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所在平台: Udemy |
课程主页: https://www.udemy.com/course/signals-and-systems-basics-convolution-transforms/
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课程名称：信号与系统：信号处理的基础 课程概述： “信号与系统”是电子、电气和通信工程师的基础学科，构成了信号处理、控制系统和通信的核心。掌握此课程能够帮助学员理解音频处理、图像分析和无线通信等实际应用。该课程通过视频进行教学，涵盖了信号与系统的所有基础知识。课程由Hitesh Dholakiya教授主讲，内容包括以下专题： 1. 信号概述：信号的基本概念及应用，信号的分类，标准信号（冲激信号、阶跃信号、斜坡信号、Signum信号、矩形信号、Sinc信号和采样），信号的操作（时间移位、时间折叠、时间缩放和算术操作），信号函数的绘图、偶信号与奇信号的识别，信号的周期性，以及信号的能量与功率。 2. 系统概述：系统的基本概念及应用，系统的分类，线性与非线性系统，时不变与时变系统，线性时不变系统（LTI）与线性时变系统（LTV），静态与动态系统，因果与非因果系统，可逆与不可逆系统，稳定与不稳定系统，系统的冲激响应。 3. 信号与系统中的卷积：卷积的基本概念和性质，卷积的限制，卷积信号的面积，连续时间信号的卷积，滑移与移位法卷积，图像法卷积，卷积实例，线性卷积，循环卷积，去卷积，以及去卷积的长除法方法。 4. 拉普拉斯变换在信号与系统中的应用：拉普拉斯变换的基本概念及应用，拉普拉斯变换与傅里叶变换的比较，拉普拉斯变换的性质，拉普拉斯变换的ROC，单边拉普拉斯变换，标准信号的拉普拉斯变换，利用拉普拉斯变换求解系统的冲激响应，初始条件和最终条件的概念。 5. Z变换在信号与系统中的应用：Z变换的基本概念和性质，Z变换与离散时间傅里叶变换（DTFT）的关系，离散序列的Z变换，标准信号的Z变换，利用Z变换的初始值与最终值定理，Z变换的ROC，因果性与稳定性分析，Z逆变换的长除法、直接法及留数法。 6. 信号与系统中的傅里叶级数：傅里叶级数与傅里叶变换的比较，傅里叶级数系数的推导，傅里叶级数的类型（指数级数、三角级数和极坐标级数），傅里叶级数的性质，三角与指数傅里叶级数之间的关系，以及傅里叶级数的实例分析。 7. 信号与系统中的傅里叶变换：傅里叶变换的基本概念，傅里叶变换的推导，多个信号（矩形脉冲、冲激信号、DC信号、余弦信号、单位阶跃信号等）的傅里叶变换，傅里叶变换的性质，包括线性性、时间移位、频率移位、微分与积分性质等，以及无失真信号传输的理论。 8. 信号与系统中的相关性分析：相关性的基本概念、类型、应用，相关性的性质及实例，包括自相关与交叉相关的实例及Parseval定理在能量信号与能量谱密度的应用。 期待您在课程中见！谢谢！
Signals and Systems is a fundamental subject for electronics, electrical, and communication engineers. It forms the backbone of signal processing, control systems, and communications. Mastering this course helps in understanding real-world applications like audio processing, image analysis, and wireless communication.This course includes the videos related to Signals and Systems and it covers all the fundamentals of Signals and Systems.Here Prof. Hitesh Dholakiya has covered all the topics of Signals and Systems with the following outlines:1. Introduction to Signals:Basics and Applications of Signals, Classifications of Signals, Standard Signals {Impulse, Step, Ramp, Signum, Rectangular, Sinc and Sampling}, Operations on Signals {Time Shifting, Time Folding, Time Scaling & Arithmetic Operations}, Plot of Signal from the Function, Even and Odd Signals, Identification of Even and Odd Components of Signals, Periodicity of Signals, Energy and Power of Signals.2. Introduction to Systems:Basics and Applications of Systems, Classifications of Systems, Linear and Non-Linear Systems, Time Invariant and Time Variant Systems, LTI and LTV Systems, Static and Dynamic Systems, Causal and Non-Causal Systems, Invertible and Non-Invertible Systems, Stable and Unstable Systems, Impulse Response of Systems.3. Convolution in Signals and Systems:Basics and Properties of Convolution, Limits of Convolution, Area of Convoluted Signal, Convolution of Continuous Time Signals, Convolution by Slide and Shift Method, Convolution by Image Method, Convolution Examples, Linear Convolution, Circular Convolution, Deconvolution, Long Division Method of Deconvolution.4. Laplace Transform in Signals and Systems:Basics and Applications of Laplace Transform, Laplace Transform Vs Fourier Transform, Properties of Laplace Transform, ROC of Laplace Transform, Examples of ROC and Laplace Transform, Unilateral Laplace Transform, Laplace Transform of Standard Signals, Examples of Laplace Transform, Impulse Response of the system using Laplace Transform, Initial and Final Conditions using Laplace Transform.5. Z Transform in Signals and Systems:Basics and Properties of Z Transform, Relation of Z Transform with DTFT, Z Transform of Discrete Sequence, Examples of Z Transform, Z Transform of Standard Signals, Examples of Z Transform, Initial and Final Value Theorem using Z Transform, ROC of Z Transform, Examples of ROC and Z Transform, Causality and Stability using Z Transform, Long Division Method for Inverse Z Transform, Direct Method or Partial Fraction Method for Inverse Z Transform, Residue Method for Inverse Z Transform, Examples of Properties of Z Transform, Transfer Function and Impulse Response by Z Transform.6. Fourier Series in Signals and Systems:Fourier Series Vs Fourier Transform, Fourier Series Coefficient Derivation, Types of Fourier Series {Exponential, Trigonometric and Polar Fourier Series}, Properties of Fourier Series, Relation between Trigonometric and Exponential Fourier Series, Examples of Fourier Series Coefficient, Fourier Series Coefficients from Symmetry, DC Component of Fourier Series, Fundamental Component and Harmonics of Fourier Series, Examples of Trigonometric Fourier Series, Examples of Exponential Fourier Series.7. Fourier Transform in Signals and Systems: Basics of Fourier Transform, Derivation of Fourier Transform, Fourier Transform of Rectangular Pulse, Fourier Transform of Impulse Signal, Fourier Transform of DC Signal, Fourier Transform of Cosine Signal, Fourier Transform of Unit Step Signal, Fourier Transform of Shifted Unit Step Signal, Fourier Transform of Two-Sided Exponential Signal, Properties of Fourier Transform, Linearity Property of Fourier Transform, Time Shifting Property of Fourier Transform, Frequency Shifting Property of Fourier Transform, Differentiation and Integration Properties of Fourier Transform, Time Scaling Property of Fourier Transform, Multiplication and Convolution Properties of Fourier Transform, Duality Property of Fourier Transform, Distortion Less Transmission of Signal, Fourier Transform Solved Examples. 8. Correlation in Signals and Systems: Correlation Basics, Types, Applications, Properties of Correlation, Correlation Solved Examples, Auto Correlation Solved Examples, Cross Correlation Solved Examples, Parseval's Theorem for Energy Signal and Energy Spectral Density.See you in the course.Thank You.
