 1.2.4.7 The Sampling Theorem and the Aliasing Effect -- 1.2.4.8 Frequency-Sampling Theorem -- 1.3 Classification of Signals -- 1.3.1 Continuous, Discrete, and Digital Signals -- 1.3.2 Periodic and Aperiodic Signals -- 1.3.3 Energy and Power Signals -- 1.3.4 Even- and Odd-Symmetric Signals -- 1.3.5 Causal and Noncausal Signals -- 1.3.6 Deterministic and Random Signals -- 1.4 Signal Operations -- 1.4.1 Time Shifting -- 1.4.1.1 Circular Shifting -- 1.4.2 Time Reversal -- 1.4.2.1 Circular Time Reversal -- 1.4.3 Time Scaling -- 1.4.4 Zero Padding -- 1.5 Numerical Integration -- 1.6 The Organization of this Book -- 1.7 Summary -- Exercises -- 2 Continuous Signals -- 2.1 Basic Signals -- 2.1.1 The Unit-Step Signal -- 2.1.2 The Unit-Impulse Signal -- 2.1.2.1 The Impulse Representation of Signals -- 2.1.2.2 The Unit-Impulse as the Derivative of the Unit-Step -- 2.1.2.3 The Scaling Property of the Impulse -- 2.1.3 The Unit-Ramp Signal -- 2.1.4 Sinusoids -- 2.1.4.1 |
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The Polar Form of Sinusoids -- 2.1.4.2 The Rectangular Form of Sinusoids -- 2.1.4.3 The Sum of Sinusoids of the Same Frequency -- 2.1.4.4 The Complex Sinusoids -- 2.1.4.5 Exponentially Varying Amplitude Sinusoids -- 2.2 Classification of Signals -- 2.2.1 Continuous Signals -- 2.2.2 Periodic and Aperiodic Signals -- 2.2.3 Energy and Power Signals. |
2.2.4 Even- and Odd-Symmetric Signals -- 2.2.5 Causal and Noncausal Signals -- 2.3 Signal Operations -- 2.3.1 Time Shifting -- 2.3.2 Time Reversal -- 2.3.3 Time Scaling -- 2.4 Summary -- Exercises -- 3 Time-Domain Analysis of Discrete Systems -- 3.1 Difference Equation Model -- 3.1.1 System Response -- 3.1.1.1 Zero-State Response -- 3.1.1.2 Zero-Input Response -- 3.1.1.3 Complete Response -- 3.1.1.4 Transient and Steady-State Responses -- 3.1.1.5 Coding and Simulation -- 3.1.1.6 Zero-Input Response by Solving the Difference Equation -- 3.1.2 Impulse Response -- 3.1.3 Characterization of Systems by Their Responses to Impulse and Unit-Step Signals -- 3.2 Classification of Systems -- 3.2.1 Linear and Nonlinear Systems -- 3.2.2 Time-Invariant and Time-Varying Systems -- 3.2.3 Causal and Noncausal Systems -- 3.2.4 Instantaneous and Dynamic Systems -- 3.2.5 Inverse Systems -- 3.2.6 Continuous and Discrete Systems -- 3.3 Convolution-Summation Model -- 3.3.1 Properties of Convolution-Summation -- 3.3.2 The Difference Equation and the Convolution-Summation -- 3.3.3 Response to Complex Exponential Input -- 3.4 System Stability -- 3.5 Realization of Discrete Systems -- 3.5.1 Decomposition of Higher-Order Systems -- 3.5.2 Feedback Systems -- 3.6 Summary -- Exercises -- 4 Time-Domain Analysis of Continuous Systems -- 4.1 Classification of Systems -- 4.1.1 Linear and Nonlinear Systems -- 4.1.2 Time-Invariant and Time-Varying Systems -- 4.1.3 Causal and Noncausal Systems -- 4.1.4 Instantaneous and Dynamic Systems -- 4.1.5 Lumped-Parameter and Distributed-Parameter Systems -- 4.1.6 Inverse Systems -- 4.2 Differential Equation Model -- 4.3 Convolution-Integral Model -- 4.3.1 Properties of Convolution-Integral -- 4.3.2 Convolution of a Function with a Narrow Unit Area Pulse -- 4.4 System Response -- 4.4.1 Impulse Response -- 4.4.2 Response to Unit-Step Input. |
