## Circuits, Signals, and Systems, Volume 2These twenty lectures have been developed and refined by Professor Siebert during the more than two decades he has been teaching introductory Signals and Systems courses at MIT. The lectures are designed to pursue a variety of goals in parallel: to familiarize students with the properties of a fundamental set of analytical tools; to show how these tools can be applied to help understand many important concepts and devices in modern communication and control engineering practice; to explore some of the mathematical issues behind the powers and limitations of these tools; and to begin the development of the vocabulary and grammar, common images and metaphors, of a general language of signal and system theory. Although broadly organized as a series of lectures, many more topics and examples (as well as a large set of unusual problems and laboratory exercises) are included in the book than would be presented orally. Extensive use is made throughout of knowledge acquired in early courses in elementary electrical and electronic circuits and differential equations. Contents: Review of the "classical" formulation and solution of dynamic equations for simple electrical circuits; The unilateral Laplace transform and its applications; System functions; Poles and zeros; Interconnected systems and feedback; The dynamics of feedback systems; Discrete-time signals and linear difference equations; The unilateral Z-transform and its applications; The unit-sample response and discrete-time convolution; Convolutional representations of continuous-time systems; Impulses and the superposition integral; Frequency-domain methods for general LTI systems; Fourier series; Fourier transforms and Fourier's theorem; Sampling in time and frequency; Filters, real and ideal; Duration, rise-time and bandwidth relationships: The uncertainty principle; Bandpass operations and analog communication systems; Fourier transforms in discrete-time systems; Random Signals; Modern communication systems.William Siebert is Ford Professor of Engineering at MIT. Circuits, Signals, and Systems is included in The MIT Press Series in Electrical Engineering and Computer Science, copublished with McGraw-Hill. |

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### Contents

Dynamic Equations and Their Solutions for Simple Circuits | 1 |

The Unilateral Laplace Transform | 43 |

System Functions | 72 |

Poles and Zeros | 105 |

Interconnected Systems and Feedback | 139 |

The Dynamics of Feedback Systems | 163 |

DiscreteTime Signals and Linear Difference Equations | 207 |

The Unilateral ZTransform and Its Applications | 231 |

FrequencyDomain Methods for General LTI Systems | 364 |

Fourier Transforms and Fouriers Theorem | 393 |

Sampling in Time and Frequency | 429 |

Filters Real and Ideal | 471 |

DurationBandwidth Relationships and the Uncertainty Principle | 488 |

Bandpass Operations and Analog Communication Systems | 507 |

Fourier Transforms in DiscreteTime Systems | 558 |

Averages and Random Signals | 595 |

The Unit Sample Response and DiscreteTime Convolution | 260 |

Convolutional Representations of ContinuousTime Systems | 286 |

Impulses and the Superposition Integral | 314 |

Modern Communication Systems | 627 |

Epilogue | 642 |

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