This course introduces first some of the elementary ideas related to the mathematical representation of signals and systems. Then, the Fourier analysis in both continuous-time and discrete-time, as well as the sampling algorithm will be presented.
學習目標:
1. Fundamental theories and techniques related with signal and systems are learned
2. The signal representation in time-domain and frequency-domain is learned
教科書:
A. Oppenheim and A. Willsky, Signals and Systems.
課程大綱
分配時數
核心能力
備註
單元主題
內容綱要
講授
示範
隨堂作業
其他
Introduction to Signals and Systems
1. Continuous-Time and
Discrete-Time Signals
2. Exponential and Sinusoidal
Signals
3. The Unit Impulse and Unit
Step Functions
4. Continuous-Time and
Discrete-Time Systems
5. Basic System Properties
1.11.21.32.12.23.13.24.14.24.34.4
Linear Time-Invariant
Systems
1. Discrete-Time LTI Systems:
The Convolution Sum
2. Continuous-Time LTI
Systems: The Convolution
Integral
3. Properties of LTI Systems
4. Causal LTI Systems
Described by Differential and
Difference Equations
1.11.21.32.12.23.13.24.14.24.34.4
Fourier Series
Representation of
Periodic Signals
1. Fourier Series Representation
of Continuous-Time Periodic
Signals
2. Convergence of the Fourier
Series
3. Properties of
Continuous-Time Fourier
Series
4. Fourier Series Representation
of Discrete-Time Periodic
Signals
5. Properties of Discrete-Time
Fourier Series
6. Fourier Series and LTI
Systems
7. Filtering
1.11.21.32.12.23.13.24.14.24.34.4
The Continuous-Time
Fourier Transform
1.Representation of Aperiodic
Signals: the Continuous-Time
Fourier Transform
2. The Fourier Transform for
Periodic Signals
3. Properties of
Continuous-Time Fourier
Transform
4. The Convolution Property
5. The Multiplication Property
6. Systems Characterized by
Linear Constant Coefficient
Differential Equations
1.11.21.32.12.23.13.24.14.24.34.4
The Discrete-Time
Fourier Transform
1. Representation of Aperiodic
Signals: the Discrete-Time
Fourier Transform
2. The Fourier Transform for
Periodic Signals
3. Properties of Discrete-Time
Fourier Transform
4. The Convolution Property
5. The Multiplication Property
6. Duality
7. Systems Characterized by
Linear Constant Coefficient
Difference Equations
1.11.21.32.12.23.13.24.14.24.34.4
Sampling
1. Representation of a
Continuous-Time Signal by
Its Samples: The Sampling
Theorem
2. Reconstruction of a Signal
from Its Samples Using
Interpolation
3. The Effect of Undersampling:
Aliasing
4. Discrete-Time Processing of
Continuous-Time Signals
5. Sampling of Discrete-Time
Signals
This course introduces the fundamental theorems about signals and system.
達成指標:
The students learn the concepts related to signals and systems.
評量工具(可複選):
exam
2.1
培養分析問題的能力。()
為何有關:
This course introduces Fourier series and transform to analyze the signal in frequency domain. The output signal of LTI system can be obtained not only by convolution in time-domain, but also by multiplication of Fourier transform in frequency domain, followed by inverse Fourier transform.
達成指標:
The students learn the signal representation in time-domain and frequency-domain and compute the output of LTI system in many ways.