Digital Signal Processing Beihang University Wang Jun

This course mainly explains the theory, principles and implementation methods of digital signal processing. It is a basic course for electronic information majors. When studying, you need to pay attention to integrating theory with engineering practice. The course uses engineering examples of sound signal spectrum analysis, filter design, performance simulation, and hardware implementation throughout the course to cultivate students' system analysis, system design, and system implementation abilities. Its prerequisite courses include: advanced mathematics (mathematical analysis), linear algebra, complex variable functions, circuit analysis, signals and systems, etc. At the same time, it is the basis for learning subsequent professional courses in electronic information.

This course focuses on the connection with the prerequisite course "Signals and Systems" and the correlation of knowledge points. Compare the content related to signals and systems, analyze the differences and connections between continuous, discrete, and digital signals, and compare the similarities and differences between digital signal processing and continuous signal processing, which will help you understand related knowledge. From the unit pulse representation of the discrete time series, the convolutional representation of the LTI system is derived. From the complex exponential representation of discrete time series, Fourier series, Fourier transform and Z transform are derived. From the characteristic function of the LTI system, the frequency response of the LTI system is derived. From the relationship between Fourier transform and Z transform, the relationship between the zero and pole points of the rational system function and the frequency response is derived. From continuous and discrete, periodic and aperiodic, the discrete Fourier transform (DFT) is derived. From the relationship between Z transform and S transform, the IIR filter design method is derived. From the Fourier transform properties, the FIR filter design method is derived. From the difference equation, the filter structure and implementation method are derived. Finally, engineering applications of digital signal processing such as signal spectrum analysis methods are given. In addition, the course sorts out the correlations between relevant knowledge points, and you can compare relevant chapters of the course. For example: there are inherent similarities and connections between time domain sampling and frequency domain sampling, time domain cycles and frequency domain cycles, DFS and DTFT, and DFT knowledge points. Through comparative learning, learning efficiency can be improved.

This course focuses on experimentation and practice, using audio signal processing as an example, adopting a problem-based experimental teaching model, and equipped with modular experimental routines such as signal spectrum analysis, filter design, filter implementation, and comprehensive course experiments, including analog filters. , Matlab/FPGA/DSP digital filter, etc. Analog filter examples connect relevant course content such as electronic circuits, signals and systems to increase the continuity of knowledge. Examples of digital filters to strengthen the connection and difference between "digital signal processing" and "signals and systems".

• Chapter 1：introduction (9 minutes and 36 seconds)

• Chapter 2：continuous signal representation (10 minutes and 12 seconds)

• Chapter 3：Continuous FT and FS (11 minutes and 10 seconds)

• Chapter 4：Time domain analysis of continuous signal differential equations (10 minutes and 26 seconds)

• Chapter 5：Frequency domain analysis and Laplace transform of continuous signals (14 minutes and 38 seconds)

• Chapter 6：Introduction to Signal Sampling (7 minutes and 51 seconds)

• Chapter 7：Signal sampling process (11 minutes and 1 seconds)

• Chapter 8：signal reconstruction process (13 minutes and 31 seconds)

• Chapter 9：LTI system properties (11 minutes and 56 seconds)

• Chapter 10：LTI system convolution (9 minutes and 39 seconds)

• Chapter 11：LTI convolution properties (7 minutes and 34 seconds)

• Chapter 12：discrete signal representation (12 minutes and 36 seconds)

• Chapter 13：Discrete summable signal DTFT (7 minutes and 18 seconds)

• Chapter 14：DTFT symmetry (12 minutes and 32 seconds)

• Chapter 15：DTFT theorem (13 minutes and 0 seconds)

• Chapter 16：Discrete periodic signal DFS (5 minutes and 36 seconds)

• Chapter 17：DFS symmetry (13 minutes and 23 seconds)

• Chapter 18：DFS theorem (13 minutes and 50 seconds)

• Chapter 19：Rational Z transform (9 minutes and 28 seconds)

• Chapter 20：Z transform properties (14 minutes and 37 seconds)

• Chapter 21：Inverse Transformation and Difference Equations (13 minutes and 49 seconds)

• Chapter 22：Time domain analysis of difference equations (1) (10 minutes and 17 seconds)

• Chapter 23：Time domain analysis of difference equations (2) (7 minutes and 30 seconds)

• Chapter 24：LTI system Z domain analysis (12 minutes and 6 seconds)

• Chapter 25：Discrete LTI system characteristic function (10 minutes and 19 seconds)

• Chapter 26：The influence of amplitude frequency and phase frequency (1 hours and 23 minutes and 36 seconds)

• Chapter 27：Pole and zero points and system response (11 minutes and 4 seconds)

• Chapter 28：LTI system all-pass breakdown (12 minutes and 29 seconds)

• Chapter 29：system compensation (8 minutes and 59 seconds)

• Chapter 30：Linear Phase System (1) (10 minutes and 27 seconds)

• Chapter 31：Linear Phase System (2) (7 minutes and 23 seconds)

• Chapter 32：Continuous filter design (11 minutes and 39 seconds)

• Chapter 33：Impulse response invariant method (12 minutes and 53 seconds)

• Chapter 34：bilinear transformation method (11 minutes and 0 seconds)

• Chapter 35：Window function design filter principle (7 minutes and 55 seconds)

• Chapter 36：Window function method to design filters (12 minutes and 39 seconds)

• Chapter 37：Convolution and differential flow graph (8 minutes and 21 seconds)

• Chapter 38：IIR direct flow graph (8 minutes and 53 seconds)

• Chapter 39：Cascade Parallel Transpose (13 minutes and 46 seconds)

• Chapter 40：FIR flow graph (11 minutes and 56 seconds)