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信号与系统

Signals and Systems

课程介绍 Course Introduction

学分:3 | 先修课:电路分析、复变函数 | 学期:第4学期

信号与系统是电气与电子信息类的核心理论课程,研究连续与离散信号的表示、变换与通过线性时不变系统的响应。课程内容包括信号的基本运算与分解、卷积积分与卷积和、连续时间傅里叶级数与变换、拉普拉斯变换、离散时间傅里叶变换与 Z 变换、系统函数与稳定性分析。本课程为通信、控制、图像处理与数字信号处理等后续课程提供关键数学工具与分析方法。

Signals and Systems is a core theoretical course for electrical and information engineering, studying the representation and transformation of continuous and discrete signals and their responses through linear time-invariant systems. Topics include signal operations, convolution, Fourier series and transform, Laplace transform, discrete-time Fourier transform, Z-transform, system function and stability analysis. It provides essential mathematical tools for communication, control, image processing, and digital signal processing.

大作业 Final Project

作业标题:FIR数字滤波器设计与频域分析 / FIR Digital Filter Design and Frequency Domain Analysis

设计指定类型的FIR数字滤波器,包括窗函数法设计与频率采样法设计,完成频率响应分析并通过仿真验证滤波性能。

Design a specified type of FIR digital filter, including window method design and frequency sampling method design, completing frequency response analysis and verifying filtering performance through simulation.

实施步骤 Implementation Steps

📋 示例:设计一个实际应用的FIR数字滤波器,比如语音信号去噪的低通滤波器。你需要用窗函数法或频率采样法设计滤波器系数,分析幅频和相频特性,然后用MATLAB处理真实语音信号,对比滤波前后的信噪比改善了多少。
步骤 1
设计指标分析
本步骤对电气工程问题进行深入分析,明确设计指标和技术要求。电气工程涉及强电和弱电多个领域,需从功能需求、性能指标、约束条件等多维度分析。通过需求分析和指标分解确定设计输入,为后续电路设计和系统实现奠定基础。

• 分析系统功能需求和性能指标,包括频率响应、增益、带宽、信噪比、功耗等关键参数
• 确定约束条件,如电源电压、工作温度、尺寸限制、成本预算、电磁兼容要求等
• 查阅相关技术标准和规范(如GB、IEC、IEEE标准),明确设计依据和测试方法
产出:需求分析报告(含功能需求、性能指标、约束条件、设计依据、技术路线) | 质量标准:需求明确、指标具体、约束清晰、依据充分
步骤 2
窗函数法设计
本步骤进行电气系统或电路的方案设计,将功能指标转化为具体的电路结构和参数。电路设计是电气工程的核心,需在性能、功耗、成本和可靠性之间寻求最优平衡。采用模块化设计方法,通过理论计算和仿真验证迭代优化设计方案。

• 选择电路拓扑结构,确定系统架构和模块划分,设计信号流向和接口规范
• 进行元器件选型和参数计算,依据器件手册(datasheet)确定工作点和外围元件参数
• 使用Cadence、Altium Designer或Multisim绘制电路原理图,进行设计规则检查(DRC)
产出:设计文档(含电路原理图、BOM表、参数计算、元器件选型说明、接口定义) | 质量标准:拓扑合理、参数正确、选型得当、满足指标
步骤 3
频率采样法设计
本步骤进行电气系统或电路的方案设计,将功能指标转化为具体的电路结构和参数。电路设计是电气工程的核心,需在性能、功耗、成本和可靠性之间寻求最优平衡。采用模块化设计方法,通过理论计算和仿真验证迭代优化设计方案。

• 选择电路拓扑结构,确定系统架构和模块划分,设计信号流向和接口规范
• 进行元器件选型和参数计算,依据器件手册(datasheet)确定工作点和外围元件参数
• 使用Cadence、Altium Designer或Multisim绘制电路原理图,进行设计规则检查(DRC)
产出:设计文档(含电路原理图、BOM表、参数计算、元器件选型说明、接口定义) | 质量标准:拓扑合理、参数正确、选型得当、满足指标
步骤 4
频域分析
本步骤对电气工程问题进行深入分析,明确设计指标和技术要求。电气工程涉及强电和弱电多个领域,需从功能需求、性能指标、约束条件等多维度分析。通过需求分析和指标分解确定设计输入,为后续电路设计和系统实现奠定基础。

• 分析系统功能需求和性能指标,包括频率响应、增益、带宽、信噪比、功耗等关键参数
• 确定约束条件,如电源电压、工作温度、尺寸限制、成本预算、电磁兼容要求等
• 查阅相关技术标准和规范(如GB、IEC、IEEE标准),明确设计依据和测试方法
产出:需求分析报告(含功能需求、性能指标、约束条件、设计依据、技术路线) | 质量标准:需求明确、指标具体、约束清晰、依据充分
步骤 5
仿真验证与报告
本步骤使用仿真软件对电路或系统进行仿真验证,在制作实物前全面验证设计性能。仿真是现代电子设计的必要手段,可以快速验证电路功能、分析参数敏感性、发现潜在问题。通过SPICE仿真、频域分析和瞬态分析多维度验证设计。

