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课程名称：从基础到高级的信号与系统 课程概述： 本课程深入探讨信号与系统的基本概念与高级应用，分为十个章节： 第一章：信号 - 讲解确定性信号与随机信号、模拟信号与数字信号的区别。 - 介绍单位脉冲函数、单位阶跃函数、单位斜坡函数及其他基本信号。 - 分类信号为周期性与非周期性、偶函数与奇函数、因果与非因果信号，并且讨论信号的转移与缩放影响。 第二章：系统 - 讨论系统的分类，包括线性、非线性、时变与时不变系统。 - 介绍静态、动态、因果与非因果系统的特性。 - 阐明稳定性、可逆性等系统性质，并解决相关GATE考试问题。 第三章：傅里叶级数 - 介绍傅里叶级数及其在信号中的正交性和信号近似的应用。 - 涉及完全正交集合的概念及其示例，分析对称条件。 第四章：傅里叶变换 - 知识涵盖傅里叶变换的定义及Dirichlet条件。 - 详细讲解各种信号（如单位脉冲、单位阶跃、正弦函数等）的傅里叶变换及其性质。 第五章：拉普拉斯变换 - 阐述拉普拉斯变换的基本概念及其对不同信号的应用。 - 解析其性质，包括线性、时间位移、频率位移等。 第六章：Z变换 - 探讨Z变换的原理及其对单位脉冲、单位阶跃等信号的应用。 - 分析Z变换的性质，如线性、时间位移和卷积性质。 第七章：离散傅里叶变换 - 介绍离散时间傅里叶变换（DTFT）和离散傅里叶变换（DFT）的基本概念及例子。 第八章：采样定理 - 讨论采样定理的定义和Nyquist条件，并进行时域及频域分析。 第九章：信号通过LTI系统的传输 - 探讨无失真传输系统的频率响应及其脉冲响应。 第十章：卷积与相关性 - 讲解卷积的基本概念及通过图形程序进行的卷积过程。 本课程将结合实例和GATE考试的历年问题，帮助学生扎实掌握信号与系统的相关理论与实践技能。
Chapter - 1: Signals ==============1.Deterministic and random signals2.Analog and Digital Signals3.Unit impulse Function - Elementary Signals4.Unit step Function5.Unit Ramp and Parabolic & Singularity Functions 6. Exponential Functions - Elementary Signals7. Signum Function - Elementary Signals8. Rectangular Function - Elementary Signals9. Triangular Function - Elementary Signals10. Sinusoidal Functions - Elementary Signals11. Sinc & Sampling Functions - Elementary Signals12. Periodic & Non Periodic Signals- Classification13.Even and Odd Signals14.Causal and Non Causal Signals16.Rectangular Function E & P17.Unit step Function E & P18.Unit Ramp Function E & P19.Power of Sinusoidal Signal20.Effect of shifting and Scaling on E & P21.Observation Points on E & P22.Operations on Independent Variable of Signal23. GATE Previous Problems with Solutions Set - 1 24. GATE Previous Problems with Solutions Set - 2Chapter - 2: Systems================15. 1. Systems Classification - Linear & Nonlinear Systems16. 2. Systems Classification - Time Variant & time Invariant Systems17. 3. Static & Dynamic & Causal & Non Causal Systems18. 4. Examples19. 5. Stable & Unstable Systems20. 6. Examples21 7. Invertible & Non Invertible Systems23. 9. GATE Previous Problems with Solutions Set - 124. 10.GATE Previous Problems with Solutions Set - 225. 11.GATE Previous Problems with Solutions Set - 3 Chapter - 3: Fourier Series==================1. Fourier Series Introduction2.Orthogonality in Vectors3.Orthogonality in Signals4.Orthogonal Signal Space & Signal Approximation5.Mean Square Error and Complete Set6.Orthonormal Set7.Complete Set Example - 18.Complete Set Example - 29.Orthogonality in Complex Functions10.Full Wave Rectified signal EFS11.Dirichlet's Conditions for Fourier Series12.TFS and EFS Expansion Example13.Symmetric Conditions14.Check the Symmetry Conditions for Examples15 GATE Previous Problems with Solutions Set - 116.GATE Previous Problems with Solutions Set - 2 17.Exponentials periodic signal TFS & EFS18.Triangular Periodic Signal TFS & EFS19.Frequency SpectrumChapter - 4: Fourier Transform=====================1. Introduction to Fourier Transforms & Dirichlet s conditions 2. Fourier Transform of Unit Impulse function and One sided Exponential. 3. Fourier Transform of Two sided Exponential. 4. Fourier Transform of Signum Function5. Fourier Transform of Unit Step function & Sinusoidal Functions. 