ECE 310

• Signal Processing

Introduction to discrete-time systems and discrete-time signal processing: discrete-time linear systems, difference equations, z-transform, discrete convolution, stability, discrete-time Fourier transform, analog-to-digital and digital-to-analog conversion, interpolation and decimation, digital filter design, discrete Fourier transform, fast Fourier transform, spectral analysis, applications of digital signal processing.

Introduce fundamentals of discrete-time linear systems and digital signal processing. Emphasizes theory but also includes design and applications.

• Overview of digital signal processing
• Discrete-time linear shift-invariant systems
• Difference equations
• Complex numbers and functions of a complex variable
• Convolution and impulse response
• z-transform
• Transfer functions and block diagrams
• Convolution via z-transform
• Stability
• Discrete-time Fourier transform (DTFT)
• Digital frequency and frequency response
• Sampling
• Analog frequency response of a digital processor
• A/D and D/A conversion
• Interpolation and oversampling A/D, D/A
• FIR and IIR filter structures
• Generalized linear phase
• FIR filter design
• IIR filter design
• Discrete Fourier transform (DFT)
• Spectral analysis
• Fast Fourier transform (FFT)
• Applications to speech, audio/music, medical imaging, communications, etc.

Discrete-time linear shift-invariant systems (3 hrs)

Complex numbers and functions of a complex variable (2 hrs)

z-transform (3 hrs)

Convolution and impulse response (3 hrs)

Transfer function and block diagrams (2 hrs)

Discrete-time Fourier transform (DTFT) (4 hrs)

Digital frequency and frequency response (2 hrs)

A/D and D/A conversion (4 hrs)

Multirate systems (3 hrs)

FIR and IIR filter design (6 hrs)

Discrete Fourier transform (DFT) (3 hrs)

Spectral analysis (3 hrs)

Fast Fourier transform (FFT) (3 hrs)

Applications to speech, medical imaging, communications, etc. (4 hrs)

Students can access the ECE 310 course web site to obtain course documents, homework, and solutions. In the optional companion laboratory course, ECE311 Students use Labview and Matlab to complete several assignments involving design and implementation.

Analog signal processing (circuit analysis, differential equations, convolution, Fourier and Laplace transforms) ---

ECE 210 or consent of instructor

D. C. Munson, Jr., and A.C. Singer ECE 310 Course Notes, 2013.

D. G. Manolakis and V. K. Ingle, Applied Digital Signal Processing: Theory and Practice, Cambridge Univ. Press, 2011

Engineering topics: 100%

To introduce fundamentals of discrete-time linear systems and digital signal processing. Emphasizes theory but also includes design and applications.

A student completing this course should, at a minimum, be able to:

1. Determine whether systems are linear or nonlinear, causal or noncausal, shift-invariant, or shift varying. (1)

2. Model systems with difference equations and compute their solutions. (1)

3. Apply the z-transform as a tool in system modeling and analysis. (1, 6)

4. Visualize and compute discrete-time convolution. (1)

5. Apply the z-transform as a tool in system modeling and analysis, and understand the related abstract concepts of function of a complex variable and region of convergence. (1, 6)

6. Calculate impulse response and convolution using the concept of transfer function. (1)

7. Draw block diagrams of common digital filters, including those using complex arithmetic. (2)

8. Determine whether a system is stable or unstable and demonstrate an understanding of the abstract concept of stability. (1)

9. Demonstrate an understanding of the discrete-time Fourier transform and the concept of digital frequency. (1)

10. Choose the sampling rate for a digital system and understand the effects of aliasing. (1, 2)

11. Compute the analog frequency response of a digital system. (1)

12. Demonstrate familiarity with actual A/D and D/A circuits. (1, 2)

13. Mathematically analyze decimation and interpolation and their effects on oversampling A/Ds and D/As. (1, 6)

14. Decompose a high-order transfer function into a realization composed of second-order building blocks. (1, 2)

15. Design FIR filters using the window design method. (1, 2)

16. Design FIR filters using the frequency sampling method. (1, 2)

17. Design IIR filters using the bilinear transformation. (1, 2)

18. Demonstrate an understanding of the DFT and its use in spectral analysis and frequency sampling filter design. (1, 2, 6)

19. Demonstrate an understanding of the FFT and its use in fast convolution. (1, 2)

20. Explain how digital signal processing is used in applications. (6)