**PRINCE GEORGE'S COMMUNITY COLLEGE**

**Department of Physical Science and Engineering**

**Engineering Program****
Welcome to Signals and Systems: Modeling, Computation, and Analysis!**

EGR-2050 Signals and Systems: Modeling, Computation, and Analysis

Number LE01

**INSTRUCTOR**:
Dr. Scott D. Johnson, Associate Professor, Engineering Coordinator,
Physical Sciences and Engineering

**OFFICE**: Official office is CAT-229R; but unofficial office is CAT-305 (better place to find me)

**OTHER
LOCATIONS: **CH-100 (Department), the classroom proper, and the Cyber Cafe

**
PHONE NUMBERS**: 301-322-0420 (Department Main Line) or 301-386-7536 (Office)

**
E-MAIL ADDRESS:
sdjohnson@pgcc.edu**

To facilitate e-mail communication with me, please include the following:
The course designation (EGR 2050) and the *subject* of any e-mails
to me during the Fall 2014 semester. **Note: All credit students (with
the exception of Howard Community College students enrolled at Laurel College Center) are required to use Owl Mail for all college communication.**

*Example:*
EGR2050: Need help on roots of equations

**ENGINEERING PROGRAM'S WEB PAGE**: *
http://academic.pgcc.edu/engineering*

**WEB PAGE**: *http://academic.pgcc.edu/~sjohnson*

**
OFFICE HOURS**:
MW 7:15-8:30pm; TTh 2:15-3:30pm, by appointment all other times

*Note:* Part or all of the office hours might be in the classroom (CAT-305) as student questions warrant.

**
COURSE DESCRIPTION**:

Solving high-level applications in engineering, physics, chemistry, and biology require an
understanding of modeling at a system level. To fully prepare a student, this course
emphasizes system analysis. Crucial to modeling in the modern world is an understanding
of the computational modeling as well as the mathematical formulation, therefore a variety
of numerical/computational methods will be reviewed in the first part of the course and
extended for the purpose of understanding the computational methods required to do modeling
in a modern setting. Subjects to be studied include error analysis, roots of non-linear equations,
solving systems of linear equations, eigenvalues, eigenvectors, and eigenfunctions, optimization,
curve fitting including splines, Fourier analysis, modeling, numerical differentiation and
integration, and numerical solving of differential equations including, but not limited to,
predictor-corrector methods and finite element analysis. It will be assumed that the student
is at least partially familiar with this concepts from previous mathematics class.
Extra study may be required for a student lacking these skills.

These concepts will be extended into computational methods that are useful in analyzing signals and systems.
Topics will include representation of systems and signals, transfer functions, and filters.

The relationship between linear systems and both discrete time and continuous time signals and sampling
will be explored and used to better understand real world applications. Practical issues of representation
and sampling of signals will be explored with particular emphasis to best case solutions.

This will be extended in to the study and use of a number of filters, in particular digital filters.
Topics will include OTFs, DFTs, Laplace transforms, Z-transforms, Radon transforms, and convolutions.

Lastly, there will be extensive surveys of a number of advanced subjects include molecular dynamics, percolation,
and Monte Carlo simulation methods. Some new mathematical concepts will be introduced in the class.

A number of software packages and languages important to engineering are surveyed with primary emphasis
on mastering one high-level language such as MATLAB/Octave, C/gcc/g++, or Fortran/gfortran.
This course, recognizing the fact that all engineers and scientists need the aforementioned topics,
will emphasize a number of case studies in such areas as mechanical, civil, environmental, electrical,
aerospace, chemical, and biological engineering, as well as in the sciences.

Team work along with communication skills (oral, written, and graphical) are exercised throughout the course.

**PREREQUISITES**:

EGR 1010, EGR 1140, and MAT 2420.

**CREDIT HOUR EXPLANATION:**

In the Engineering program at Prince George's Community College, for all credit course, students are expected to spend a minimum of 45 combined hours of instructional time and related coursework time per credit hour. This course is a 4 credit course with a portion of that credit being laboratory. This course achieves the minimum of 180 hours of instructional time by requiring 35 hours of instructional time, 20 hours of laboratory time and 125 hours of student work outside of instructional time. Minimum outside instructional time assumes the student is aiming for a C, not an A.

