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 0 1 4
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
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
ECG Biomedical Signal (ECG) Signal 1.5 1 0.5 0-0.5-1 0 2 4 6 8 10 12 14 16 18 20 Temps [s]
Température de l'air Temperature Signal 15 10 5 0-5 -10-15 -20 140 150 160 170 180 190 200 210 220 230 Heures de 1992~1990
Pression Pressure Flow Signal 112.5 112 111.5 111 110.5 110 0.05 0.1 0.15 0.2 0.25 0.3 Temps [s]
Accélération Vibration Signal 4000 3000 2000 1000 0-1000 -2000-3000 -4000 0 0.02 0.04 0.06 0.08 0.1 0.12 Temps [s]
Speech Signal sin 2 500 t y t Speech signals are examples of information-bearing signals that evolve as functions of signal independent variable, time
Image Signal I B x, y An image signal is an example of a signal that depends on two independent variables, spatial.
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
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
Signal Processing
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
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
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
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
Digital Signal Processors (DSPs) Digital signal processing operations are implemented using Digital Signal Processors (DSP) Tarek A. Tutunji
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.
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
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)') 0.6 0.4 0.2 0-0.2-0.4-0.6 0 5 10 15 20 25 30 Time (sec) Tarek A. Tutunji
x[n] Discrete-Time Signal using MATLAB >> n=1:8; >> x=[2 3 4 7 1 2-2 2]; >> plot(n,x,'x') >> stem(n,x,'filled') >> xlabel('n') >> ylabel('x[n]') 7 6 5 4 3 2 1 0-1 -2 1 2 3 4 5 6 7 8 n Tarek A. Tutunji
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
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
Sampling Process Analog Signal Sampling Interval (Ts) Sampled Numbers
Sampling
Quantization Analog Signal Discete-Time Signal Discete-Time Discrete-Value Signal
Analog and Discrete-Time Signals
Analog and Discrete-Time Signals
Calculus Review Differentiation Difference Integration Summation
Differential and Difference Equations
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
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
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
Signal Processing Applications: Communication
Signal Processing Applications: Control
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
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
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