We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byChloe Chopin
Modified about 1 year ago
Leo Lam © Signals and Systems EE235
Why did the statistician drown in the river? Because it had an average depth of 6 inches. Leo Lam ©
Today’s menu To Do: –Join Facebook Group –Read Lab 1 Intro: Signals Intro: Systems More: Describing Common Signals
Definition: Signal A signal is a set of information or data that can be modeled as a function of one or more independent variables. Leo Lam ©
Taking a signal apart Leo Lam © a0a0 T t (seconds) A+a 0 A sound signal Offset (atmospheric pressure) Frequency Amplitude
Frequency Leo Lam © t (seconds)f (Hz) = time-domainfrequency-domain
t to f Leo Lam © t (seconds) F (Hz)
Combining signals Leo Lam ©
Summary: Signals Signals carry information Signals represented by functions over time or space Signals can be represented in both time and frequency domains Signals can be summed in both time and frequency domains Leo Lam ©
Systems A system describes a relationship between input and output Examples? Leo Lam © v(t)y(t)g(t)
Definition: System A system modifies signals or extracts information. It can be considered a transformation that operates on a signal. Leo Lam ©
Motivation: Complex systems Leo Lam ©
Filters All kinds, and everywhere Leo Lam ©
Surprising high pass Leo Lam ©
Summary: System System transforms an input to an output System can extract information System can “shape” signals (filters) Leo Lam ©
Signals: A signal is a mathematical function –x(t) –x is the value (real, complex) y-axis –t is the independent variable (1D, 2D etc.) x-axis –Both can be Continuous or Discrete –Examples of x… Leo Lam ©
Signal types Continuous time / Discrete time –An x-axis relationship Discrete time = “indexed” time Leo Lam ©
Signals: Notations A continuous time signal is specified at all values of time, when time is a real number. Leo Lam ©
Signals: Notations A discrete time signal is specified at only discrete values of time (e.g. only on integers) Leo Lam ©
What types are these? Leo Lam © )90.3 FM radio transmitted signal 2)Daily count of orcas in Puget Sound 3)Muscle contraction of your heart over time 4)A capacitor’s charge over time 5)A picture taken by a digital camera 6)Local news broadcast to your old TV 7)Video on YouTube 8)Your voice (c) ((c)) (c) (continuous) (c) (d) (discrete)
Analog / Digital values (y-axis) An analog signal has amplitude that can take any value in a continuous interval (all Real numbers) Leo Lam © Where Z is a finite set of values
Analog / Digital values (y-axis) An digital signal has amplitude that can only take on only a discrete set of values (any arbitrary set). Leo Lam © Where Z and G are finite sets of values
Nature vs. Artificial Natural signals mostly analog Computers/gadgets usually digital (today) Signal can be continuous in time but discrete in value (a continuous time, digital signal) Leo Lam ©
Brake! X-axis: continuous and discrete Y-axis: continuous (analog) and discrete (digital) Our class: (mostly) Continuous time, analog values (real and complex) Clear so far? Leo Lam ©
Common signals (memorize) Building blocks to bigger things Leo Lam © constant signal t a 0 unit step signal t 1 0 unit ramp signal t 1 u(t)=0 for t<0 u(t)=1 for t≥0 r(t)=0 for t<0 r(t)=t for t≥0 r(t)=t*u(t) for t≥0
Sinusoids/Decaying sinusoids Leo Lam ©
Decaying and growing Leo Lam ©
Generalizing the sinusoids Leo Lam © General form: x(t)=Ce at, a=σ+jω Equivalently: x(t)=Ce σt e jωt Remember Euler’s Formula? x(t)=Ce σt e jωt amplitude Exponential (3 types) Sinusoidal with frequency ω (in radians) What is the frequency in Hz?
Imaginary signals Leo Lam © z r a b z=a+jb real/imaginary z=re jΦ magnitude/phase real imag Remember how to convert between the two?
Signal Basics ELEC 309 Prof. Siripong Potisuk. What is a function? A rule of correspondence that maps or assigns to each element (x) of a given set A.
DCSP-2: Fourier Transform I Jianfeng Feng
What is a signal ? A function of one or more independent variables which contain some information. Voltage, Current,temperature are all different signals.
Signals and Systems Fall 2003 Lecture #5 18 September Complex Exponentials as Eigenfunctions of LTI Systems 2. Fourier Series representation of.
An Introduction to Fourier and Wavelet Analysis: Part I Norman C. Corbett Sunday, June 1, 2014.
| Page Angelo Farina UNIPR | All Rights Reserved | Confidential Digital sound processing Convolution Digital Filters FFT.
Leo Lam © Signals and Systems EE235 Leo Lam.
2.3 Continuity When you plot function values generated in a laboratory or collected in a field, you can connect the plotted points with an unbroken curve.
MULTIMEDIA TUTORIAL PART - III SHASHI BHUSHAN SOCIS, IGNOU.
Design of Digital IIR Filter DR. Wajiha Shah. A digital filter is simply a discrete-time, discrete-amplitude convolver. Filtering is in essence the multiplication.
DCSP-2: Fourier Transform I Jianfeng Feng Department of Computer Science Warwick Univ., UK
Leo Lam © Signals and Systems EE235. Courtesy of Phillip Leo Lam ©
ANALOG TO DIGITAL CONVERSION Lecture 3,4 Syed M. Zafi S. Shah احسان احمد عرساڻي
Chapter 2: Digital Modulation Introduction –Electronic communications is the transmission, reception and the processing of the information with the use.
DCSP-12 Jianfeng Feng
Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function.
Copyright © Cengage Learning. All rights reserved. 1.2 Functions.
1 The z-Transform ECON 397 Macroeconometrics Cunningham.
Signals and Fourier Theory Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W:
Eeng Chapter 3: Pulse Code Modulation Pulse Code Modulation Quantizing Encoding Analogue to Digital Conversion Bandwidth of PCM Signals.
All slides © S. J. Luck, except as indicated in the notes sections of individual slides Slides may be used for nonprofit educational purposes if this copyright.
© Boardworks Ltd of 64 © Boardworks Ltd of 64 A-Level Maths: Core 3 for Edexcel C3.2 Algebra and functions 2 This icon indicates the slide.
Info 2040 Foundation of Quantitative Analysis Week 2-1.
Lecture 4: Phasors; Discrete-Time Sinusoids Sections 1.4, 1.5.
INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences 2007 Pearson Education Asia Chapter 2 Functions and Graphs.
History of image processing History of image processing In the 1970s, digital image processing proliferated, when cheaper computers and dedicated hardware.
1 Envelope Detector Conventional DSB-AM signals are easily demodulated by an envelope detector It consists of a diode and an RC circuit, which is a simple.
Chapter 1 Algebra, Mathematical Models, and Problem Solving.
DCSP-14 Jianfeng Feng Department of Computer Science Warwick Univ., UK
Lectures 8, 9 and 10 Finite Difference Discretization of Hyperbolic Equations: Linear Problems.
© 2016 SlidePlayer.com Inc. All rights reserved.