3.4 Classification of discrete time systems 3.5 Impulse Response 3.6 Frequency Domain Representation of Discrete-Time Signals and Systems 6 3 4. The z-Transform 4.1 Definition of z-Transform 4.2 Region of Convergence 7 3 4.3 Inverse z-Transforms 4.4 The properties of z-Transform 5. Transform Function 5.1 Equivalent Description of Digital Filters 5.2 The Frequency Response of LTI Systems 5.3 Transfer Functions for Systems Characterized by Linear Constant Coefficient Difference Equations 5.4 Digital filter Structures and Realization 5.4 Digital filter Structures and Realization 6. The Discrete Fourier Transform (DFT) 6.1 Four Fourier Transform Pairs 6.2 Representation of Periodic Sequences: The Discrete Fourier Series 6.3 Periodic Convolution 6.4 The Discrete Fourier Transform 6.4 The Discrete Fourier Transform 6.5 Circular Convolution of Finite-Length Sequences Two Lecture Lecture 8 3 Lecture 9 3 Lecture Tutorial 10 3 Lecture 11 3 Lecture Tutorial Lecture 12 3 13 3 6.6 Linear Convolution Using the Discrete Fourier Transform 7.Computation of the Discrete Fourier Transform 7.1 Decimation-In-Time FFT Algorithms 7.2 Decimation-In-Frequency FFT Algorithms 8. Digital Filters Design based on Matlab 8.1 Filter Design Methods 8.2 Filter Design and Analysis Tool 8.3 Analyzing the Filter 8.4 Converting the Filter Structure 8.5 Exporting a Filter Design 8.6 Saving and Opening Filter Design Sessions Discussion, Problem solving, etc Final exam 14 3 Lecture Tutorial 15 3 Lecture 16 3 Lecture 17

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1. Introduction : Signal and Signal Processing――3 hours

? ? ? ? What is signal? What is digital signal? What are the advantages of digital signal processing? How have the techniques of DSP being developed? Where is the DSP applied?

1.1 Characterization and Classification of Signals. Continuous/Discrete;

1-Dimensional/Multi-Dimensional; Real-valued/Complex-Valued; Scale/Vector;

Analog/Quantized/Sampled/Digital

1.2 The objective of signal processing

To extract useful information carried by signals : Classification, detection, prediction,…

To improve the quality of a signal : Noise-cancellation, interference cancellation, echo-cancellation,…

1.3 Typical signal processing operations (1) Elementary time-domain operation: Scaling ( gain, attenuation) Delay (advance)

Addition (subtraction, integration, differentiation) (2) Analysis : Cross-correlation (3) Filtering : Convolutional integral

1.4 Typical Applications of DSP 1.5 History and Features of DSP

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2. Sampling and Reconstruction――6 hours

? ? ? ? The definition and properties of Fourier transform and Fourier series The convolution theorem and its physical meaning What is the effect of sampling on the original frequency spectrum? How should one choose the sampling interval T( or sampling rate fs=1/T)? (Review of continuous time and system) 2.1 Fourier series 2.2 Fourier Transform 2.3 convolution integral

2.4 sampling Theorem

3. Discrete-time Signals and Systems—8 hours

? How to represent discrete time signal? ? What is the basic discrete time signal? ? What is the typical discrete time signal? ? What is the basic operations on sequence? ? The properties of discrete LTI system ? Impulse response of discrete LTI system ? DTFT and its properties

3.1 Basic sequences

3.2 Basic operations for sequence 3.3 Combination of basic operations 3.4 Classification of discrete time systems 3.5 Impulse Response

3.6 Frequency Domain Representation of Discrete-Time Signals and Systems

4. The z-Transform ――6 hours

? Definition of z-transform ? Region of convergence of z-Transform ? Unit circle ? Poles/Zeros ? Inverse z-transform ? Properties of z-transform

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4.1 Definition of z-Transform 4.2 Region of Convergence 4.3 Inverse z-Transforms 4.4 The properties of z-Transform

5. Transform Function---7 hours

? The Frequency Response of Linear Time Invariant Systems ? System Functions for Systems Characterized by Linear Constant Coefficient Difference Equations ? Frequency Response for Rational System Functions ? Relationship between Magnitude and Phase ? Realization of FIR & IIR filter

5.1 Equivalent Description of Digital Filters

Impulse response h(n) I/O convolutional equation Block processing I/O difference equation Transfer function H(z) Pole/zero Pattern filter design method Filter design specification Frequency response H(ej?) Block-diagram realization Sample processing 5.2 The Frequency Response of LTI Systems

5.3 Transfer Functions for Systems Characterized by Linear Constant Coefficient Difference Equations

5.4 Digital filter Structures and Realization

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