• 建立仿真模型,设置元器件模型参数和激励源,确保仿真模型准确反映实际电路
• 进行直流工作点分析、交流小信号分析、瞬态分析、噪声分析和蒙特卡洛分析
• 进行参数扫描和温度扫描,分析关键参数变化对系统性能的影响
产出:仿真报告(含仿真电路、波形曲线、性能参数、参数扫描结果、问题分析) | 质量标准:模型准确、覆盖全面、波形合理、指标达标

Steps

Step 1
Design Specification Analysis
This step conducts in-depth analysis of electrical engineering problems, clarifying design specifications and technical requirements. Electrical engineering covers multiple fields of power and electronics, requiring multi-dimensional analysis from functional requirements, performance indicators, constraint conditions, etc. Determine design inputs through requirements analysis and specification decomposition, laying the foundation for subsequent circuit design and system implementation.

• Analyze system functional requirements and performance indicators, including frequency response, gain, bandwidth, SNR, power consumption and other key parameters
• Determine constraint conditions, such as supply voltage, operating temperature, size limits, cost budget, EMC requirements, etc.
• Consult relevant technical standards and specifications (GB, IEC, IEEE standards), clarify design basis and test methods
Deliverable: Requirements analysis report (including functional requirements, performance specifications, constraints, design basis, technical route) | Quality standard: Clear requirements, specific indicators, clear constraints, sufficient basis
Step 2
Window Method Design
This step performs scheme design of electrical systems or circuits, translating functional specifications into specific circuit structures and parameters. Circuit design is the core of electrical engineering, requiring optimal balance among performance, power consumption, cost and reliability. Adopt modular design methods, iteratively optimize design schemes through theoretical calculation and simulation verification.

• Select circuit topology, determine system architecture and module division, design signal flow and interface specifications
• Perform component selection and parameter calculation, determine operating point and peripheral component parameters based on device datasheets
• Draw circuit schematics using Cadence, Altium Designer or Multisim, perform design rule check (DRC)
Deliverable: Design document (including circuit schematic, BOM table, parameter calculation, component selection description, interface definition) | Quality standard: Reasonable topology, correct parameters, appropriate selection, meeting specifications
Step 3
Frequency Sampling Design
This step performs scheme design of electrical systems or circuits, translating functional specifications into specific circuit structures and parameters. Circuit design is the core of electrical engineering, requiring optimal balance among performance, power consumption, cost and reliability. Adopt modular design methods, iteratively optimize design schemes through theoretical calculation and simulation verification.

• Select circuit topology, determine system architecture and module division, design signal flow and interface specifications
• Perform component selection and parameter calculation, determine operating point and peripheral component parameters based on device datasheets
• Draw circuit schematics using Cadence, Altium Designer or Multisim, perform design rule check (DRC)
Deliverable: Design document (including circuit schematic, BOM table, parameter calculation, component selection description, interface definition) | Quality standard: Reasonable topology, correct parameters, appropriate selection, meeting specifications
Step 4
Frequency Domain Analysis
This step conducts in-depth analysis of electrical engineering problems, clarifying design specifications and technical requirements. Electrical engineering covers multiple fields of power and electronics, requiring multi-dimensional analysis from functional requirements, performance indicators, constraint conditions, etc. Determine design inputs through requirements analysis and specification decomposition, laying the foundation for subsequent circuit design and system implementation.

• Analyze system functional requirements and performance indicators, including frequency response, gain, bandwidth, SNR, power consumption and other key parameters
• Determine constraint conditions, such as supply voltage, operating temperature, size limits, cost budget, EMC requirements, etc.
• Consult relevant technical standards and specifications (GB, IEC, IEEE standards), clarify design basis and test methods
Deliverable: Requirements analysis report (including functional requirements, performance specifications, constraints, design basis, technical route) | Quality standard: Clear requirements, specific indicators, clear constraints, sufficient basis
Step 5
Simulation Verification and Report
This step uses simulation software for circuit or system simulation verification, comprehensively verifying design performance before physical implementation. Simulation is an essential means in modern electronic design, enabling quick verification of circuit functionality, analysis of parameter sensitivity, and discovery of potential problems. Multi-dimensional design verification through SPICE simulation, frequency domain analysis and transient analysis.

• Build simulation model, set component model parameters and excitation sources, ensuring the simulation model accurately reflects the actual circuit
• Perform DC operating point analysis, AC small signal analysis, transient analysis, noise analysis and Monte Carlo analysis
• Conduct parameter sweep and temperature sweep, analyze the influence of key parameter changes on system performance
Deliverable: Simulation report (including simulation circuit, waveform curves, performance parameters, parameter sweep results, problem analysis) | Quality standard: Accurate model, comprehensive coverage, reasonable waveforms, specifications met
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