# Ppt on amplitude shift keying graph

##### Precalculus 4.5 Graphs of Sine and Cosine 1 Bellwork 60° 13 Find the two sides of this triangle.

left endpoint: solve bx-c=0 ·Interval right endpoint: solve bx-c=2π ·Vertical shifts are caused by d Precalculus 4.5 Graphs of Sine and Cosine 7 Steps to Graph ·Find amplitude ·Find left endpoint ·bx-c=0 ·Find right endpoint ·bx-c=2π ·Find the period · 2π/b ·Find key points by: ·Dividing period-interval into four equal parts ·Add “period/4” starting/

##### TRIGONOMETRY, 5.0 STUDENTS KNOW THE DEFINITIONS OF THE TANGENT AND COTANGENT FUNCTIONS AND CAN GRAPH THEM. Graphing Other Trigonometric Functions.

! y=A ???[B(θ-h)]+k 2: Graphing Trigonometric Functions 2: Example for Graphing Graph y=csc(  -  /2)+1. The vertical shift is 1. Use this information to graph the function. Amplitude is 1. The period is 2  /1 or 2 . The phase shift -(-  /2/1) or  /2. 2: Example for Graphing YOU TRY! Graph y=csc(2  -  /2)+1. 2: Example for Graphing YOU TRY! Graph y=csc(2  -  /2)+1/

##### Outline Revisit Analog Modulation Schemes Amplitude Modulation (AM) Frequency Modulation (FM) Analog-to-Digital Conversion - Sampling Digital Modulation.

a.k.a discrete-time). Amplitude Modulation (AM) Frequency Modulation (FM) Phase Modulation (PM) Amplitude Shift Keying (ASK) Frequency Shift Keying (FSK) Phase Shift Keying (PSK) Digital Modulation Schemes Figure 4-8 WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998 Amplitude Change Figure 4-9 WCB//i will start to vary/deviate from f c with the amount of. The conversion can be seen from the graph fcfc fifi vsvs 0 k f = Conversion gain Frequency Modulation (FM) Fact in FM : Instantaneous frequency f/

##### CHAPTER 4 – LESSON 1 How do you graph sine and cosine by unwrapping the unit circle?

-2-- 30-60-90 45-45-90 Graphs of Functions Sine Graphs of Functions Cosine Graphs of Functions Tangent Graphs of Functions Sine Cosine Graphs of Functions Tan Cotangent Graphs of Functions Secant Cosecant Chapter 4 - Lesson 2 Transforming Trig Functions Essential Question: How can we use the amplitude, period, phase shift and vertical shift to transform the sine and cosine curves? Key Question: How do the values of A/

##### Start Up Day 26 1.Graph each function from -2π to 2π 2.Find a polynomial function with zeros of: 0, -4, 3i 12/18/2015 by C.Kennedy1 The range of y = sin.

. The range of the cosine curve is ________________. OBJECTIVE: SWBAT use trigonometric graphs to define and interpret features such as domain, range, intercepts, periods, amplitude, phase shifts, vertical shifts and asymptotes. SWBAT to graph Sine and Cosine functions with and without graphing technology. EQ: What are the key points for the basic Sine and Cosine parent graphs & where do they come from? How do the values of “a/

##### Graphs of Tangent and Cotangent Functions

new reference period into 4 equal parts to create new x values for the key points Adjust the y values of the key points by applying the amplitude (a) and the vertical shift (d) Graph key points and connect the dots Key Steps in Graphing Secant and Cosecant Identify the key points of your reciprocal graph (sine/cosine), note the original zeros, maximums and minimums Find the new period (2/

##### CSEP 590tv: Quantum Computing Dave Bacon Aug 3, 2005 Today’s Menu Public Key Cryptography Shor’s Algorithm Grover’s Algorithm Administrivia Quantum Mysteries:

is it unitary? Quantum Fourier Transform And about that inverse QFT: It performs the inverse Fourier transform on the amplitudes! In Class Problem #1 Period Finding quantum oracle Problem: find in as few queries as possible Period Finding / [Long List] Pell’s equation [Hallgren 02] Hidden shift problems [van Dam, Hallgren, Ip 03] Graph traversal [CCDFGS 03] Spatial search [AA 03, CG 03/04, AKR 04] Element distinctness [Ambainis 03] Various graph problems [DHHM 04, MSS 03,…] Testing matrix multiplication [/

