EE 453 – Digital Signal Processing

Designation:

Senior/Grad-level technical elective for Electrical Engineering students

Catalog Data:

Design of FIR and IIR filters; DFT and its computation via the FFT; applications of the DFT; filter implementation; finite arithmetic effects. Prerequisite: EE 351 or EE317.

Prerequisites by topic:

  1. Understanding sampling and reconstruction in both the time and frequency domains.
  2. Understanding linear time-invariant systems, system properties, the convolution sum, and properties of convolution.
  3. Understanding the system frequency response, magnitude response, phase response, and eigenresponse.
  4. Understanding the Z-transform and its application to identifying system properties, solving difference equations, finding system outputs, system identification, and filter design via pole-zero placement.
  5. Understanding the qualitative characterization of magnitude response based on pole and zero locations.
  6. Understanding the discrete Fourier transform as a practical approach to evaluating the frequency response/discrete-time Fouriertransform.
  7. Understanding Matlab as a tool for signal processing.

Course Objectives:

This course introduces students to the fundamental techniques and applications of digital signal processing. Through lectures, homeworks, and laboratory experiments students learn:

  1. How to analyze signals using the discrete Fourier transform.
  2. The circular convolution, its relationship to linear convolution, and how linear convolution can be achieved via the discrete Fourier transform.
  3. Decimation in time and frequency FFT algorithms for efficient computation of the DFT.
  4. How to alter the sampling rate of a signal using decimation and interpolation; also, applications of multirate filtering to subband coding, compact disc, oversampling A/D, and transmultiplexing.
  5. How to design FIR digital filters using the window method, frequency sampling, and minimax optimal design.
  6. How to design IIR filters using prototypical analog filters, analog to digital mapping via impulse invariance and the bilinear transform, and frequency transformations.
  7. Direct form I and II, parallel, cascade, and lattice filter structures and their sensitivity to finite precision input, arithmetic, and coefficient quantization.

Topics:

  1. Introduction: signal types, DSP objectives, DSP applications, EE351 review (7 classes)
  2. Discrete Fourier Transform, circular convolution, and filtering via the DFT (7 classes)
  3. Fast Fourier Transform: decimation in time and frequency algorithms (5 classes)
  4. Multirate DSP: sampling rate conversion; efficient structures; applications (5 classes)
  5. FIR filter design methods (7 classes)
  6. IIR Filter design methods (7 classes)
  7. Discrete-time filter structures and finite precision effects (4 classes)

Class/laboratory schedule:

Three 50-minute lectures per week and three 3-hour laboratories during the semester.

Computer Usage:

The Matlab signal processing software is used in nearly all homework assignments. Matlab assignments included: i) Filtering signals to remove sinusoidal interference using a notch filter and analyzing via the DFT; ii) filtering via the DFT; iii) Implementing a 16-point radix two FFT; iv) performing signal decimation and interpolation and analyzing the output spectrum via the DFT; v) FIR filter design via the window, frequency sampling, and minimax optimal designs; vi) IIR filter design using Chebyshev and Butterworth prototypes and the bilinear transform.

Laboratory projects and assignments:

Three DSP laboratory experiments are a required part of this course. Laboratory experiments are conducted using the Hypersignal software, with a digital computer interfaced to a DSP board. The experiments explore: i) sampling; ii) FIR filter design and its use in building a graphics equalizer; iii) IIR filter design and its use in removing Gaussian noise. Working in teams, observational skills, and application of DSP theory and techniques are emphasized in the laboratory meetings.

Contribution to meeting the professional component:

This course introduces students to DSP design and analysis techniques that are core knowledge for DSP engineers, and which serve as solid grounding for graduate level work in DSP. Sustainability and economic issues are discussed in the context of advantages of DSP over analog signal processing, in the development of filter structures, and in efficient methods for decimation and interpolation filtering. Economic issues are also introduced via discussion of mainstream applications (e.g. CD, touch-tone phone, image and video compression) that have contributed to growth in the consumer electronics industry.

Relationship to program outcome:

  1. Graduates will understand

    1. the FFT algorithm for DFT computation;
    2. how sampling rate conversion affects the spectrum of signals;
    3. how stopband attenuation, passband ripple, transition width, and filter order interplay in the tradeoff between digital filter performance and implementation complexity;
    4. frequency transformations and bilinear transformation for mapping analog prototype filter designs to digital filter designs;
    5. The effects of input quantization, finite precision arithmetic, and finite precision coefficients on the performance and properties (stability) of digital filters [Ref: Outcome O.3.1.1.]

  2. Graduates will be able to design digital FIR and IIR filters, as well as multirate systems for various applications [Ref: Outcome O.3.1.2]
  3. Graduates will understand sampling in both time and frequency and its effect on signals and their information content. [Ref: Outcome O.3.2.1.]
  4. Graduates will be exposed in a modest way to more advanced DSP topics. Thus, they will perceive that there are many topics in DSP, including statistical signal processing, wavelets and filterbanks, digital image processing, and speech processing, that will require continual learning. [Ref: Outcome O.4.2.1.]
  5. Graduates will be able to productively contribute to group laboratory projects. [Ref. Outcome O.5.1.1]
  6. Graduates will be able to complete accurate lab reports. [Ref. Outcome O.5.2.1]