## Signals and Systems with MATLAB ApplicationsThis text contains a comprehensive discussion of continuous and discrete time signals and systems with many examples from MATLAB--software used to write efficient, compact programs to solve electrical and computer engineering problems of varying complexity. Intended for junior- and senior-level electrical engineering students and for self-study by working professionals, it discusses Laplace transformation and circuit analysis, impulse response, Fourier series, Z transform, and the Discrete Fourier transform and FFT. Solutions to all exercises are included in this revised edition. |

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### Contents

The Laplace Transform of Common Functions of Time 212 | 13 |

The Laplace Transform of Common Waveforms 223 | 27 |

Exercises 622 | 34 |

Solutions to Exercises 237 | 43 |

Alternate Method of Partial Fraction Expansion 315 | 19 |

Exercises 320 | 21 |

Solutions to Exercises 624 | 22 |

Chapter 4 | 4 |

Chapter 8 | 8 |

Chapter 9 | 9 |

Fourier Transform Pairs of Common Functions 817 | 23 |

The System Function and Applications to Circuit Analysis 834 | 41 |

Discrete Time Systems and the Z Transform | 1 |

Transform of Common Discrete Time Functions 911 | 19 |

The Transfer Function of Discrete Time Systems 938 | 41 |

Exercises 952 | 57 |

Complex Admittance Ys 410 | 11 |

Summary 416 | 17 |

Exercises 418 | 23 |

Chapter 5 | 1 |

Solution of Single State Equations | 7 |

Summary 1169 | 11 |

The State Transition Matrix | 13 |

Eigenvectors 518 | 19 |

Circuit Analysis with State Variables 522 | 27 |

Relationship between State Equations and Laplace Transform 528 | 33 |

Exercises 539 | 41 |

Chapter 7 | 3 |

Chapter 6 | 6 |

Fourier Series | 1 |

Waveforms in Trigonometric Form of Fourier Series 711 | 15 |

Circuit Analysis with Trigonometric Fourier Series 729 | 29 |

Computation of Average Power from Fourier Series 742 | 43 |

The Discrete Fourier Transform DFT 101 | 71 |

The Fast Fourier Transform FFT 1017 | 87 |

Chapter 11 | 1 |

Graphical Evaluation of the Convolution Integral | 6 |

Design of Type I Chebyshev Analog LowPass Filters 1122 | 27 |

HighPass BandPass and BandElimination Filters 1139 | 45 |

Signals and Systems with MATLAB Applications Second Edition | 70 |

Exercises 1173 | 73 |

Appendix | 1 |

Subplots A18 | 18 |

Appendix | 33 |

Cramers Rule C16 | 1 |

Special Forms of Matrices | 5 |

Gaussian Elimination Method C19 | 19 |

Signals and Systems with MATLAB Applications Second Edition | 28 |

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### Common terms and phrases

amplitude analog filter Butterworth low-pass filter capacitor Circuit for Example circuit of Figure coefficients complex frequency domain compute convolution integral cosine cutoff frequency defined delta function denominator denoted Derive the Fourier differential digital filter eigenvalues eigenvectors equations evaluate exponential express F(co Fourier transform frequency components function f(t half-wave symmetry harmonics high-pass impulse response initial conditions input LAB Applications linear low-pass filter magnitude MATLAB Applications multiplication numerator obtain odd function output partial fraction expansion pass-band period plot poles polynomial Proof pulse rad/s rational function residues resistor ripple Second Edition shifting property shown in Figure Signals and Systems Solution square waveform substitution syms Systems with MAT Systems with MATLAB tables of integrals TLAB transfer function transform pair transition matrix trigonometric Fourier series Type I Chebyshev unit step function vector voltage Waveform for Example waveform of Figure zero