16.362 Signal and System I Signal energy and power Instantaneous power Energy in time interval t1 to t2 Average power in time interval t1 to t2 Total energy.

Slides:

Advertisements

Similar presentations

DCSP-11 Jianfeng Feng

Advertisements

Symmetry and the DTFT If we know a few things about the symmetry properties of the DTFT, it can make life simpler. First, for a real-valued sequence x(n),

Transformations of Continuous-Time Signals Continuous time signal: Time is a continuous variable The signal itself need not be continuous. Time Reversal.

Fourier Transform – Chapter 13. Fourier Transform – continuous function Apply the Fourier Series to complex- valued functions using Euler’s notation to.

Review of Frequency Domain

Linear SystemsKhosrow Ghadiri - EE Dept. SJSU1 Signals and Systems Linear System Theory EE Lecture Eight Signal classification.

EECS 20 Chapter 10 Part 11 Fourier Transform In the last several chapters we Viewed periodic functions in terms of frequency components (Fourier series)

Lesson 3 Signals and systems Linear system. Meiling CHEN2 (1) Unit step function Shift a Linear system.

Lecture 2: Signals Concepts & Properties

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communication Systems ECE Spring 2009 Shreekanth Mandayam ECE Department Rowan University.

Discrete-Time Signals Week 2. Continuous-Time Versus Discrete-Time Signals Continuous-time signal: a signal defined by a function of a continuous-time.

EECS 20 Chapter 9 Part 21 Convolution, Impulse Response, Filters In Chapter 5 we Had our first look at LTI systems Considered discrete-time systems, some.

Introduction to signals

The z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl.

Mathematical Description of Continuous-Time Signals

Signal and System I Continuous-time filters described by differential equations + Recall in Ch. 2 Continuous time Fourier transform. LTI system.

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communication Systems ECE Spring 2008 Shreekanth Mandayam ECE Department Rowan University.

Discrete-Time Convolution Linear Systems and Signals Lecture 8 Spring 2008.

Signals and Systems Discrete Time Fourier Series.

Systems: Definition Filter

1.4 The Unit Impulse and Unit Step Functions The Discrete-Time Unit Impulse and Unit Step Sequences The Discrete-Time Unit Impulse Sequence.

Continuous Time Signals

Chapter 2: Discrete time signals and systems

Course Outline (Tentative)

ENERGY AND POWER SIGNALS Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING.

ECE 8443 – Pattern Recognition ECE 3163 – Signals and Systems Objectives: Useful Building Blocks Time-Shifting of Signals Derivatives Sampling (Introduction)

Basic signals Why use complex exponentials? – Because they are useful building blocks which can be used to represent large and useful classes of signals.

Signal Operations. 2 Basic Operation of the Signals. Basic Operation of the Signals Time Shifting Reflection and Folding Time Scaling.

Signal and Systems Prof. H. Sameti Chapter 5: The Discrete Time Fourier Transform Examples of the DT Fourier Transform Properties of the DT Fourier Transform.

1 Chapter 1 Fundamental Concepts. 2 signalpattern of variation of a physical quantity,A signal is a pattern of variation of a physical quantity, often.

Signal and System I The unit step response of an LTI system.

Signals and Systems Dr. Mohamed Bingabr University of Central Oklahoma

Lecture 14 Introduction to dynamic systems Energy storage Basic time-varying signals Related educational materials: –Chapter 6.1, 6.2.

Chapter 6: Sampled Data Systems and the z-Transform 1.

1 Fourier Representation of Signals and LTI Systems. CHAPTER 3 EKT 232.

Basic Operation on Signals Continuous-Time Signals.

Fourier Series Representations

Course Outline (Tentative) Fundamental Concepts of Signals and Systems Signals Systems Linear Time-Invariant (LTI) Systems Convolution integral and sum.

Fourier Analysis of Signals and Systems

Signals and Systems Lecture # 7 System Properties (continued) Prepared by: Dr. Mohammed Refaey 1Signals and Systems Lecture # 7.

