In this course, the goals are to analyze the continuous and discrete time signals and systems.
Prerequisite(s)
-
Corequisite(s)
-
Special Requisite(s)
-
Instructor(s)
Assoc. Prof. Esra Saatçi
Course Assistant(s)
Schedule
Thursday 09:00-11:00, Friday 09:00-11:00
Office Hour(s)
Moday
Teaching Methods and Techniques
The course is taught by lectures at the rate of 2 hours per week and practical sessions at the rate of 2 hours per week. A part of the lectures will consist of delivery of the course material using powerpoint. The lectures will follow a textbook and will contain supporting material for the practical sessions. The lectures will include discussion questions which will be used to stimulate in-class discussion.
Principle Sources
Signals and Systems, Second Edition, A. V. Oppenheim, A. S. Willsky with S. H. Nawab, Prentice-Hall, 1997.
Other Sources
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Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction to the course
Oral presentation
2. Week
Continuous and discrete time signals. Definition and some examples of signals and systems. Graphical representations of signals. Signal energy and power. Transformations of the independent variable in a signal. Periodic signals. Even and odd signals and even-odd decomposition of a signal. Continuous time exponential and sinusoidal signals and their properties.
Oral presentation
3. Week
Discrete time exponential and sinusoidal signals and their properties. Definitions and properties of discrete time and continuous time unit impulse and unit step functions. Continuous time and discrete time systems. First and second order system examples.
Oral presentation
4. Week
Cascade, parallel and feedback interconnections of systems. Basic system properties: Memoryless, invertibility, causality, stability, time invariance and linearity. Properties of linear systems.
Oral presentation
5. Week
Discrete time LTI systems and the convolution sum. Continuous time LTI systems and the convolution integral.
Oral presentation
6. Week
Properties of LTI systems. Causal LTI systems described by differential and difference equations. Block diagram representations of first-order systems.
Oral presentation
7. Week
Fourier series representation of periodic signals. The response of LTI systems to complex exponentials. Fourier series representation of continuous time periodic signals. Convergence of the Fourier series. Properties of the CTFS.
Oral presentation
8. Week
Midterm
9. Week
Fourier series representation of discrete time periodic signals. Properties of the DTFS. Fourier series and LTI systems.
Oral presentation
10. Week
Representation of aperiodic continuous signals: The continuous time Fourier transform. Convergence of Fourier transforms. The Fourier transform for periodic signals. Properties of the CTFT.
Oral presentation
11. Week
Convolution and multiplication properties of the CTFT. Representation of aperiodic discrete signals: The discrete time Fourier transform. Periodicity of the DTFT.
Oral presentation
12. Week
Convergence issues associated with the DTFT. The DTFT for periodic signals. Properties of the DTFT. Convolution and multiplication properties of the DTFT.
Oral presentation
13. Week
Representation of a continuous time signal by its samples: The Sampling Theorem. Impulse train sampling. Exact recovery by an ideal lowpass filtler. Sampling with a Zero-Order Hold. Reconstruction of a signal from its samples using interpolation. The effect of undersampling: Aliasing.
Oral presentation
14. Week
Recapitulation
Oral presentation
15. Week
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
30
Homework / Term Projects / Presentations
1
20
Final Exam
1
50
Program Outcomes
PO-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
PO-2
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
PO-4
Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language.
PO-8
Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO-9
Awareness of professional and ethical responsibility.
PO-10
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
PO-11
Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.
Learning Outcomes
LO-1
Define and classify the concept of a signal and of a system and operate with useful signal models: unit step, unit impulse, sinusoid, and exponential function.
LO-2
Describe the concept of a system’s impulse response and convolution im LTI systems and calculate the response of an LTI system to an arbitrary input by using its impulse response and convolution.
LO-3
Express a periodic signal in a Fourier series and an aperiodic signal by a Fourier transform.
LO-4
Relate frequency-domain descriptions of signals and systems to their characteristics in the time domain.
LO-5
Use frequency-domain techniques to solve input/output problems and to design LTI systems.
LO-6
Explain the sampling theorem, including what is required to recover original continuous time signal from its equally spaced samples exactly.
