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S. Prasad Portland State University ECE 223 Fall 2
007 Lecture 14
ECE 223 Signals and Systems II
Dr. Shalini Prasad
Electrical and Computer Engineering
sprasad@pdx.edu
http://www.ece.pdx.edu/~prasads
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ECE 223 Lecture 14: Discrete and Continuous Time Fourier Transforms and Their Properties, Study notes of Signals and Systems
Information about lecture 14 of ece 223: signals and systems ii at portland state university, taught by dr. Shalini prasad. The lecture covers the discrete time fourier transform (dtft) and continuous time fourier transform (ctft), their properties, and applications. Students are expected to have read chapters 3 and 4 of the textbook and are preparing for exam 2, which will focus on these topics.
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S. Prasad Portland State University
ECE 223
Fall 2
Lecture 14
ECE 223 Signals and Systems II
Dr. Shalini Prasad
Electrical and Computer Engineering
sprasad@pdx.edu
http://www.ece.pdx.edu/~prasads
S. Prasad Portland State University
ECE 223
Fall 2
Lecture 14
Homework Assignment IV
• Problems: 4.16 (a), 4.17(a), 4.18(a),
4.25(a), 4.26(a)
Due Fri., Nov 30
Read
Chapter 3: Sections 3.11-3.12, 3.14-3.
Chapter 4: Section 4 and 5 (FFTand Sampling)
S. Prasad Portland State University
ECE 223
Fall 2
Lecture 14
Exam 2
Topics:
• DTFT, CTFT , Properties of FT and
applications of FT, Interpretation of FT
• Total Score 60 points• 4 questions, problem 1: 20 pts, Problem 2:
10 pts, Problem 3: 19 pts, Problem 4: 11pts
S. Prasad Portland State University
ECE 223
Fall 2
Lecture 14
Discrete Time Fourier Transform
(DTFT)
Low frequency and high frequency discrete-time signals
Determine transforms of most simple signals by applyingthe definition
Find the inverse transform.
Sufficient conditions for convergence and inversetransform convergence.
Relationship of symmetry and periodicity of the transformto properties of the signal.
The relationship of the output of an LTI system to theFourier transforms of the input signal and the impulseresponse of the system.
S. Prasad Portland State University
ECE 223
Fall 2
Lecture 14
Continuous Time Fourier
Transform (CTFT)
- The tradeoffs of using the Fourier transform versus the Laplace transform. - How the DTFT of a periodic signal is related to the DTFS coefficients.
S. Prasad Portland State University
ECE 223
Fall 2
Lecture 14
Fourier Transform & Series
Properties
- Properties of the four transforms• Effect of windowing on the magnitude spectrum. - How to identify the magnitude spectrum of basic time-domain signals that have beenwindowed. - How each of the properties is relevant to practical applications and design, asdiscussed in class.