Academic year 2015-16
Signals and Systems
| Degree: | Code: | Type: |
| Bachelor's Degree in Computer Science | 21409 | Core subject, 2nd year |
| Bachelor's Degree in Telematics Engineering | 21720 | Core subject, 2nd year |
| Bachelor's Degree in Audiovisual Systems Engineering | 21598 | Core subject, 2nd year |
| ECTS credits: | 8 | Workload: | 200 hours | Trimester: | 1st and 2nd |
| Department: | Dept. of Information and Communication Technologies |
| Coordinator: | Xavier Serra |
| Teaching staff: | Xavier Serra, Gemma Piella, Constantine Butakoff, Azadeh Faridi, ... |
| Language: | |
| Timetable: | |
| Building: | Communication campus - Poblenou |
This is an introductory course to digital signal processing designed for the second year students of Computer Engineering, Telematics and Audiovisual Systems. The course aims that students attain an understanding of the basic mathematical concepts used in the study of digital signals and systems and that they learn how to use these concepts in concrete engineering problems.
The course syllabus includes a mathematical part and another more focused on signal processing from an engineering standpoint. Among the more mathematical topics it includes the study of complex numbers, the discrete Fourier transform and Z transform. On the signal processing topics it includes the study of sinusoidal signals, its sampling and its spectral representation, and the study of FIR and IIR digital filters.
The course is organized methodologically in three types of educational activities: lectures and theoretical seminars, practical classes and laboratories. In the lectures the teacher explains the theoretical concepts of the syllabus. In the seminars, the teacher works with small groups of students to discuss and solve problems related to each one of the topics of the lectures with active participation of students. Finally, in the laboratories, which take place in computer rooms, students do programming exercises under the supervision of the teacher. In these labs the students design and implement algorithms associated with each signal processing concept discussed in the course.
The course is organized in three types of educational activities: theoretical classes, seminars and practices/laboratories. The final grade is the result of combining continuous assessment and three exams.
Below is evaluating each activity:
Theory (17 points)
• First exam, week 7 of the first quarter (5 points) [recoverable]
• Second exam, week 4 of the second quarter (6 points) [recoverable]
• Third exam, during final exams (6 points) [recoverable]
Laboratories (11 points)
• Delivery of reports (2 points)
• First exam, week 7 of the first quarter (three point) [recoverable]
• Second exam, week 4 of the second quarter (4 points) [recoverable]
• Third exam, during final exams (2 points) [recoverable]
Seminars (7 points)
• Tests in class
The final grade is calculated as follows:
Note * = 10 * (theory (minimum 8.5 points) + Labs (minimum 5.5) + seminars) / 35
To pass the course should take about 5 out of 10. You have to obtain 17.5 of the 35 maximum points and a minimum of 8.5 points in the theory and a minimum of 5.5 points the practice.
The course is divided into three periods / parts assessed in three written exams. The exams have a part to assess the theoretical part and another to assess the practical part of the course.
Before each lab the exercises to be done during practice are given. During the labs the students solve practical problems and implement algorithms with Octave and / or Matlab. The reports are delivered through Moodle, individually, at the end of each class. The assessment reports of the labs counts two points in the final.
Before each seminar a series of problems for students are given to be worked individually before meeting as a preparation for tje seminar. These problems relate to concepts and skills covered in class and put theory into practice in laboratories. During the seminar all students must participate in solving a selection of the problems. The evaluation of this activity is based on individual exercises given by the teacher during the class. This evaluation counts seven points in the final.
If the sum of all points is 17.5 (50%) but has not reached the minimum established on tests of theory and practice, the final grade will be 4.9.
The parts listed as recoverable they can be recovered with a test that will take place during the evaluation period in July.
