EE 351 – Discrete-time Systems

Designation:

Junior-level technical elective for Electrical Engineering students

Catalog Data:

Introduction to discrete-time signal processing; sampling, linear time-invariant systems, discrete-time Fourier transform and discrete Fourier transform, Z transform. Prerequisite: EE 350.

Prerequisites by topic:

1. Understanding elementary continuous-time signals (delta and unit step) and concepts such as periodicity, even-odd signals, and time transformations.
2. Understanding linear constant coefficient differential equations and their solutions.
3. Understanding continuous-time systems, system properties, impulse response, the convolution integral, and properties of convolution.
4. Understanding the Fourier series decomposition of continuous-time periodic signals.
5. Understanding the system eigenresponse and its use for computing the system output when a periodic input signal is applied.
6. Understanding the continuous-time Fourier transform and its properties, for measuring the spectral content of an aperiodic continuous-time signal.
7. Understanding the Laplace transform and its uses in solving differential equations and in characterizing properties of systems.
8. Understanding Matlab and its use in simulating signals, in filtering, and in analyzing signals and systems in the frequency domain.

Course Objectives:

This course provides foundational education for students in sampling of continuous-time signals and in time, frequency, and Z-domain descriptions of discrete-time signals and systems. Through lecture and out-of-class assignments, students learn:

1. How to design a sampling and reconstruction system to meet specific requirements.
2. How to solve (discrete-time) difference equations.
3. How to determine the system frequency response and eigenresponse.
4. Z-domain descriptions of signals and systems, for use in solving difference equations, in determining whether or not a system is causal and stable, in performing convolution sums, and in qualitative assessment of system frequency response.
5. How to design simple frequency-selective filters via pole and zero placement.
6. The discrete Fourier transform for practical evaluation of a signal’s spectral content and a system’s frequency response.

Topics:

1. Introduction: signal types, signal processing objective and applications (3 classes)
2. Fundamental discrete-time signals, periodicity, and time transformations (4 classes)
3. Ideal and practical sampling and reconstruction systems (8 classes)
4. Discrete-time linear systems: difference equations, impulse response, convolution sum and properties (9 classes)
5. Discrete-time Fourier transform and Frequency Response (8 classes)
6. Z-transform (8 classes)
7. Discrete Fourier Transform (3 classes)

Class/laboratory Schedule:

Three 50-minute lectures per week.

Computer Usage:

The Matlab signal processing software is used in most homework assignments. Matlab assignments include: i) building a 512-level uniform quantizer; ii) iterating difference equations; iii) exploring frequency selectivity by filtering sinusoids; iv) frequency response evaluation and approximation using the DFT; v) linear and nonlinear phase characteristics and their effects; vi) notch filter design and filtering to cancel 60 Hz interference.

Contribution to meeting the professional component:

This course provides EE grounding in sampling, discrete-time signals, and discrete systems. The course culminates with simple frequency-selective filter design based on pole-zero placement, and with signal (spectrum) analysis via the Discrete Fourier Transform. This course is a prerequisite for the senior elective courses EE453 (Digital Signal Processing) and EE429 (Digital Control Systems). Topics pertaining to sustainability are considered in a minor way through discussion of the differences between analog and digital signal processing, and through the development of various digital filter structures for implementing the filtering operation.

Relationship to program outcomes:

The course relates to the following program outcomes:

1. Graduates will understand the requirements on sampling without aliasing, the spectrum of the sampled signal, and both ideal and practical A/D and D/A systems [Ref: Outcome O.3.2.1.]
2. Graduates will be able to solve difference equations, to filter signals, and to determine the properties of discrete-time systems. [Ref: Outcome O.3.2.1.]
3. Graduates will be able to determine the system eigenresponse and will understand the significance of both the magnitude and the phase response of linear, time-invariant systems. [Ref: Outcome O.3.2.1.]
4. Graduates will be able to design simple frequency-selective filters using pole-zero placement, and to determine the spectral content of signals via the discrete Fourier transform. [Ref: Outcome O.3.1.2.]
5. Graduates will learn that discrete-time signals and systems is fundamental background required in senior elective courses in digital signal processing (EE453), in digital control (EE429), and in image processing (EE485). [Ref: Outcome O.4.2.1.]