4.4.3 Characterization of Systems by Their Responses to Impulse and Unit-Step Signals -- 4.4.4 Response to Complex Exponential Input -- 4.5 System Stability -- 4.6 Realization of Continuous Systems -- 4.6.1 Decomposition of Higher-Order Systems -- 4.6.2 Feedback Systems -- 4.7 Summary -- Exercises -- 5 The Discrete Fourier Transform -- 5.1 The Time-Domain and the Frequency-Domain -- 5.2 The Fourier Analysis -- 5.2.1 The Four Versions of Fourier Analysis -- 5.3 The Discrete Fourier Transform -- 5.3.1 The Approximation of Arbitrary Waveforms with Finite Number of Samples -- 5.3.2 The DFT and the IDFT -- 5.3.2.1 Center-Zero Format of the DFT and IDFT -- 5.3.3 DFT of Some Basic Signals -- 5.4 Properties of the Discrete Fourier Transform -- 5.4.1 Linearity -- 5.4.2 Periodicity -- 5.4.3 Circular Time Reversal -- 5.4.4 Duality -- 5.4.5 Sum and Difference of Sequences -- 5.4.6 Upsampling of a Sequence -- 5.4.7 Zero Padding the Data -- 5.4.8 Circular Shift of a Sequence -- 5.4.9 Circular Shift of a Spectrum -- 5.4.10 Symmetry -- 5.4.11 Circular Convolution of Time-Domain Sequences -- 5.4.12 Circular Convolution of Frequency-Domain Sequences -- 5.4.13 Parseval's Theorem -- 5.5 Applications of the Discrete Fourier Transform -- 5.5.1 Computation of the Linear Convolution Using the DFT -- 5.5.2 Interpolation and Decimation -- 5.5.2.1 Interpolation -- 5.5.2.2 Decimation -- 5.5.2.3 Interpolation and Decimation -- 5.5.3 Image Boundary Representation -- 5.6 Summary -- Exercises -- 6 Fourier Series -- 6.1 Fourier Series -- 6.1.1 |
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FS as the Limiting Case of the DFT -- 6.1.2 The Compact Trigonometric Form of the FS -- 6.1.3 The Trigonometric Form of the FS -- 6.1.4 Periodicity of the FS -- 6.1.5 Existence of the FS -- 6.1.6 Gibbs Phenomenon -- 6.2 Properties of the Fourier Series -- 6.2.1 Linearity -- 6.2.2 Symmetry -- 6.2.2.1 Even Symmetry -- 6.2.2.2 Odd Symmetry. |
6.2.2.3 Half-Wave Symmetry -- 6.2.3 Time Shifting -- 6.2.4 Frequency Shifting -- 6.2.5 Time Reversal -- 6.2.6 Convolution in the Time-Domain -- 6.2.7 Convolution in the Frequency-Domain -- 6.2.8 Duality -- 6.2.9 Time Scaling -- 6.2.10 Time-Differentiation -- 6.2.11 Time-Integration -- 6.2.11.1 Rate of Convergence of the Fourier Series -- 6.2.12 Parseval's Theorem -- 6.3 Approximation of the Fourier Series -- 6.3.1 Aliasing Effect -- 6.4 Applications of the Fourier Series -- 6.4.1 Analysis of Rectified Power Supply -- 6.5 Summary -- Exercises -- 7 The Discrete-Time Fourier Transform -- 7.1 The Discrete-Time Fourier Transform -- 7.1.1 The DTFT as the Limiting Case of the DFT -- 7.1.2 The Dual Relationship between the DTFT and the FS -- 7.1.3 The DTFT of a Discrete Periodic Signal -- 7.1.4 Determination of the DFT from the DTFT -- 7.2 Properties of the Discrete-Time