##### 4.5 Graphs of Sine and Cosine FUNctions How can I sketch the graphs of sine and cosine FUNctions?

Amplitude and Period of Sine FUNctions amplitude (new word, old concept) – the maximum displacement from equilibrium. For y = asinx and y = acosx, the amplitude is a. Let’s graph y = 2sinx. First, we will graph y = sinx. Next, we will label the five new key points, and graph the/of your endpoints, then average that value with each endpoint.) Key Points (-π/4,0) (0,2) (π/4,0) (π/2,-2) (3π/4,0) The graph! Good news! Vertical shifts are easy! We just shift up or down after we are finished with everything else./

##### 14.1, 14.2 (PC 4.5 & 4.6): Graphing Trig Functions HW: p.912 (3-5 all) HW tomorrow: p.913 (6, 10, 16, 18), p.919 (12-16 even) Quiz 14.1, 14.2: Tuesday,

x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = sin x is 1.) Graph of y = cos x Cosine graph is periodic (period for y = cos x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = cos x is 1.) Graphing: Amplitude = Period = Phase Shift : solve equations and/

##### Do Now:. 4.5 and 4.6: Graphing Trig Functions Function table: When you first started graphing linear functions you may recall having used the following.

for y = cos x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = cos x is 1.) Graphing: Amplitude = Period = Divide the period by 4 to get four equal subintervals. Phase Shift : solve equations and. This will give you the left and right endpoints of a period. Vertical Shift = The graph of is a reflection in the/

##### Chapter 14 Day 8 Graphing Sin and Cos. A periodic function is a function whose output values repeat at regular intervals. Such a function is said to have.

, to find the period when B is not one, the period of the function is the following: 2π Steps for Graphing 1. “Shift” the graph up or down and draw in the new midline. 2. Mark off the amplitude. 3. Determine the period and scale your graph accordingly. 4. Mark key points and sketch the graph. *Be careful if the A is negative, make sure to flip/

##### Week 2 Things you want to know.

stability. Also, PM is adaptable to data applications Examples of Phase Shift Bit Rate = Baud rate x Bits per Symbol PSK and QAM Phase Shift Keying (PSK) Most popular implementation of PM for data In BPSK (Binary PSK): one bit per phase change In QPSK: two bits per phase change (symbol) Quadrature Amplitude Modulation (QAM) Uses two AM carriers with 90o phase angle between/

##### 2.6 Graphs of the Sine and Cosine Functions xxy = sin x 00=SIN(B2) π/6=PI()/6=SIN(B3) π/3=PI()/3=SIN(B4) π/2=PI()/2=SIN(B5) 2π/3=B5+PI()/6=SIN(B6) 5π/6=B6+PI()/6=SIN(B7)

The cycle will begin at 0 and end at π/2 There are five key points of a sinusoidal graph: The beginning of the cycle, the points where sin(x)= 0, and the local maximum and minimum. Since this graph is not shifted horizontally, the beginning points is (0,0). Notice that there are / + v ω = -π/2 (However we need ω > 0) Let’s remember that sin x is an odd function, where f(-x) = -f(x) So The amplitude is |-2| = 2 so the largest value of y is 2. The period is T = 2π/ω = φ = 0, v = 0, so there is no horizontal /

##### GRAPHING TRIGONOMETRIC FUNCTIONS

amplitude (plus the phase shift) and to select a Ymax at least one value higher than that value. Select an appropriate y-scl based on the size of your amplitude. A “1” value will probably be sufficient. Leave Xres = 1. Viewing the Graph Press the y= key. Check to be sure the “Plot 1” key is not highlighted. Enter the equation under Y1=. Press the graph key. SAMPLE GRAPH/

