Department of Electrical and Telecommunications Engineering Technology TEL (718) FAX: (718) Courses Description:

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1 NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street Brooklyn, NY Department of Electrical and Telecommunications Engineering Technology TEL (718) FAX: (718) Course Title: Courses Description: EET 3102 Signals and Systems This course introduces the students to the modeling concepts used when dealing with signal and system. Such a course is part of a sequence of courses that form part of most engineering curricula in Electrical Engineering Technology in most colleges. A variety of numerical and symbolic methods on discrete and analog systems are introduced such as the Laplace transform, the z- transform, DTFT, DFT, FFT. Synthesis and analysis are explored using Matlab and Simulink. Relevant examples from Electrical Engineering Technology as well as Industrial design are presented and discussed. Credit hours: 4 course credits, consisting of 3 classroom hours, and 3 Lab hours Prerequisites: EET 2140 Co-requisites: MAT 1575 Course Objectives/Course Upon completion of this course the student will be able Outcomes to: 1. Acquire the theoretical knowledge of model engineering systems using a mathematical approach. (ABET Criteria 3a, 3b, 3d) 2. Acquire the theoretical knowledge of the tools required for system analysis. (ABET Criteria 3a, 3b, 3f) 3. Acquire the mathematical knowledge about converting analog to digital systems (A/D AND D/A converters). (ABET Criteria 3a, 3b, 3f) 4. Acquire knowledge in writing Matlab codes. (ABET Criteria PC a) 5. Acquire simulation knowledge of a 2 port system. (ABET Criteria 3a, 3b, 3c, PC a) Required text: 1. M. Kalechman, Practical Matlab Applications for Engineers, CRC Press, Kamen & Hech, Fundamentals of Signal and Systems,

2 Prepared by: Using the Web and Matlab, Prentice Hall, 2000 M. Kalechman Instructional Objectives and Assessment The following assessment techniques are correlated to the course objectives as follows: Objectives: 1. Recognize when an engineering system problem can be model using a block box approached and solved it numerically, symbolically, or analytically. 2. Apply numerical and symbolic methods in the conversion of analog signals to digital sequences (AD) or from digital signals to analog continuous (DA) signals. 3. Define the systems gain or system transfer function, and be able to apply methods for finding (the roots of the system transfer function) its poles and zeros in order to explore the system stability and its oscillatory behavior. 4. Understand linear differential equations and a system of algebraic equations and be able to model and study them in terms of its system matrices, matrix inverse, ranks, and matrix conditional number 5. Understand the concepts of convolution and correlation (auto & cross) both in the time domain and its relations in the frequency domain and its many applications in systems, controls and communications. Assessment: Students will demonstrate skills in modeling and solving linear time invariant, nonlinear, and transient (with initial conditions) systems. Students will show skills in calculating and representing spectral analysis of continuous and discrete signals by using the Matlab language using a numerical or symbolic approach. Students will perform the analysis involved in the sampling process, and explore the effects of over-sampling and undersampling with respect to the Nyquist sampling rate and explore its effects in both the time and frequency domains. Students will use Matlab and Simulink to determine its transfer function, its system impulse response, and its pole-zero constellation of typical engineering/industrial problem. Students will demonstrate skills in performing matrix algebra by representing a system in the form of a set of first order diff equations, and matrix format. Systems of nonlinear equations are also explored. Bode, Nyquist and root locus system plots are explored. Students will demonstrate skills in performing algebraic manipulations with convolutions and correlations operators, as well as algebra involving impulses (Dirak impulse) and study the effects in both the time and the frequency domain.

