ELEC SIGNALS and SYSTEMS. Text Book:

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1 ELEC SIGNALS and SYSTEMS PROF. KALYANA C. VELUVOLU IT1-817 Tel: School of Electronics Engineering Kyungpook National University Text Book: MJ Roberts, "Signals and Systems: Analysis using Transform Methods and Matlab", 2e, McGraw Hill, Simon Haykins and Barry Van Veen, Signals and Systems (2nd Ed.), J ohn Wiley & Sons, References: Mrinal Mandal and Amir Asif, Continuous and Discrete Time Signals and Systems, Cambridge University Press, Oppenheim, Alan V., and A. S. Willsky. Signals and Systems. Prentice Hall, Week # Syllabus 1 Introduction to Signals and Systems (Chapter 1) 2 Mathematical Descriptions of Continuous-Time Signals (Chapter 2) 3 Discrete-time Signal Description (Chapter 3) 4 Description of Systems (Chapter 4) 5 Time-Domain System Analysis (Chapter 5) 8 9 Continuous-time Fourier Methods (Chapter 6) 10 Discrete-time Fourier Methods (Chapter 7) 11 The Laplace Transforms (Chapter 8) 12 The Laplace Transforms / The Z Transforms (Chapter 8/9) 6 Time-Domain System Analysis (Chapter 5) 13 The Z Transforms (Chapter 9) 7 Continuous-time Fourier Methods (Chapter 6) 14 Applications LECTURE NOTES DOWNLOAD LECTURE NOTES DOWNLOAD

2 GRADING Assignments Mid term Exam Final Exam Attendance 20% 38 % 38% 4 % Assignments constitute 20% of the grading. A total 3-4 Assignments will be given and students are required to submit it by the due date. Signals and Systems - Introduction A signal is any physical phenomenon which conveys information Systems respond to signals and produce new signals Excitation signals are applied at system inputs and response signals are produced at system outputs Copying of the solutions from solution manuals and from friends will be penalized. 5 6 A Communication System as a System Example A communication system has an information signal plus noise signals This is an example of a system that consists of an interconnection of smaller systems A Communication System Example Snapshot of Pathfinder exploring the surface of Mars. (Top figure) The 70-meter (230-foot) diameter antenna located at Canberra, Australia. (Bottom figure) The surface of the 70-meter reflector must remain accurate within a fraction of the signal s wavelength. (Courtesy of Jet Propulsion Laboratory.) The minimum distance from the Earth to Mars is about 54.6 million km. The farthest apart they can be is about 401 million km. 7

3 Signal Types Conversions Between Signal Types Sampling Quantizing Encoding 9 10 Message Encoded in ASCII Noisy Message Encoded in ASCII Progressively noisier signals 11 12

4 Bit Recovery in a Digital Signal Using Filtering Image Filtering to Aid Perception Original X-Ray Image Filtered X-Ray Image Discrete-Time Systems In a discrete-time system events occur at points in time but not between those points. The most important example is a digital computer. Significant events occur at the end of each clock cycle and nothing of significance (to the computer user) happens between those points in time. Discrete-time systems can be described by difference (not differential) equations. Let a discrete-time system generate an excitation signal y[n] where n is the number of discrete-time intervals that have elapsed since some beginning time n = 0. Then, for example a simple discrete-time system might be described by y[ n]= 1.97y[ n 1] y[ n 2] Discrete-Time Systems The equation says in words y[ n]= 1.97y[ n 1] y[ n 2] The signal value at any time n is 1.97 times the signal value at the previous time [n -1] minus the signal value at the time before that [n - 2]. If we know the signal value at any two times, we can compute its value at all other (discrete) times. This is quite similar to a second-order differential equation for which knowledge of two independent initial conditions allows us to find the solution for all time and the solution methods are very similar

5 Discrete-Time Systems y[ n]= 1.97y[ n 1] y[ n 2] We could solve this equation by iteration using a computer. Initial Conditions yn=1;yn1=0; while 1, yn2=yn1;yn1=yn;yn=1.97*yn1-yn2; end Discrete-Time Systems y[ n]= 1.97y[ n 1] y[ n 2] With the initial conditions y[1] = 1 and y[0] = 0 the response is We could also describe the system with a block diagram. ( D means delay one unit in discrete time.) Feedback Control Systems To objective is to change the behavior of the system to obtain desired output/ performance. Illustrative Example Autonomous Car LIDAR Video Camera GPS RADAR Sensor 19 On-board Computer UltraSonic Sensor RADAR Sensor

6 Control System with Feedback Illustration Example: Requirement Control Input/Action Output/ Performance It s the pathway to transfer information from output to input to aid the control decision Feedback systems can be continuous-time or discrete-time or a mixture of the two. 21 Illustration Example: Illustration Example: Accelerate (Gas) Decelerate (Breaking) +20 Output/ -20 Output/

7 Illustration Example: CLOSED LOOP SYSTEM Illustration Example: No Change 0 Output/??? Output/ ?????? NO FEEDBACK OPEN LOOP System Feedback Systems In a feedback system the response of the system is fed back and combined with the excitation is such a way as to optimize the response in some desired sense. Examples of feedback systems are 1. Temperature control in a house using a thermostat 2. Water level control in the tank of a flush toilet. 3. Pouring a glass of lemonade to the top of the glass without overflowing. 4. A refrigerator ice maker that keeps the bin full of ice but does not make extra ice. 5. Driving a car. Feedback Systems Below is an example of a discrete-time feedback system. The response y[n] is fed back through two delays and gains b and c and combined with the excitation x[n]. Different values of a, b and c can create dramatically different responses to the same excitation. Feedback systems can be continuous-time or discrete-time or a mixture of the two

8 Feedback Systems Sound Recording System Responses to an excitation that changes from 0 to 1 at n = Control System Example(s) Recorded Sound as a Signal Example s i gn al Boston Dynamics 31 NASA space shuttle launch (Courtesy of NASA.) F-35 Pitch Yaw Control

9 Car Suspension System and Response Suspension response is the Output Safety Control Protocols in Autonomous Vehicles Road excitation is the Input Microelectromechanical System Accelerometers for Biomedical Sensing 3-axis accelerometers Structure of lateral capacitive accelerometers SEM view of Analog Device s ADXLO5 surface-micromachined polysilicon accelerometer G. Shafiq, & K. C. Veluvolu et.al, Autonomous Identification of Seismocardiogram for Systolic Time Interval Estimation, Nature Scientific Reports, Vol. 2016, No , Nov

10 Remote Sensing Biomedical Signal Processing Perspectival view of Mount Shasta (California), derived from a pair of stereo radar images acquired from orbit with the shuttle Imaging Radar (SIR-B) Morphological types of nerve cells (neurons) identifiable in monkey cerebral cortex, based on studies of primary somatic sensory and motor cortices Biomedical Signal Processing Why are Sensors and Systems important? EEG Signals collected during various stages of sleep and awake 40

11 Reasons for Crash of Air France Faulty Speed Sensor (due to icing) 2. Auto-Pilot disengages Summary A signal is any physical phenomenon which conveys information Systems respond to signals and produce new signals Excitation signals are applied at system inputs and response signals are produced at system outputs 3. Wrong Action from the Pilot Damn it, we re going to crash, this can t be happening : Last words from Pilot (10 Seconds before the actual crash) Discrete-time systems Events occur at points in time but not between those points Summary Feedback Systems - the response of the system is fed back and combined with the excitation is such a way as to obtained desired behavior/result Various systems Signal processing; communication systems; control systems; biomedical systems; automobile systems; 43