##### 4.5 Graphs of Sine and Cosine Functions

the period and amplitude Find the period and amplitude Describe the relationship between the graphs of f and g Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts. p. 294 #15 Describe the relationship between the graphs of f and g Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts. p. 294 #21 Sketch the graphs of f and/

##### 4.5 – Graphs of Sine and Cosine A function is periodic if f(x + np) = f(x) for every x in the domain of f, every integer n, and some positive number p.

interval on the x-axis. 5.Divide the interval into fourths to plot “key points”. 6.Graph one period. Extend if necessary. 4.5 – Graphs of Sine and Cosine Graph the equation y = 3 sin(2x − π) amplitude: period: phase shift: interval: 3 = π π2π2π 4.5 – Graphs of Sine and Cosine Graph the equation y = amplitude: period: p. s.: interval: 4π4π2π2π = 2π(2)= 4π = −π(2)= −2/

##### 1 ANALOGUE TELECOMMUNICATIONS 2 MAIN TOPICS (Part I) 1)Introduction to Communication Systems 2)Filter Circuits 3)Signal Generation 4)Amplitude Modulation.

is needed 136 Frequency Shift Keying (FSK) Carrier Modulating signal FSK signal 137 FSK (cont’d) The frequency of the FSK signal changes abruptly from one that is higher than that of the carrier to one that is lower. Note that the amplitude of the FSK signal remains/, 8.65, etc. These points are useful for determining the deviation and the value of k f of an FM modulator system. 146 Graph of Bessel Functions 147 FM Side-Bands Each (J) value in the table gives rise to a pair of side- frequencies. The higher /

##### 4.1 and 4.2 Sine Graph Sine & Cosine are periodic functions, repeating every period of 2  radians: 0 x y 180  360 2  90  /2 270 3  /2 1 y = sin (x)x.

1 2 -2 y = A sin (Bx – C)amplitude = | A | period = 2  B phase shift = C (right/left) B y = sin (x) y = 2 sin (x) y = sin (2x) y = sin (x -  /2) Does the graph ever shift vertically? – YES y = A sin (Bx – C)/Graphing Guidelines 1.Calculate period 2. Calculate interval (period / 4) 3.Calculate phase shift-‘start-value’ 4. Create X/Y chart w/ 5 key points from ‘start-value’ Equation of a Cosine Curve 0 x y 180  360 2  90  /2 270 3  /2 1 2 -2 y = A cos (Bx – C)amplitude = | A | period = 2  B phase shift/

##### GAMPS COMPRESSING MULTI SENSOR DATA BY GROUPING & AMPLITUDE SCALING

c(i) + i 2 V w(i,j) Grouping & amplitude scaling is modeled as facility location Complete graph, every signal is represented by a node Cost opening a facility: /same group at time t Part of IBT dataset Similarity Query Compression by Interval Sharing Key Idea: If two sensors have near overlapping time series they can share a part/ humidity, sampling rate once every 30 seconds Signals not overlapping, but still correlated Shifting or scaling may help Question: Can we exploit this correlation ? We propose a/

##### Tangent and Cotangent Graphs

graph reflects about the x-axis. c indicates the phase shift, also known as the horizontal shift. b affects the period. y = a tan b (x - c) y = a cot b (x - c) Unlike sine or cosine graphs, tangent and cotangent graphs have no maximum or minimum values. Their range is (-∞, ∞), so amplitude/ shift of a cotangent graph. For a cotangent graph, c is the value of x in the key vertical asymptote. For this graph, c = because the key asymptote shifted left to . An equation for this graph can be written as or Graphs /

##### Graphing Sine and Cosine. Video Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max.

(X) y 2 = sin (1/2x) Press Graph Y = A sin (Bx ± C) ± D Amplitude Period Change 2  |b| Vertical Shift up/down Horizontal Shift Left/Right C B Examples-- Y = 3sin (x +  ) -3 A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ Y = cos (x - 2  ) A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ Y = -2sin (2x) A= _______ Period/

##### Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 4 Graphs of the Circular Functions.