6. Fourier Transform of Rectangular & Sinc & Fampling Functions.7. Fourier Transform of Triangular Function.8. Fourier Transform of Trapezoidal Signal.9. Linearity property of Fourier Transform 10. Time scaling property of Fourier Transform 11. Time shifting property of Fourier Transform 12. Frequency shifting property of Fourier Transform13. Differentiation in Time property of Fourier Transform14. Integration in Time domain Property of Fourier Transform15. Differentiation in Frequency domain Property of Fourier Transform16. Conjugation Property of Fourier Transform17. Duality Property of Fourier Transform 18. Modulation Property of Fourier Transform 19. Area Under time and Frequency Domain Signals. 20. Time Convolution Property of Fourier Transform 21. Frequency Convolution Property of Fourier Transform 22. Parseval's relation 23. Fourier Transform of Periodic Signal 24. GATE Previous Problems with Solutions Set - 125. GATE Previous Problems with Solutions Set - 2 Chapter - 5: Laplace Transform=====================1. Laplace Transform of impulse function with ROC2. LT of unit step Function with ROC3. LT of left side unit step Function with ROC4. LT of Exponential Functions with ROC5. LT of Complex Exponentials & cos and sin Functions with ROC6. LT and ROC of both side Exponentials7. LT and ROC of damped sin Function8. LT and ROC of Damped cos Function9. LT and ROC of Hyperbolic sin and cos Functions10. Linearity Property of LT11. Time shifting Property of LT12. Frequency shifting Property of LT13. Time scaling and Time Reversal Property of LT14. Time Differentiation Property of LT15. Differentiation in S-domain Property of LT16. Conjugation property of LT17. Initial and Final value Theorems of LT18. Convolution Property of LT19. GATE Previous Problems with Solutions Set - 120. Laplace Transform Example Set - 121. Laplace Transform Example Set - 2Chapter - 6: Z-Transform================= 1. Z-Transform and ROC of unit impulse and step Functions 2. ZT and ROC of u(-n) and -u(-n-1) 3. ZT and ROC of exponentials a^nu(n) and -a^nu(-n-1) 4. ZT and ROC of complex exponentials and coswn.u(n) 5. ZT and ROC of sinwn.u(n) 6. ZT Properties - Linearity 7. ZT Properties - Time shifting 8. ZT properties - Multiplication with exponential 9. ZT Properties - Time Reversal 10. ZT Properties - Time Expansion 11. ZT Properties - Differentiation in Z-Domain 12. ZT Properties - Conjugation 13. ZT Properties - Convolution 14. ZT Properties - Initial value Theorem 15. ZT Properties - Final value Theorem 16. GATE Previous Problems with Solutions Set - 1 17. GATE Previous Problems with Solutions Set - 2 18. GATE Previous Problems with Solutions Set - 3Chapter - 7: Discrete Fourier Transform==========================1. DTFT(Discrete Time Fourier Transform)2. DTFT of Impulse & Unit step Functions3. DTFT of DT Exponential Sequence4. DFT-Discrete Fourier Transform5. DFT example6. GATE Previous Problems with Solutions Set - 17. GATE Previous Problems with Solutions Set - 2Chapter - 8: Sampling Theorem=======================33. 1. Sampling Theorem Definition.34. 2. Nyquist Condition - NR Calcutions35. 3. Time Domain & Frequency Domain Analysis(spectral)36. 4. GATE Previous Problems with Solutions Set - 1Chapter - 9: Signal Transmission Through LTI System===================================1.Distortionless transmission system and frequency respons2.Impulse Response of Distortionless transmission system3.Filter Characteristics of LTI Systems4.Signal Bandwidth vs System Bandwidth.Chapter - 10: Convolution & Correlation===========================1.Convolution & Examples2.Convolution Graphical procedure exponential with unit step3.Convolution Graphical procedure two rectangular signals4.Triangular and rectangular convolution
