Introduction to Signal Processing D R. T A R E K T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y

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1 Introduction to Signal Processing D R. T A R E K T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y

2 What is a Signal? A physical quantity that varies with time, frequency, space, or any other independent variable or variables. Signal carries information and can be described as a function of independent variables in math Tarek A. Tutunji

3 What is a signal? Dynamical phenomenon sensor Physical quantity signal Speech Image Temperature Force Microphone Camera Thermocouple Strain Gauge Current varies with time Voltage varies with time

4 ECG Biomedical Signal (ECG) Signal Temps [s]

5 Température de l'air Temperature Signal Heures de 1992~1990

6 Pression Pressure Flow Signal Temps [s]

7 Accélération Vibration Signal Temps [s]

8 Speech Signal sin t y t Speech signals are examples of information-bearing signals that evolve as functions of signal independent variable, time

9 Image Signal I B x, y An image signal is an example of a signal that depends on two independent variables, spatial.

10 Moving Image Signal A one-dimensional signal depends on one independent variable while an M-dimensional signal depends on M independent variables Example: color TV signal is a three-channel, threedimensional signal and can be presented by the vector I r ( x, y,t ) I( x, y,t ) I ( x, y,t ) g I b( x, y,t ) Tarek A. Tutunji

11 Systems A System is a physical device and/or software realizations that performs an operation on a signal A System is a collection of one or more devices, processors, or computer-implemented algorithms that operate on an input signal x to produce an output signal y When a signal is passed through a system. Then the signal is processed. Such operations are called Signal Processing For example a filter is used to reduce the noise corrupting a signal Tarek A. Tutunji

12 Signal Processing

13 Analog vs. Digital Signal Processing Most signals in science and engineering are Analog (i.e. signals are functions of continuous variable). These can be processed directly by analog systems such as filters. Analog signals can be converted to digital signals using A/D Digital Signal Processing uses a program to implement an algorithm while Analog Signal Processing is implemented using an electrical circuits Advantages of Digital over Analog Processing Flexibility Accuracy Reliability Sophistication Tarek A. Tutunji

14 Signal Processing Analog Implementation: H/W Examples: Filters and Op-Amps Digital Implementation: S/W on DSP chip Examples: Algorithm / C++ Program Tarek A. Tutunji

15 Digital Signal Processing Algorithm is a method or set of rules for implementing a system by a program that performs mathematical operations Digital Signal Processing is defined as the arithmetic processing of signals sampled at regular intervals We are interested in performing computationally efficient and fast algorithms using Digital Signal Processing Operations Filtering, Correlation, and Spectral Analysis Tarek A. Tutunji

16 Digital Signal Processing Digital Signal Processing provides an alternative where the signal is transformed to Digital through A/D interface, run through DSP, then output is transferred back to Analog through D/A DSP may be a programmable computer or a programmable microprocessor Applications: Speech Processing, Signal Transmission, Image Processing, Oil Exploration, and Control Tarek A. Tutunji

17 Digital Signal Processors (DSPs) Digital signal processing operations are implemented using Digital Signal Processors (DSP) Tarek A. Tutunji

18 DSPs A digital signal processor (DSP) is an optimized microprocessor used in real-time signal processing applications. DSPs are typically embedded in larger systems (e.g., a desktop computer) handling general-purpose tasks. A DSP system typically consists of a processor, memory, analog-to-digital converters (ADCs), and digital-toanalog converters (DACs). The main difference with typical microprocessors is they are faster.

19 Continuous-Time vs. Discrete-Time Signals Continuous (or analog) signals are defined for every value of time in a continuous interval x( t ) cos t, Discrete-time signals are defined only at specific values of time x( n) cos n, n 0, 1, 2,... t Discrete-time signals can be obtained by: Sampling Tarek A. Tutunji

20 x(t) Continuous-Time Signal using MATLAB x( t) exp( 0.1 t)*sin 0. 75t 0.8 >> t=1:0.1:30; >> x=exp(-.1*t).*sin(2/3*t); >> plot(t,x) >> grid >> xlabel('time (sec)'); >> ylabel('x(t)') Time (sec) Tarek A. Tutunji

21 x[n] Discrete-Time Signal using MATLAB >> n=1:8; >> x=[ ]; >> plot(n,x,'x') >> stem(n,x,'filled') >> xlabel('n') >> ylabel('x[n]') n Tarek A. Tutunji

22 Continuous-Valued vs. Discrete-Valued Signals A continuous-valued signal takes all possible values in a range A discrete-valued signal takes on values from a finite set of possible values Digital Signal is a discrete-time signal having a discrete value. Tarek A. Tutunji

23 Analog-to-Digital Conversion Sampling. The conversion of a continuous-time signal into a discrete-time signal obtained by taking samples of the continuous-time signal at discrete-time instants Quantization. The conversion of a discrete-time continuousvalued signal into a discrete-time, discrete-valued signal (i.e. digital signal) Coding. Each discrete value is represented by a binary sequence Analog Signal Discete-Time Signal Discete-Time Discrete-Value Signal Sampling Quantization Coding Tarek A. Tutunji

24 Sampling Process Analog Signal Sampling Interval (Ts) Sampled Numbers

25 Sampling

26 Quantization Analog Signal Discete-Time Signal Discete-Time Discrete-Value Signal

27 Analog and Discrete-Time Signals

28 Analog and Discrete-Time Signals

29 Calculus Review Differentiation Difference Integration Summation

30 Differential and Difference Equations

31 Math Intro: Continuous-Time Signals The single-sided Laplace transform of a continuous-time signal, x(t), is given by The Fourier transform of x(t) is given by Where ω is in units of radians per second Notice that when x(t)=0 for t 0, the Laplace transform is equivalent to the Fourier transform by setting s = jω Tarek A. Tutunji

32 Math Intro: Discrete-Time Signals The z-transform of a discrete-time signal, x[n], is defined as The discrete-time Fourier transform (DTFT) of a signal are defined by Note that the DTFT can be derived from the z- transform by setting Tarek A. Tutunji

33 Deterministic vs. Random Signals Deterministic signals can be uniquely described by mathematical expression, table, or set of rules. Therefore, all past, present, and future values of the signal are known precisely Random signals cannot be described mathematically with a high degree of accuracy or are too complicated to describe mathematically Theoretical analysis of random signals are provided by theory of probability an stochastic processes Tarek A. Tutunji

34 Signal Processing Applications: Communication

35 Signal Processing Applications: Control

36 Signal Processing Applications Image Processing Pattern recognition; Robotic vision; Image enhancement; Animation Instrumentation and Control Spectrum analysis; Position control; Noise reduction; Military Secure communication; Radar processing; Sonar processing; Missile guidance Speech and Audio Speech recognition; Digital audio Tarek A. Tutunji

37 Signal Processing Applications Telecommunication Video conferencing; Data communication Biomedical ECG (Electrocardiograph); X-ray storage/enhancement Consumer Cellar mobile phones; Digital television; Digital camera; Internet music; Interactive entertainment systems Tarek A. Tutunji

38 Conclusion Signals are physical quantities that carry information and vary with time, space, or frequency Signal processing are operations that are carried on signals in order to extract better information Signal processing can be analog or digital Signal processing is used in mechatronics applications for instrumentation and control Tarek A. Tutunji