.  Its x-intercepts are of the form x = n .  Its period is .  Its graph has no amplitude, since there are no minimum or maximum values.  The graph is symmetric with respect to the origin, so the function is an odd function. For all x in the/ phase shift is units to the right. Copyright © 2013, 2009, 2005 Pearson Education, Inc. 25 Example 5 GRAPH y = c + acot(x – d) (cont’d) To locate adjacent asymptotes, solve Divide the interval into four equal parts and evaluate the function at the three key x-/

##### Next  Back Tangent and Cotangent Graphs Reading and Drawing Tangent and Cotangent Graphs Some slides in this presentation contain animation. Slides will.

= tan x, there is no phase shift. The y-intercept is located at the point (0,0). We will call that point, the key point. Next  Back A tangent graph has a phase shift if the key point is shifted to the left or to the right. /Unlike sine or cosine graphs, tangent and cotangent graphs have no maximum or minimum values. Their range is (-∞, ∞), so amplitude is not defined. However, it is important to determine whether a is positive or negative. When a is negative, the tangent or cotangent graph will “flip” or /

x = nπ.  Its period is π.  Its graph has no amplitude, since there are no minimum or maximum values.  The graph is symmetric with respect to the origin, so the /shift is units to the right. Copyright © 2009 Pearson Addison-Wesley1.1-25 4.3-25 Example 5 GRAPHING A COTANGENT FUNCTION WITH VERTICAL AND HORIZONTAL TRANSLATIONS (continued) To locate adjacent asymptotes, solve Divide the interval into four equal parts to obtain the key x-values Evaluate the function for the key x-values to obtain the key/

##### Graphing Sinusoidal Functions y=sin x. Recall from the unit circle that: –Using the special triangles and quadrantal angles, we can complete a table.

at (0,0), ( ,0) and (2 ,0). Parent Function Key Points * Notice that the key points of the graph separate the graph into 4 parts. y= a sin b(x-c)+d a = amplitude, the distance from the center to the maximum or minimum. If |a|/-c) + d d= vertical shift If d is positive, graph shifts up d units. If d is negative, graph shifts down d units. In trigonometric functions, these vertical shifts are called the vertical displacement. y = sin x +2 What changed? Which way did the graph shift? By how many units? y /

##### Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions Section 7.

Graph transformations of the cosecant and secant functions Set your viewing window to the following settings: x min: 0 x max: 2π x scl: π/6 y min: -2 y max: 2 y scl: 1 Change your table to the following setting: Independent: 2. Ask Amplitude: a Period: π/b Phase Shift: c Vertical Shift: d Key/3π/4 π0 xcot x 0UD π/41 π/20 3π/4 πUD y = 2 tan x Page 196 #25 Page 196 #31 Amplitude: a Period: 2π/b Phase Shift: c Vertical Shift: d Key Points xcsc x 0UD π/21 πUD 3π/2 2πUD xsec x 01 π/2UD π 3π/2UD 2π1 Page 196 #37 /

##### Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching.

Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching graphs. What does the “normal” sine graph look like? What does the “normal” cosine graph look like? Sine Wave Tracer Draw the “normal” graph for each. Label the 5 key points. Maximum? Minimum? Crossings? Period? Amplitude? Parent Equation General Equation Period: 2/

##### Graphing Sinusoidal Functions Y=cos x. y = cos x Recall from the unit circle that: – Using the special triangles and quadrantal angles, we can complete.

o and 2 , there are two zeros at Parent Function Key Points * Notice that the key points of the graph separate the graph into 4 parts. y = a cos b(x-c)+d a = amplitude, the distance between the center of the graph and the maximum or minimum point. If |a| > 1/ c is positive, the graph shifts right c units (x-c)=(x-)+c)) What changed? Which way did the graph shift? By how many units? y = a cos b(x-c) + d d= vertical shift If d is positive, graph shifts up d units If d is negative, graph shifts down d units y /