**COURSE LEARNING OUTCOMES:**

- Students passing this course will be able to accomplish all of the outcomes listed below.
- Students will demonstrate their attainment of these outcomes through the planned assessments. So, for each course learning outcome, indicate briefly the planned assessment tools, such as cases, essay, multiple choice questions, etc.
- Courses seeking general education status must address all pertinent general education outcomes in the below alignment.

Upon successful completion of the course a student will be able to:

Course Outcome |
Program Outcome # |
MO # |
Assessment |

Give an error on solutions to numerically solved problems and qualify that error. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate the ability to use the appropriate numerical methods to solve complex science or engineering problems. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Use a software package to aid in the solution of a complex science or engineering problem. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Solve for the roots, minimum and maximum of an equation, solve a system of equations, fit a curve to a set of data, and perform numerical differentiation and integration. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate an understanding of the numerical techniques to solve differential equations. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Solve basic linear algebra systems. In particular show the ability to apply eigenvalues and eigenvectors. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate an understanding of the basic concepts of signals and linear systems, Laplace Transforms, z-transforms, and development and application of FFTs. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate an understanding of frequency analysis of signals in continuous and discrete-time. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate an understanding of systems analysis. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate an understanding of how to apply techniques to model real-world systems. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

Demonstrate an understanding of how to apply a digital filter in signal processing applications. |
1,2,3,4,5,6,7 |
1.1,1.2,1.3,1.4,2.1,2.2,2.3,3.1,4.1,4.2,4.3 |
Homework and projects |

**REQUIRED TEXTBOOKS: **

Digital Filters
3^{rd} Edition. Hamming, R. W. Dover Publications, Inc. New York (1989).

A First Course in Numerical Analysis
2^{nd} Edition. Ralston, A. & Rabinowitz, P. Dover Publications, Inc. New York (1978).

Schaum's Outline of Signals and Systems
2^{nd} Edition.
Hsu, H.
McGraw-Hill. (2010).

Schaum's Outline of Numerical Analysis
2^{nd} Edition.
Scheid, Francis.
McGraw-Hill. (1989).

Schaum's Outline of Finite Element Analysis
1^{st} Edition.
Buchanan, George.
McGraw-Hill. (1994).

Pocket Book for Technical Writing for Engineers and Scientists
3^{rd} Edition.
Finkelstein, Leo.
McGraw-Hill. (2007).

Numerical Methods for Engineers
6^{th} Edition. Chapra,Steven and Canale, Raymond.
McGraw-Hill. (2009/2010).

Getting Started with MATLAB: A Quick Introduction for Scientists and Engineers.
Pratap, Rudra.
Oxford University Press. (2009).

**
OTHER REQUIRED COURSE MATERIALS: **

Pens, Pencils, Eraser, Straight edge, Paper, Textbooks, and Calculator are required for every class.

**
OUTSIDE CLASS REQUIREMENTS: **

As with any class an amount of time at least equivalent to two times the credit hours is expected to be performed for homework and labs. Please allot sufficient time for homework.

Homework will be assigned each week including the first week.

**
GRADING CRITERIA:**

Evaluation of student performance is to be based on:

Unannounced quizzes and homework will account for approximately 15% of the semester grade. Homework consists of essays that are to be written in standard English format and problem sets. A grade of zero will be given to anyone who copies their homeworks (or quizzes from neighboring students). All work is subject to re-grade if academic dishonesty is suspected. Turn work in on time.

Fundamentals of Signals and Systems (split into what would traditionally be called a Midterm and Final), including numerical methods, exam to count as 20% of the grade. Using other resources (students next to you, computers of any type) is considering cheating and a grade of zero will be given to the student.

Four extensive projects will be assigned that will constitute 50% of the total grade. These projects are to be an original individual work. A grade of zero will be given to anyone who copies their projects. All work is subject to re-grade if academic dishonesty is suspected. Turn work in on time.

