Signals & Systems - Chapter 3

Similar documents
EEE 303: Signals and Linear Systems

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser

Chapter 3 Fourier Series Representation of Periodic Signals

Response of LTI Systems to Complex Exponentials

EE415/515 Fundamentals of Semiconductor Devices Fall 2012

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia

Department of Electronics & Telecommunication Engineering C.V.Raman College of Engineering

Frequency Response. Lecture #12 Chapter 10. BME 310 Biomedical Computing - J.Schesser

CS 688 Pattern Recognition. Linear Models for Classification

( ) ( ) (a) w(x) = a v(x) + b. (b) w(x) = a v(x + b) w = the system IS linear. (1) output as the sum of the outputs from each signal individually

FOURIER ANALYSIS Signals and System Analysis

( A) ( B) ( C) ( D) ( E)

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times.

Chapter4 Time Domain Analysis of Control System

(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is

Week 06 Discussion Suppose a discrete random variable X has the following probability distribution: f ( 0 ) = 8

Revisiting what you have learned in Advanced Mathematical Analysis

Fourier Series: main points

EXERCISE - 01 CHECK YOUR GRASP

x, x, e are not periodic. Properties of periodic function: 1. For any integer n,

SOLVED EXAMPLES. Ex.1 If f(x) = , then. is equal to- Ex.5. f(x) equals - (A) 2 (B) 1/2 (C) 0 (D) 1 (A) 1 (B) 2. (D) Does not exist = [2(1 h)+1]= 3

PREPARATORY MATHEMATICS FOR ENGINEERS

Right Angle Trigonometry

Erlkönig. t t.! t t. t t t tj "tt. tj t tj ttt!t t. e t Jt e t t t e t Jt

A L A BA M A L A W R E V IE W

Frequency Measurement in Noise

EE Control Systems LECTURE 11

Trigonometric Formula

Fourier Series and Parseval s Relation Çağatay Candan Dec. 22, 2013

Advanced Engineering Mathematics, K.A. Stroud, Dexter J. Booth Engineering Mathematics, H.K. Dass Higher Engineering Mathematics, Dr. B.S.

LINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

UNIT I FOURIER SERIES T

Linear Algebra Existence of the determinant. Expansion according to a row.

Fourier. Continuous time. Review. with period T, x t. Inverse Fourier F Transform. x t. Transform. j t

1. Accident preve. 3. First aid kit ess 4. ABCs of life do. 6. Practice a Build a pasta sk

Data Structures Lecture 3

Boyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues

From Fourier Series towards Fourier Transform

Gavilan JCCD Trustee Areas Plan Adopted October 13, 2015

Mathematical Preliminaries for Transforms, Subbands, and Wavelets

1- I. M. ALGHROUZ: A New Approach To Fractional Derivatives, J. AOU, V. 10, (2007), pp

5'-33 8 " 28' " 2'-2" CARPET 95'-7 8' " B04B 1'-0" STAIR B04 UP 19R F B F QT-1/ C-1 B WD/ P-2 W DW/P-1 C DW/P-1 8' " B05 B04A

Continuous-Time Fourier Transform. Transform. Transform. Transform. Transform. Transform. Definition The CTFT of a continuoustime

Practice papers A and B, produced by Edexcel in 2009, with mark schemes. Practice Paper A. 5 cosh x 2 sinh x = 11,

Helping every little saver

[ ] Review. For a discrete-time periodic signal xn with period N, the Fourier series representation is

Quantum Mechanics & Spectroscopy Prof. Jason Goodpaster. Problem Set #2 ANSWER KEY (5 questions, 10 points)

National Quali cations

INTERQUARTILE RANGE. I can calculate variabilityinterquartile Range and Mean. Absolute Deviation

Chapter 5 Transient Analysis

Written Homework # 2 Solution

Vr Vr

PROPOSED SITE PLAN SCALE 1/32"=1'-0"

AE57/AC51/AT57 SIGNALS AND SYSTEMS DECEMBER 2012

ENJOY ALL OF YOUR SWEET MOMENTS NATURALLY

P a g e 5 1 of R e p o r t P B 4 / 0 9

1973 AP Calculus BC: Section I

Dec. 3rd Fall 2012 Dec. 31st Dec. 16th UVC International Jan 6th 2013 Dec. 22nd-Jan 6th VDP Cancun News

Inverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289.