##### Section 4.6 Graphs of Other Trigonometric Functions.

at drawing these graphs using graph paper is strongly recommended. Tangent and Cotangent Three key elements of tangent and cotangent: 1.For which angles are tangent and cotangent equal to 0? These will be x-intercepts for your graph. 2.For /graph between the asymptotes. y = tan x y = cot x Transformations |A| = amplitude π/B = period (distance between asymptotes). C/B gives phase shift from zero. Examples—Graph the Following Secant and Cosecant The graphs of secant and cosecant are derived from the graphs/

##### Thinking about angles and quadrants Special Triangles Graphing Write and scratch Practice 1What goes with what, I forgot. Rectangles Practice 2 Here are.

and use even-odd properties to simplify 1)Find Amplitude and period 2)Find Phase Shift, and vertical shift 3)Find starting and ending x-coordinates 4)Divide into 4 equal parts 5)Label key points 6) Connect Remember, cos(x) = cos/Amplitude = T = P.S. = V.S. = Starting point is phase shift. Ending point is Phase shift + Period 3 5 + You will take the starting and ending points and find the average, then find the average again to break it up into four equal regions You want to study the sine and cosine graphs/

two key points on the cosecant graph are. In the remaining examples we will use a sine or cosine graph as an aid in sketching the graph of a cosecant or secant function, respectively. cont’d 20 Example 7 Graph one cycle of Solution: First, we sketch the graph of There is a vertical translation of the graph of y = sin x one unit downward. The amplitude is/

##### Lesson 4-6 Graphs of Secant and Cosecant. 2 Get out your graphing calculator… Graph the following y = cos x y = sec x What do you see??

the new end (bx - c = π) 4.Find the new interval (new period / 2) to divide the new reference period into 2 equal parts to create new x values for the key points 5.Adjust the y values of the key points by applying the amplitude (a) and the vertical shift (d) 6.Graph key points and connect the dots

##### Carrier-Amplitude modulation In baseband digital PAM: (2d - the Euclidean distance between two adjacent points)

, with a roll-off factor a=0.5. The carrier frequency is f c =40/T. evaluate and graph the spectrum of baseband signal and the spectrum of the amplitude-modulated signal Carrier-Phase Modulation This type of digital phase modulation is called Phase-Shift-Key where gT(t) is the transmitting filter pulse shape. when gT(t) is a rectangular pulse we expressed/

##### Graphs of the Sine and Cosine Functions Section 6.

Sine and Cosine Functions Section 6 Objectives Graph transformations of the sine function Graph transformations of the cosine function Determine the amplitude & period Graph using key points Find an equation for a sinusoidal graph Amplitude: a Period: 2π/b Phase Shift: c Vertical Shift: d Key Points xsin x 00 π/21 π0 3π/2 2π0 xcos x 01 π/20 π 3π/20 2π1 Page 187 #25 Page 187 #33/

##### Graphs of Cosine Section 4-5. 2 Objectives I can determine all key values for 6 trig functions I can graph cosine functions I can determine amplitude,

Section 4-5 2 Objectives I can determine all key values for 6 trig functions I can graph cosine functions I can determine amplitude, period, and phase shifts of cosine functions 3 Cosine Function Graph of the Cosine Function To sketch the graph of y = cos x first locate the key points. These are the maximum points, the minimum points, and the intercepts. 1001cos x 0x Then/

##### Graphing y = tan x x = 0, tan (0) = _____ (, ) x = π/4, tan (π/4) = _____ (, ) x = π/2, tan (π/2) = _____ (, ) x = -π/4, tan (-π/4) = _____ (, ) x = -π/2,

asymptotes 2.Find T 3.Find 3 key points Graph y = 2 cot x –2 Graph y = cot(4x – π/2) 0 < Bx - C < π Graphing Trigonometric Functions Standard form: y = A tan (Bx - C) + D or y = A cot (Bx - C) + D Amplitude = “none” (but it does // B, (C + π) / B Vertical shift = D Domain (tan x): -∞ ≤ x ≤ +∞, x ≠ n(π/2), n odd integer Domain (cot x): -∞ ≤ x ≤ +∞, x ≠ n(π) Range: -∞ ≤ y ≤ +∞ Three key points: (, ), (, ), (, ) Drawing the curve: (1) Determine D, the vertical phase shift. This will be the “new” horizontal axis/

##### Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–2) CCSS Then/Now New Vocabulary Key Concept: Logarithm with Base b Example 1: Logarithmic.

