3 Semester Credit Hours

Course Description

Introduction to the concepts, techniques, and applications of digital signal processing (DSP) via the context of a real-time DSP system for the filtering of analog signals.

The central relationship of a digital filter’s frequency response to the frequency response of an equivalent analog filter is established using time and frequency domain models for analog-to-digital and digital-to-analog conversion. A discussion of oversampling as a means of shifting the workload in a real-time DSP system from analog to digital filtering is then used to introduce detailed time and frequency domain models of downsampling and upsampling. Techniques for the design of a digital filter’s frequency response are then presented in view of the various tradeoffs (linear phase, arithmetic complexity, coefficient quantization, arithmetic quantization) between practically realizable implementations of infinite impulse response (IIR) and finite impulse response (FIR) filters.

The Discrete Fourier Transform (DFT) and its computation using Fast Fourier Transform (FFT) algorithms are introduced as a practical means of frequency analysis, particularly in the context of examining a digital filter’s frequency response during the design process. The relationship of the DFT to the multidimensional DFT, the Discrete Cosine Transform (DCT), the Time-Dependent Fourier Transform (TDFT), and the Complex Cepstrum are also discussed.

Prerequisites

• One year of college-level calculus (NMTH 1111 and NMTH 1112)
• A course in linear algebra and differential equations (NMTH 2301)
• A calculus-based course in probability theory and statistics (NMTH 3701)
• An undergraduate course in Signals and Systems (NEEC 3501)
• General prerequisite: Students must have the knowledge resulting from completing all coursework in the curriculum for a BS degree in Electrical Engineering from an ABET-accredited engineering program in the United States or a CEAB-accredited program in Canada, or the equivalent from a foreign institution; performance level in this coursework should be equivalent to a cumulative undergraduate GPA of 2.9 or better on 4.0 scale
  

Course Objectives

At the end of this course, you should be able to:

• Describe, design, and analyze DSP systems for the filtering of analog signals
• Describe and apply in the context of DSP systems the time- and frequency-domain models of analog-to-digital and digital-to-analog conversion
• Describe, design, and analyze the incorporation of oversampling into a DSP system to control the workload tradeoff between analog and digital filtering
• Explain and apply in the context of oversampled DSP systems the time- and frequency-domain models of downsampling and upsampling
• Design and analyze practically realizable digital filters for meeting desired frequency response specifications
• Design and analyze implementation structures for practically realizable digital filters
• Explain and apply in the context of digital filter design the tradeoffs between the use of finite impulse response (FIR) and infinite impulse response (IIR) filters
• Explain and apply in the context of digital filter design the use of the Discrete Fourier Transform (DFT) in examining frequency content
• Explain the concepts underlying the Fast Fourier Transform (FFT) algorithms for the efficient computation of the DFT
• Explain the interrelationships between the DFT and the Discrete Cosine Transform (DCT)
• Explain the interrelationships between the Fourier transform, the time-dependent Fourier transform, the Uniform Filterbank, and the Complex Cepstrum.
• Explain the issues involved in extending one-dimensional DSP to multiple dimensions.

Course Topics

The following topics will be covered in the order given.

• Introduction; overview
• Basic signals & systems
• Linear time-invariant (LTI) systems and convolution
• Discrete-time Fourier transform (DTFT)
• Sampling
• Laplace transform
• Non-integer delay
• FIR and IIR filters
• Z transform
• Z transform and filters
• Analog-to-digital conversion
• Digital-to-analog conversion
• Digital filters of analog signals
• Upsampling
• Downsampling
• Oversampling
• Phase
• Filter design introduction
• FIR windowing design
• FIR optimal design
• Optimal FIR filter design
• Analog Butterworth filters
• IIR filter design
•  Discrete Fourier Transform (DFT) Introduction
• DFT wraparound
• DFT properties
• DFT overlap add
• Fast Fourier transform (FFT)
• Filter structures I: introduction
• Filter structures II: direct forms
• Filter structures III: coefficient quantization
• Filter structures IV: arithmetic quantization
• Filter structures V: cascade and parallele forms
• All-pass systems
• Minimum phase systems
• Time-dependent Fourier transform (TDFT) introduction
• TDFT
• Multidimensional DSP (MDSP)
• Complex cepstrum