2006 Fall Welcome to Signals and Systems

2006 Fall Signals and Systems Lecture 2 Complex Exponentials Unit Impulse and Unit Step Signal Singular Functions.

EE3010_Lecture3 Al-Dhaifallah_Term Introduction to Signal and Systems Dr. Mujahed Al-Dhaifallah EE3010: Signals and Systems Analysis Term 332.

Lecture 01 Signal and System Muhammad Umair Muhammad Umair, Lecturer (CS), KICSIT.

INTRODUCTION TO SIGNALS

Signal and System I The representation of discrete-time signals in terms of impulse Example.

Discrete-time Signals Prof. Siripong Potisuk. Mathematical Representation x[n] represents a DT signal, i.e., a sequence of numbers defined only at integer.

1 Fourier Representation of Signals and LTI Systems. CHAPTER 3 UniMAP.

Today's lecture Continuous and discrete-time signals The sequence

Chapter 1: Overview of Signals and Systems. Signals Can be measured –Voltages –Currents –Tempertures –Pressures –Images –etc.

Chapter 2. Signals and Linear Systems

ENEE 322: Continuous-Time Fourier Transform (Chapter 4)

Continuous-time Signals ELEC 309 Prof. Siripong Potisuk.

Continuous-Time Signals David W. Graham EE Continuous-Time Signals –Time is a continuous variable –The signal itself need not be continuous We.

Dr. Michael Nasief Digital Signal Processing Lec 7 1.

الفريق الأكاديمي لجنة الهندسة الكهربائية 1 Discrete Fourier Series Given a periodic sequence with period N so that The Fourier series representation can.

Discrete Time Signal Processing Chu-Song Chen （陳祝嵩） Institute of Information Science Academia Sinica 中央研究院資訊科學研究所.

1.3 Exponential and Sinusoidal Signals

CEN352 Dr. Nassim Ammour King Saud University

Signals and systems By Dr. Amin Danial Asham.

Sinusoids: continuous time

Discrete-Time Complex

Discrete Fourier Transform Dr.P.Prakasam Professor/ECE.

COSC 3451: Signals and Systems

Discrete-Time Signal Description

Signals & Systems (CNET - 221) Chapter-1 Introduction to Signals

1.1 Continuous-time and discrete-time signals

Signals & Systems (CNET - 221) Chapter-1

Lecture 2: Signals Concepts & Properties

Chapter 3 Sampling.

Presentation transcript:

Signal and System I Signal energy and power Instantaneous power Energy in time interval t1 to t2 Average power in time interval t1 to t2 Total energy Average power over infinite period

Signal and System I Signal energy and power– discrete time Instantaneous power Energy in time interval N1 to N2 Average power in time interval N1 to N2 Total energy Average power over infinite period

Signal and System I Transform of the independent variable (1) Time-shift New point located at

Signal and System I Transform of the independent variable New point located at (1) Time-shift

Signal and System I Transform of the independent variable New point located at (2) Time-reversal

Signal and System I Transform of the independent variable New point located at (3) Scale

Signal and System I Example /3 2/3

Signal and System I Periodical signal Even and odd signals even odd Any signal has its even and odd signal part Even part Odd part

Signal and System I Exponential and Sinusoidal signals a>0, exponentially increase with t. Real exponential:C, and a are real numbers a<0, exponentially decrease with t. Complex exponential:C, and a are real numbers Euler’s relation:

Signal and System I Exponential and Sinusoidal signals Energy in one period: Average power:

Signal and System I Exponential and Sinusoidal signals, discrete-time a>0, exponentially increase with n. Real exponential:C, and a are real numbers a<0, exponentially decrease with n. Complex exponential:C, and a are real numbers Periodicity properties of discrete-time complex exponential:  0 has a period of 2  N has a period of 2  /  0

Signal and System I Example:

Signal and System I Discrete-time unit impulse and unit step function Unit impulse Unit step

Signal and System I Discrete-time unit impulse and unit step function

Signal and System I continuous-time unit impulse and unit step function Unit impulse Unit step

Signal and System I continuous-time unit impulse and unit step function

Signal and System I Continuous-time and discrete-time systems Continuous-time Discrete-time System diagram and properties will be discussed in later chapters.