Logarithmic Form Example 3: Evaluate Logarithmic Expressions Key Concept: Parent Function of Logarithmic Functions Example 4: Graph Logarithmic Functions Key Concept: Transformations of Logarithmic Functions Example 5: Graph Logarithmic Functions Example 6: Real-World Example/ Standards F.IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.BF.3 Identify the effect on the graph of replacing f(x) by/

graph. The points are collected over a number of samples to produce a scatter plot. Data Graph Spectrum Analyzer Probing This probe can be used as a multi-channel graph, displaying amplitude/value in a column. Shift The input data is adjusted to either move the inputs back by a specified shift value to do predictions /learning environment Emphasis on understanding rather than focusing on complex mathematical derivations Key concepts reinforced by interactive examples Over 200 fully functional simulations of /

##### Phases of the Business Cycle. Business Cycle Definition: alternating increases and decreases in the level of business activity of varying amplitude and.

divisible into shorter cycles of similar character with amplitudes approximating their own.” -- Burns and Mitchell, 1946 Recessions /economic growth Recession years are shaded blue: note downward slope on graph indicating that GDP is decreasing. U.S. real gross domestic/2002 by The McGraw-Hill Companies, Inc. All rights reserved. Three Key Aspects of the Economy Economic Growth Inflation Employment The State of the / plunge in the demand for hides Thus small shifts in demand growth at the consumer level are amplified/

##### Building the Future of. 2012 – 2013 Key Accomplishments Began System Wide Digital Conversion Began System Wide Digital Conversion – Student Centered Learning.

School District in Alabama to Receive Accreditation – Shifts Accreditation Burden from Schools to the School District – Avoids \$170,000 in Accreditation Costs 2012 – 2013 Key Accomplishments District-Wide Talent Management & Development District/ between logarithmic & exponential equations; graph each Use law of cosines & law of sines Graph & determine domain, range, amplitude & period of cosine & sine functions Number Sense, Quadratic Functions, and Matrices Graph & solve quadratic equations & inequalities/

##### Graphing the Other Trigonometric Functions DR. SHILDNECK FALL.

a vertical reflection and a horizontal shift. By remembering a few key aspects of the graphs (their patterns), you can easily and quickly sketch the graphs of tangent and cotangent functions. Tangent vs. Cotangent – Key Components At x=0:- The /graph has the “other” characteristic. The tangent goes up (left to right), the cotangent goes down. Half way in between the primary components, the curve has a point the same distance as the amplitude up (or down) from the axis. ASSIGNMENT Unit 4 Assignment 2 – Graphs/

##### Chapter 4 Angles and Their Measure. Angles An angle is formed by two rays that have a common endpoint called the vertex. One ray is called the initial.

 2 3  y = sin x, 0 < x < 2  The Graph of y=sinx Graphing Variations of y=sinx Identify the amplitude and the period. Find the values of x for the five key points – the three x- intercepts, the maximum point, and the minimum point. Start/graph of y = A sin Bx has amplitude = | A| period = 2  /B. The graph of y = A sin Bx has amplitude = | A| period = 2  /B. x y y = A sin Bx Amplitude: | A| Period: 2  /B Amplitudes and Periods The graph of y = A sin (Bx – C) is obtained by horizontally shifting the graph/

interval 15 © 2010 Pearson Education, Inc. All rights reserved EXAMPLE 3 Graphing y = sin bx Solution continued Divide this interval into four equal parts to find the x-coordinates for the key points: (y values do not change.) To find the period of divide/). 24 © 2010 Pearson Education, Inc. All rights reserved PROCEDURE FOR GRAPHING y = a sin b(x – c) AND y = a cos b(x – c) Step 1Find the amplitude, period, and phase shift. amplitude = |a| phase shift = c period = Step 2The starting point for the cycle is x/