Block 1. Introduction to Signals and Systems
a. Definition of signals and systems in engineering
b. Mathematical representation of signals
c. Mathematical representation systems
Block 2. Sinusoides
a. Sine and cosine functions
b. Sinusoidal signals
c. Complex sinusoids
d. Phasor and sum of phasors
e. Physics of tunning fork
Block 3. Spectral representation of temporal signals
a. Spectrum sum of sinusoids
b. Amplitude modulation
c. Product sinusoides
d. Periodic waves, periodic sounds
e. Fourier Series
f. Spectrum of Fourier series
g. Fourier analysis of periodic signals
h. Time-frequency spectrum
i. Frequency modulation, chirp signals
Section 4. Sampling and Aliasing
a. Sampling
b. Sampling theorem
c. Aliasing and Folding
d. Spectral view of sampling
e. Stroboscopic proof of sampling
f. Conversion from discrete to continuous signals
Block 5. Finite Impulse Response filters, FIR
a. Discrete-time systems
b. Moving Average Filter
c. The general FIR filter
d. Impulse response filter FIR
e. Implementation of FIR filters
f. Discrete Convolution signals
g. Systems linear time-invariant,
h.Convolution of discrete signals
i. LTI systems, and LTI cascade FIR filters i.Sistemes
Block 6. Frequency response of FIR filters
a. Sinusoidal response of FIR filters
b. Overlay and frequency response
c. Steady state and transient response
d. Properties frequency response
e. Graphic representation of the frequency response
f. LTI Systems Cascade
g. Filter Moving Average
h. Temporal filtering signals sampled
Block 7. Transform Z
a. Definition of the Z transform
b. The Z transform and linear systems
c. Properties of the Z transform
d. The Z transform as operator
e. Convolution Transform and Z
f. Relationship between the Z domain and the frequency domain
g. Useful filters
h. Practical design of band-pass filters
i. Properties of linear phase filters
Block 8. Infinite impulse response filters, IIR
a. The equation of general differences IIR filters
b. Response time domain
c. System function of IIR filter
d. Poles and zeros
e. Frequency response of an IIR filter
f. The three domains
g. Z inverse transform and applications
h. Response and steady state stability
i. Filters second order
j. Frequency response of second-order filters
k. Example of a low-pass filter IIR
Block 9. Signals and continuous time LTI systems
a. Continuous Time Signals
b. Signal Impulse
c. Continuous Time Systems
d. Systems linear time invariant
e. Basic LTI Impulse response systems
f. Convolution impulses
g. Evaluation of the convolution integral
h. Properties of LTI Systems
Block 10. Continues Fourier Transform
a. Definition of the Fourier transform
b. Fourier transform and spectrum
c. Existence and convergence of the Fourier transform
d. Examples of pairs of Fourier
e. Properties of Fourier pairs
f. Convolution Property
g. Basic LTI Systems
h. Table of properties of the Fourier transform
i. Properties of LTI Systems
Block 11. filtering, modulation and sampling
a. Systems linear time invariant
b. Modulation amplitude sinusoidal
c. Sampling and reconstruction
Block 12. Calculating spectrum
a. Finite sum of Fourier
b. Too many Fourier transforms?
c. Time window
d. Analysis of a sum of sinusoids
e. Discrete Fourier Transform
f. Spectral analysis of finite signals
g. Spectral analysis of periodic signals
h. The spectrogram
i. Short time Fourier Transform, STFT
Basic Textbooks
• James H. McClellan, Ronald W. Schafer, and Mark A. Yoder, 2003. Signal Processing First (SPF). Prentice Hall International Edition
Complementary reading
• A. V. Oppenheim and R. W. Schafer. 1999 Discrete-Time Signal Processing.
Prentice Hall.
• John G. Proakis and Dimitris G. Manolakis. 1998. Treatment of digital signals. Prentice Hall.
• C. Sidney Burrus et al. Exercises in 1998. Treatment of Señal utilizando matlab v.4. Prentice-Hall.
Educational resources
Resources related to SP First: http://users.ece.gatech.edu/mcclella/SPFirst/
• For each seminar session is available a collection of problems Moodle course.
• For each practice session there is available the exercises in the Moodle of the course.