Fourier Transform -- 7.2.1 Linearity -- 7.2.2 Time Shifting -- 7.2.3 Frequency Shifting -- 7.2.4 Convolution in the Time-Domain -- 7.2.5 Convolution in the Frequency-Domain -- 7.2.6 Symmetry -- 7.2.7 Time Reversal -- 7.2.8 Time Expansion -- 7.2.9 Frequency Differentiation -- 7.2.10 Difference -- 7.2.11 Summation -- 7.2.12 Parseval's Theorem and the Energy Transfer Function -- 7.3 Approximation of the Discrete-Time Fourier Transform -- 7.3.1 Approximation of the Inverse DTFT by the IDFT -- 7.4 Applications of the Discrete-Time Fourier Transform -- 7.4.1 Transfer Function and the System Response -- 7.4.2 Digital Filter Design Using DTFT -- 7.4.2.1 Rectangular Window -- 7.4.2.2 Hamming Window -- 7.4.3 Digital Differentiator -- 7.4.4 Hilbert Transform -- 7.4.5 Downsampling -- 7.5 Summary -- Exercises -- 8 The Fourier Transform -- 8.1 The Fourier Transform -- 8.1.1 The FT as a Limiting Case of the DTFT -- 8.1.2 Existence of the FT -- 8.2 Properties of the Fourier Transform -- 8.2.1 Linearity. |
8.2.2 Duality -- 8.2.3 Symmetry -- 8.2.4 Time Shifting -- 8.2.5 Frequency Shifting -- 8.2.6 Convolution in the Time Domain -- 8.2.7 Convolution in the Frequency Domain -- 8.2.8 Conjugation -- 8.2.9 Time Reversal -- 8.2.10 Time Scaling -- 8.2.11 Time Differentiation -- 8.2.12 Time Integration -- 8.2.13 Frequency Differentiation -- 8.2.14 Parseval's Theorem and the Energy Transfer Function -- 8.3 Fourier Transform of Mixed Class of Signals -- 8.3.1 The FT of a Continuous Periodic Signal -- 8.3.2 Determination of the FS from the FT -- 8.3.3 The FT of a Sampled Signal and the Aliasing Effect -- 8.3.4 The FT and the DTFT of Sampled Aperiodic Signals -- 8.3.5 The FT and the DFT of Sampled Periodic Signals -- 8.3.6 Approximation of the Continuous Signal from Its Sampled Version -- 8.4 Approximation of the Fourier Transform -- 8.5 Applications of the Fourier Transform -- 8.5.1 Transfer Function and the System Response -- 8.5.2 Ideal Filters and Their Unrealizability -- 8.5.3 Modulation and Demodulation -- 8.5.3.1 Double Sideband, Suppressed Carrier (DSB-SC), Amplitude Modulation -- 8.5.3.2 Double Sideband, with Carrier (DSB-WC), Amplitude Modulation -- 8.5.3.3 Pulse Amplitude Modulation (PAM) -- 8.6 Summary -- Exercises -- 9 The z-Transform -- 9.1 Fourier Analysis and the z-Transform -- 9.2 The z-Transform -- 9.3 Properties of the z-Transform -- 9.3.1 Linearity -- 9.3.2 Left Shift of a Sequence -- 9.3.3 Right Shift of a Sequence -- 9.3.4 Convolution -- 9.3.5 Multiplication by n -- 9.3.6 Multiplication by an -- 9.3.7 Summation -- |
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9.3.8 Initial Value -- 9.3.9 Final Value -- 9.3.10 Transform of Semiperiodic Functions -- 9.4 The Inverse z-Transform -- 9.4.1 Finding the Inverse z-Transform -- 9.4.1.1 The Partial Fraction Method -- 9.4.1.2 The Long Division Method -- 9.5 Applications of the z-Transform -- 9.5.1 Transfer Function. |
9.5.2 Characterization of a System by Its Poles and Zeros. |
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