##### Modulation Formats. Optical communication systems are carrier systems. This implies that a wave of a frequency much higher than that of the information.

impart information on the optical carrier. Amplitude, E 0 [1]Amplitude, E 0 ; the format that modulates the amplitude of the optical carrier is called “amplitude modulation”. If the information is digital then the format is known as “ amplitude shift keying” or ASK for short. The/ the receiver in normalise form. The ratio R/B represents the spectral efficiency whose upper limits is C/B. The graph in the next slide illustrates the Harley – Shannon law. The curve corresponding to R = C separates the regions; /

##### Lesson 43 – Trigonometric Functions Math 2 Honors - Santowski 10/9/20151Math 2 Honors - Santowski.

 identify transformations and state how the key features have changed (iii) Graph and analyze y = tan( ½ x +  /4) – 3  identify transformations and state how the key features have changed 10/9/201537 Math 2 Honors - Santowski 38 (G) Writing Sinusoidal Equations ex 1. Given the equation y = 2sin3(x - 60  ) + 1, determine the new amplitude, period, phase shift and equation of the axis of the/

##### Precalculus 1/9/2015 DO NOW/Bellwork: 1) Take a unit circle quiz 2) You have 10 minutes to complete AGENDA Unit circle quiz Sin and Cosine Transformations.

go back to the quadratic equation in graphing form: y = a(x – h) 2 + k If a < 0: reflection across the x axis |a| > 1: stretch; and |a| < 1: shrink (h, k) was the vertex (locator point) h gave us the horizontal shift k gave us the vertical shift Transforming the Cosine (or Sine (Sinusoid) Key Points Amplitude – increase the output by a factor of/

##### Trigonometric Functions

Functions Use reciprocal identities Graph of y = sec x Key Points Graphing the Tangent Function Properties of the Tangent Function Transformations of the Graph of the Tangent Functions Graphing the Cotangent Function Graphing the Cosecant and Secant Functions Phase Shifts; Sinusoidal Curve Fitting Section 5.6 Graphing Sinusoidal Functions y = A sin(!x), ! > 0 Amplitude jAj Period y = A sin(!x { Á) Phase shift Phase shift indicates amount of shift To right if/

##### Introduction Basic concepts Terminology.

FSK, and PSK. Amplitude-Shift Keying 2 binary values represented by 2 amplitudes. Typically, “0” represented by absence of carrier and “1” by presence of carrier. Prone to errors caused by amplitude changes. Frequency-Shift Keying 2 binary values represented by/ AS backbone; all areas connected to it. OSPF 3 Type of service routing: Routing updates: Uses different graphs labeled with different metrics. Routing updates: Adjacent routers exchange routing information. Adjacent routers are on different LANs. /

##### 1 In The Name of God, The Merciful, The Compassionate Advanced Computer Networks Department of Computer Engineering Sharif University of Technology –

Techniques: ASK, FSK, and PSK. Techniques: ASK, FSK, and PSK. 60 Amplitude-Shift Keying 2 binary values represented by 2 amplitudes. 2 binary values represented by 2 amplitudes. Typically, “0” represented by absence of carrier and “1” by presence of /; all areas connected to it. 376 OSPF 3 Type of service routing: Type of service routing: –Uses different graphs labeled with different metrics. Routing updates: Routing updates: –Adjacent routers exchange routing information. –Adjacent routers are on different/

##### Gettin’ Triggy wit it H4Zo.

where sin(t) >0 sin(t) > 0 The Sine Function Sine Function Graph of the Sine Function To sketch the graph of y = sin x first locate the key points. These are the maximum points, the minimum points, and the intercepts./amplitude, period, and phase shift of y = 2sin(3x-  ) Solution: Amplitude = |A| = 2 period = 2  /B = 2  /3 phase shift = -C/B =  /3 Example cont. y = 2sin(3x-  ) Amplitude Period: 2π/b Phase Shift: -c/b Vertical Shift 6.6 More Trig. Graphs Objective: Students will look at more trig. graphs/