IIT JEE MATHS MATRICES AND DETERMINANTS

National Quali cations

By Tom Irvine December 27,

Topic 5:Discrete-Time Fourier Transform (DTFT)

Opening. Monster Guard. Grades 1-3. Teacher s Guide

A Study of the Solutions of the Lotka Volterra. Prey Predator System Using Perturbation. Technique

q-..1 c.. 6' .-t i.] ]J rl trn (dl q-..1 Orr --l o(n ._t lr< +J(n tj o CB OQ ._t --l (-) lre "_1 otr o Ctq c,) ..1 .lj '--1 .IJ C] O.u tr_..


RUTH. land_of_israel: the *country *which God gave to his people in the *Old_Testament. [*map # 2]

Section 3: Antiderivatives of Formulas

ECE351: Signals and Systems I. Thinh Nguyen

, University. 1and. y T. since. g g

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?

Lecture 21 : Graphene Bandstructure

Chapter Taylor Theorem Revisited

16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 3: Ideal Nozzle Fluid Mechanics

2 T. or T. DSP First, 2/e. This Lecture: Lecture 7C Fourier Series Examples: Appendix C, Section C-2 Various Fourier Series

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

Introduction to Laplace Transforms October 25, 2017

How to Make a Zia. (should you ever be inclined to do such a thing)

1. Be a nurse for 2. Practice a Hazard hunt 4. ABCs of life do. 7. Build a pasta sk

Colby College Catalogue

GUC (Dr. Hany Hammad) 4/20/2016

ASSERTION AND REASON

NEW FLOODWAY (CLOMR) TE TE PIN: GREENS OF ROCK HILL, LLC DB: 12209, PG: ' S67 46'18"E APPROX. FLOODWAY NEW BASE FLOOD (CLOMR)

Colby College Catalogue

ELECTROMAGNETIC COMPATIBILITY HANDBOOK 1. Chapter 12: Spectra of Periodic and Aperiodic Signals

1a.- Solution: 1a.- (5 points) Plot ONLY three full periods of the square wave MUST include the principal region.

rhtre PAID U.S. POSTAGE Can't attend? Pass this on to a friend. Cleveland, Ohio Permit No. 799 First Class

Linear Systems Analysis in the Time Domain

A Review of Complex Arithmetic

Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder

Wireless & Hybrid Fire Solutions

Next we encountered the exponent equaled 1, so we take a leap of faith and generalize that for any x (that s not zero),

: A

T HE 1017TH MEETING OF THE BRODIE CLUB The 1017th Meeting of the Brodie Club was held at 7:30 pm on January 15, 2008 in the R amsay Wright Laboratorie

Continous system: differential equations

Job No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet

Digital Signal Processing. Digital Signal Processing READING ASSIGNMENTS. License Info for SPFirst Slides. Fourier Transform LECTURE OBJECTIVES

82A Engineering Mathematics

Country

Transcription:

.EgrCS.cm, i Sigls d Sysms pg 9 Sigls & Sysms - Chpr S. Ciuus-im pridic sigl is rl vlud d hs fudml prid 8. h zr Furir sris cfficis r -, - *. Eprss i h m. cs A φ Slui: 8cs cs 8 8si cs si cs Eulrs Apply U. Ciuus-im pridic sigl is rl vlud d hs fudml prid. h zr Furir sris cfficis r, - *, - * -. Eprss i h m. cs A φ Slui: S. A discr-im pridic sigl is rl vlud d hs fudml prid 5. h zr Furir sris cffici r, - *, - * Eprss i h m A. si A φ Slui: 5 5 & i : r gr y hr is si 5 si 5 cs cs } { } { Eulrs Apply

U. A discr-im pridic sigl is rl vlud d hs fudml prid 9. h zr Furir sris cffici r, - *, - * - Eprss i h m A A si φ. Slui: S. Fr h ciuus-im prid sigl 5 cs si drmi h fudml frqucy d h Furir sris cfficis such h Slui: Apply Eulrs h Fudml Frqucy ; - ; 5-5 * -; 5 5 5 5 U. Fr h ciuus-im prid sigl cs si 7 5 drmi h fudml frqucy d h Furir sris cfficis. Slui: S. Us h Furir sris lysis qui clcul h cfficis h ciuus-im pridic sigl.5.5 ih fudml frqucy. Slui: Ciuus-im sysm, hv: Furir Sris SyhsisEqui d d Furir Sris AlysisEqui.EgrCS.cm, i Sigls d Sysms pg