An essay surveying the material in the course. This essay is to include not just the methods but a practical guide on when to use the different numerical methods and how to use systems methods and how they related to the numerical methods. This is worth approximately 15% of the semester grade.This project is to be an original individual work. A grade of zero will be given to anyone who copies their projects. All work is subject to re-grade if academic dishonesty is suspected. You must turn this in on time, NO exceptions.

**The scale used for grades in this class is the "Modern Standard Grading Scale" as defined in the COLLEGE RESOURCES and SERVICES link below.**

**Q GRADES: **

Students are expected to attend and participate in class activities. Students who either never attended the class or who ceased attendance during the first 20 percent of the course will be assigned a "Q" grade by the instructor. The Q grade is a final grade and will not be replace with a different grade at a later time. Although the Q grade will not impact students' GPA, the issuance of a Q grade will likely decrease students' financial aid awards.

Faculty are required to report the date of last attendance for each student receiving Q or F grade(s) in order for the college to report this date to a variety of federal agencies as mandated. The date of last attendance is considered the date of the student's termination from the course, regardless of the date of grade submission. Early termination from a course may result in reduction in student loans and financial aid (e.g., Pell, VA benefits) and may require the student to reimburse funds to the funding agency.

**HOW ASSIGNMENTS ARE TO BE SUBMITTED: **

Homework is due at the start of class (or before) except for in-class projects.

Laboratory work is to be submitted in appropriate binders follow any standard laboratory format (this will be reviewed in class).

Make-up homework, quizzes, and/or tests are up to the discretion of the teacher (excused absences only). No makeup will be possible for laboratory work, sufficient time should be available to recover if an absence is necessary.

**COURSE OUTLINE:**

New topics are to be covered each week and include but are not limited to the following subjects. This outline is subject to change.

Week 1 Introduction to Computational Methods for signals and systems and beyond

Week 2 Modeling and Error Analysis

Week 3 Review of numerical analysis: Roots of Equations, optimization, curve fitting

Week 4 Review of numerical analysis: Numerical differentiation and integration

Week 5 Linear Algebraic Equations (eigenvalues,eigenvectors,eigenfunctions)

Week 6 Linear Algebraic Equations

Week 7 Linear systems: Signals and sampling

Week 8 Linear systems: Signals and sampling

Week 9 Filters, in particular digital filters, transformations

Week 10 OTFs, DFTs, Laplace transforms, Z-transforms, Radon transforms, and convolutions

Week 11 Fourier Analysis and other similar analysis techiques

Week 12 State-space Analysis

Week 13 Differential Equations

Week 14 Finite Differences and Finite Element method

Week 15 Simulation methods: Molecular Dynamics, Monte Carlo, and Percolation

A new chapter should be read each week usually following the title of the topic above. Problems will be based off of the reading.

Quizzes will all be unannounced so be prepared.

Tests will be announced a week before and will depend on our progress in the classroom.

**CLASSROOM POLICIES:**

Food and drink in limited quantities (snacks, not meals) are permitted in restricted areas (not near electronics) and will be revoked if proper cleanliness is found wanting.

Cell phones must be in vibrate mode and are only to be answered for emergencies (step outside please).

Common courtesy is to apply at all times.

**
IMPORTANT DATES:**

Labor Day - College closed - No classes |
Sat.-Mon., August 30 - September 1 |

Last day to apply for fall graduation |
Monday, September 15 |

Last day to change from "audit to credit" or "credit to audit" for full-semester classes |
Friday, September 19 |

Midterm - middle of semester; class will speed up |
Wednesday, October 15 |

College Enrichment Day - No classes (for students; NOT faculty) |
Tuesday, October 28 |

Last day to withdraw from full-semester classes |
Friday, November 14 |

Thanksgiving Break Start - No classes |
Wed., November 26 |

College closed - no classes |
Thurs.-Sun., Nov. 27 - Nov. 30 |

Last Day of Regular Classes |
Sunday, December 7 |

Final exam period/last week of classes |
Monday, December 8 |

Open Registration begins |
Monday, December 8 |

Winter Break - College closed |
Saturday-Sunday, December 20 - January 4 |

Classes begin Spring 2015 |
Tuesday, January 20 |

**LAB INFORMATION: **

Computer programming maybe done in class (CAT-305) on the portable PCs during designated time periods.