Note: The following provides a suggested course description, objectives, and an outline. These may be modified pending discussion with the Faculty Chairs, proposing faculty, and other curriculum reviewers.

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

Course Objectives: At the end of this course, you should be able to: Understand, design, and analyze DSP systems for the filtering of analog signals. Understand and apply in the context of DSP systems the time- and frequency-domain models of analog-to-digital and digital-to-analog conversion. Understand, design, and analyze the incorporation of oversampling into a DSP system to control the workload tradeoff between analog and digital filtering. Understand 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. Understand 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. Understand and apply in the context of digital filter design the use of the Discrete Fourier Transform (DFT) in examining frequency content. Understand the concepts underlying the Fast Fourier Transform (FFT) algorithms for the efficient computation of the DFT. Understand the interrelationships between the DFT and the Discrete Cosine Transform (DCT). Understand the interrelationships between the Fourier transform, the time-dependent Fourier transform, the Uniform Filterbank, and the Complex Cepstrum. Understand the issues involved in extending one-dimensional DSP to multiple dimensions.

Course Outline by Topical Areas:

Introduction; overview
Signals & systems background
Discrete-time Fourier transform
Sampling
Laplace transform
Fractional delay
FIR and IIR filters
Z transform
Analog to digital conversion
Digital to analog conversion
DSP systems for analog filtering
Downsampling
Upsampling
Oversampling
Phase
FIR filter design
IIR filter design
DFT
FFT
Filter implementation structures
Minimum phase
Time-dependent Fourier transform
DCT
Multidimensional DSP
Complex cepstrum