.5 v dd d.5 d.5 cs.5 d.5 si.5 U. Us h Furir sris lysis qui clcul h cfficis h ciuus-im pridic sigl.5 msc.5 msc msc ih fudml frqucy. Slui: 5S. Csidr hr ciuus-im pridic sigls hs Furir sris rprsis r s flls: 5 cs 5 si 5 Us Furir sris prpris hlp sr h fllig qusis: Which f h hr sigls isr rl vlud? b Which f h hr sigls isr v? Slui: if * h h sigl is rl hris i is. : cug ms h AB* A-B Furir sris cfficis r K hris W h { K } { - * -K } hr is Rl Furir sris cfficis r cs - hris W h { cs} { - * cs-} hr is Rl Furir sris cfficis r si - hris W h { si} { - * -si-} hr is Rl.EgrCS.cm, i Sigls d Sysms pg

b Fr sigl b v is Furir Sris Cffici mus b v I hr rds h rliship - - is ru Which ms ly is v sic ly his fuci - 5U. Csidr hr ciuus-im pridic sigls hs Furir sris rprsis r s flls: si cs5.9 si hr is igr 5 hr is rl hr is igr Us Furir sris prpris hlp sr h fllig qusis: Which f h hr sigls isr rl vlud? b Which f h hr sigls isr v? Slui: S. Us h lysis qui vlu h umricl vlus f prid f h Furir sris cfficis f h pridic sigl Slui: Fr Discr-im sysm, hv > > {δ m 8δ m}. m > > δ Furir Sris Syhsis Equi Furir Sris Alysis Equi firs udrsd h sigl { m 8 m } m usig h dfiii f impuls fuci c ri: m 8 m hris W s h h sigl is pridic ih fudml prid f. If yu d s i, us fid vlu, 8,,,, 5 8, hich rps vry fur rms δ 8 hr: >, -, -, U. Us h lysis qui vlu h umricl vlus f prid f h Furir sris cfficis f h pridic sigl Slui: {δ 5m δ 5m}. m.egrcs.cm, i Sigls d Sysms pg

7S. L b rl d dd pridic sigl ih prid 7 d Furir cffici. Giv h 5,, 7. Drmi h vlus f, -, - d -. Slui: Usig h prpris f Furir Sris culd s: Prid ih prid 7 7 *7 5 *7 *7 7 rl d dd is purly imgiry d dd - - - - - - - - 7U. L b rl d dd pridic sigl ih prid 9 d Furir cffici. Giv h 5, 7 -. Drmi h vlus f, -, - d -. Slui: 8S. Drmi h Furir sris rprsis h fllig sigls: Ech illusrd i h fllig figur - - - 5 - b Ech illusrd i h fllig figur -5 - - - - 5 c Ech illusrd i h fllig figur.egrcs.cm, i Sigls d Sysms pg

-5 - - 7 9 d Ech illusrd i h fllig figur - - - - 5 - is pridic sigl ih prid d - - Slui: d Igri by pr udv uv d vdu.egrcs.cm, i Sigls d Sysms pg

.EgrCS.cm, i Sigls d Sysms pg 5 b dd v d d d d si si c si si d d d d d

d d ll 8U. Drmi h Furir Sris rprsi h sigl sh i h fllig figur: - - Slui: 9S. A discr-im pridic sigl is rl vlud d hs fudml prid 5. h zr Furir sris cfficis r, - *, * - Eprss i h m A A si φ. Slui: 5 dd 5 5 cs 5 cs8 5 cs 5 cs8 5 5 5 5 8 5 5 8 5 5 9U. A discr-im pridic sigl is rl vlud d hs fudml prid 7. h zr Furir sris cfficis r, - *, * - Eprss i h m A A si φ. Slui: S. Drmi h Furir sris cfficis h fllig discr-im pridic sigl. Pl h mgiud d phs f ch s f cfficis..egrcs.cm, i Sigls d Sysms pg

Slui: firs rm scd rm hr sics prid si cs X U. Drmi h Furir sris cfficis h fllig discr-im pridic sigl. Pl h mgiud d phs f ch s f cfficis. Slui: si7 S. h sigl rprsd by h fllig Furir sris cfficis is pridic ih prid 8. Drmi h sigl....... -8 8 Slui: 8 cs cs cs U. h sigl rprsd by h fllig Furir sris cfficis is pridic ih prid 7. Drmi h sigl....... Slui:.EgrCS.cm, i Sigls d Sysms pg 7