Background | |

Complex Numbers | |

Sinusoids | |

Sketching Signals | |

Cramer''s Rule | |

Partial Fraction Expansion | |

Vectors and Matrices | |

Miscellaneous | |

Introduction to Signals and Systems | |

Size of a Signal | |

Classification of Signals | |

Some Useful Signal Operations | |

Some Useful Signal Models | |

Even and Odd Functions | |

Systems | |

Classification of Systems | |

System Model: Input-Output Description | |

Time-Domain Analysis of Continuous-Time Systems | |

Introduction | |

System Response to Internal Conditions: Zero-Input Response | |

The Unit Impulse Response h(t) | |

System Response to External Input: Zero-State Response | |

Classical Solution of Differential Equations | |

System Stability | |

Intuitive Insights into System Behavior | |

Appendix 2.1: Determining the Impulse Response | |

Signal Representation by Fourier Series | |

Signals and Vectors | |

Signal Comparison: Correlation | |

Signal Representation by Orthogonal Signal Set | |

Trigonometric Fourier Series | |

Exponential Fourier Series | |

Numerical Computation of Dn | |

LTIC System response to Periodic Inputs | |

Appendix | |

Continuous-Time Signal Analysis: The Fourier Transform | |

Aperiodic Signal Representation by Fourier Integral | |

Transform of Some Useful Functions | |

Some Properties of the Fourier Transform | |

Signal Transmission through LTIC Systems | |

Ideal and Practical Filters | |

Signal Energy | |

Application to Communications: Amplitude Modulation | |

Angle Modulation | |

Data Truncation: Window Functions | |

Sampling | |

The Sampling Theorem | |

Numerical Computation of Fourier Transform: The Discrete Fourier Transform(DFT) | |

The Fast Fourier Transform (FFT) | |

Appendix 5.1 | |

Continuous-Time System Analysis Using the Laplace Transform | |

The Laplace Transform | |

Some Properties of the Laplace Transform | |

Solution of Differential and Integro-Differential Equations | |

Analysis of Electrical Networks: The Transformed Network | |

Block Diagrams | |

System Realization | |

Application to Feedback and Controls | |

The Bilateral Laplace Transform | |

Appendix 6.1: Second Canonical Realization | |

Frequency Response and Analog Filters | |

Frequency Response of an LTIC System | |

Bode Plots | |

Control System Design Using Frequency Response | |

Filter Design by Placement of Poles and Zeros of H(s) | |

Butterworth Filters | |

Chebyshev Filters | |

Frequency Transformations | |

Filters to Satisfy Distortionless Transmission Conditions | |

Discrete-Time Signals and Systems | |

Introduction | |

Some Useful Discrete-Time Signal Models | |

Sampling Continuous-Time Sinusoids and Aliasing | |

Useful Signal Operations | |

Examples of Discrete-Time Systems | |

Time-Domain Analysis of Discrete-Time Systems | |

Discrete-Time System Equations | |

System Response to Internal Conditions: Zero-Input Response | |

Unit Impulse Response h[k] | |

System Response to External Input: Zero-State Response | |

Classical Solution of Linear Difference Equations | |

System Stability | |

Appendix 9.1: Determining Impulse Response | |

Fourier Analysis of Discrete-Time Signals | |

Periodic Signal Representation by Discrete-Time Fourier Series | |

Aperiodic Signal Representation by Fourier Integral | |

Properties of DTFT | |

DTFT Connection with the Continuous-Time Fourier Transform | |

Discrete-Time Linear System Analysis by DTFT | |

Signal Processing Using DFT and FFT | |

Generalization of DTFT to the Z-Transform | |

Discrete-Time System Analysis Using the Z-Transform | |

The Z-Transform | |

Some Properties of the Z-Transform | |

Z-Transform Solution of Linear Difference Equations | |

System Realization | |

Connection Between the Laplace and the Z-Transform | |

Sampled-Data (Hybrid) Systems | |

The Bilateral Z-Transform | |

Frequency Response and Digital Filters | |

Frequency Response of Discrete-Time Systems | |

Frequency Response From Pole-Zero Location | |

Digi | |

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