3 Grading Procedure: Midterm: 15% Final Exam: 25% Labs: 20% Quizzes: 15% Homework: 10% Projects: 15% Course Outline: Week Lecture Topic Laboratory 1 & 2 1. Mathematical representation of analog and digital time domain signals. (Kalechman/1-10)(Kamen/2-18) 1. Verify Euler s identities using Matlab. 2. Verify the orthogonally property of the Hermite, exponentials, sinusoids, Laguerre and the sinc family of functions. (Kalechman/17-20, 72-75, ) 1. Mathematical representation of analog and digital time domain systems. (Kalechman/10-14) (Kamen/72-78) 4 1. Mathematical representation of the conversion of analog to digital systems. 2. The sampling process: up sampling and down sampling. Kalechman(4/R.1.1- R.1.15) Kamen(70-75, ) 1. Explore the responses of linear time domain systems using differential equations in Matlab. Kalechman(15, ) 1. Using Matlab to explore the sampling and reconstruction processes of typical signals used in linear analysis. 2. Explore the Nyquist theorem and the Nyquist sampling rate. 3. Explore decimate, up and down sampling. 4. Implementation of a moving average system.

4 Kalechman(38/R.1.117, 44/R R.1.138) Kalechman(76-82) 5 & 6 1. The Fourier series and the Fourier Transform. 2. Properties of the Fourier transform. 3. Line, phase and power spectrum. 4. Parseval s Theorem and the Gibbs discontinuities. Kalechman( ) Kamen( ) 1. Evaluate the Fourier Series of a square and a triangular wave and obtain the line, phase and power spectrums. 2. Use and explore the following window functions: Boxcar, Hamming, Hanning, Blackman, Bartlett, Gaussian, Cauchy, Parzan, etc. to limit a signal and its effects on frequency. Kalechman(342/R R.4.75, 47/R R.1.161) 7 & 8 1. Mid-term Exam 2. The convolution integral for continuous systems. 3. Properties and algebra using convolutions. 4. Linear time invariant systems. 5. Nonlinear systems. 6. Calculating system response. 7. Frequency domain analysis. 1. Evaluation of convolutions using standard signals by numerical techniques in the time domain and its effects in the frequency domain. Kalechman( ) Kalechman( ,

5 336/R.4.49-R.4.66) Kamen(75-84, ) 9 & The Laplace transform. 2. Relation between the Fourier and the Laplace transforms. 3. Transform properties and the initial and final value theorems. 4. Solving systems of differential equations using the Laplace transforms. 5. First order, second order and higher order systems. 6. Detail study of the second order system (Over-damped, critically damped and underdamped). 1. Explore the Laplace transform using the Matlab Symbolic Tool Box. 2. Revisit the system convolution and the second order systems in the time and frequency domain. Kalechman(361/R R.4.121) Kamen(64-84) Kalechman(345/R.4.74 to R.4.115) Kamen( ) Analog filters, normalized prototype. 2. Magnitude and phase considerations. 3. Frequency scaling and impedance scaling. 4. Active and passive filters. 5. T and sections. 6. Butterworth, Chebyshev (type1 &2), Elliptic & Bessel filters. 1. Using Matlab to performs frequency and impedance scaling. 2. Design Butterworth, Chebyshev(type1 &2), Elliptic & Bessel filters at the component level. Kalechman( ) Kalechman( )

6 12 1. Discrete systems, system difference equations, recursive and nonrecursive (memoryless). 2. Causal & non-causal difference equations. 3. The discrete impulse response. 4. DTFT, DFT, Z-transform and the Fast Fourier Transform. 1. Explore the DTFT, DFT, Z-transform and the Fast Fourier Transform using the Matlab Symbolic Tool Box. 2. Solve discrete difference equations in time and frequency. Kalechman( ) Kalechman( ) Linear convolution and the circular convolution. 2. Overlap and add method. 3. Overlap and save method. 4. The FFT and IFFT. Kalechman( ) 1. Compare the linear convolution with the circular convolution. 2. Implement the linear convolution using the overlap and add method, and the overlap and save method, as well as the FFT and IFFT. Kalechman( ) Digital filters, the normalized prototype. 2. Magnitude and phase considerations. 3. Implementation using the following: Bilinear transformation, Impulse invariant method and the Yule-Walker Algorithm. 1. Explore using Matlab filter implementation using the Bilinear transformation, Impulse invariant method and the Yule-Walker Algorithm. 2. Design Butterworth, Chebyshev (types1 & 2), Elliptic & Bessel digital

7 Kalechman(570/R R.6.45, 583/R.6.81-R.6.109) filters. Kalechman(588/R R.6.135, 625, ) 15 Final Exam

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