baud rate. Bit rate = 2ƒ * n. (See Table 2.9) Any Limit on Bit Rate? The **formula** Bit rate = 2ƒ * n seems to imply that there is no upper bound for the data rate given the/encode a 0 bit. Modulation Techniques **Amplitude** **shift** **keying** (ASK) Frequency **shift** **keying** (FSK) Phase **shift** **keying** (PK) Modulation Techniques This modulation technique is called **Amplitude** **Shift** **keying** (ASK) technique. **Amplitude** **Shift** **Keying** Values represented by different **amplitudes** of carrier Usually, one **amplitude** is zero –i.e. presence /

is a linear function of bandwidth and transmission time and directly proportional to both. Shannon’s **Formula** Where I = information capacity (bps) B = bandwidth (Hz) = signal to noise /**Amplitude** **Shift** **Keying** (ASK) Frequency **Shift** **Keying** (FSK) Phase **Shift** **Keying** (PSK) Quadrature **Amplitude** Modulation (QAM) **Amplitude** **Shift** **Keying** (ASK) A binary information signal directly modulates the **amplitude** of an analog carrier. Sometimes called Digital **Amplitude** Modulation (DAM) Where v ask (t) = **amplitude** **shift** **keying**/

**Key** Points Electrical signals can take many forms and can be analogue or digital A simple analogue form is where a voltage is proportional to the **amplitude**/Education Limited 2004 OHT 1.238 Sequential Logic Introduction Bistables Memory Registers **Shift** Registers Counters Monostables or one-shots Astables Timers Chapter 10 Storey: Electrical/first-order systems can be described by the initial and final value **formulae** Circuits that contain both capacitance and inductance are usually second-/

interval over which the channel impulsive response is considered stationary Typical assumption: Doppler spread and coherence time are related by the **formula**: K: constant in the range of 0.25 to 0.5 89 Time Variance: Fast Fading The channel changes /to the BER of these regions is larger Gaussian frequency **shift** **keying** (GFSK) Encodes data as a series of frequency changes in a carrier Noise usually changes the **amplitude** of a signal Modulation that ignores **amplitude** (e.g., broadcast FM) Relatively immune to /

Cisco Systems, Inc. All rights reserved. FWL 1.0—3-13 Calculating dB The **formula** for calculating dB is as follows: dB = 10 log10 (Pfinal/Pref) dB = /**Amplitude** –Frequency –Phase or angle The three corresponding techniques are as follows: –**Amplitude** modulation (AM) –Frequency modulation (FM) –Phase modulation (PM) Other modulation techniques –**Amplitude** **shift** **keying** (ASK) — Turning the **amplitude** all the way off –Frequency **shift** **keying** (FSK) — Hopping to an extreme frequency –Phase **shift** **keying** (PSK) — **Shifting**/

**Amplitude**: **Amplitude**-**Shift**-**Keying** (ASK) Change in Frequency: Frequency-**Shift**-**Keying** (FSK) Change in Phase: Phase-**Shift**-**Keying** (PSK) Hybrid changes (more than one parameter). Ex. Phase and **Amplitude** change: Quadrature **Amplitude** Modulation (QAM) Binary Modulations – Basic Types These two have constant envelope (important for **amplitude**/ Performance M-ary PSK Error Performance Operation Point Comparison Summary of Useful **Formulas** Summary of Digital Communications -1 Legend of variables mentioned in this section/

+ 45 o ) …and the equation has a positive phase **shift** Phase **Shift** The power relationships developed for dc circuits apply to ac circuits except you must use rms values when calculating power. The general power **formulas** are: Power in Resistive AC Circuits Assume a sine wave with/ value. It is equal to 0.707 times the peak value. rms stands for root mean square. Selected **Key** Terms Radian Phase **Amplitude** Pulse Harmonics The maximum value of a voltage or current. A type of waveform that consists of two equal and/

**Amplitude** **Shift** **Keying** (ASK) Phase **Shift** **Keying** (PSK) Frequency **Shift** **Keying** (FSK) Multilevel Signaling (Mary Modulation) Mary **Amplitude** Modulation Mary Phase **Shift** **Keying** (Mary PSK) Mary Frequency **Shift** **Keying** (Mary FSK) Quadrature **Amplitude** Modulation (QAM) **Amplitude** **Shift** **Keying** (ASK) In ASK the binary data modulates the **amplitude** of the carrier signal Phase **Shift** **Keying**/ (Part III) Max. data rate = 2B log2 M bits/sec Nyquist **Formula** It states that if a signal consists of M levels then the maximum data/

+ 45o) …and the equation has a positive phase **shift** PolyPhase power An important application of phase-**shifted** sine waves is in electrical power systems. Electrical utilities / composed only of the fundamental frequency and odd harmonics (of the proper **amplitude**). Oscilloscope A device that traces the graph of a measured electrical signal on/µs Selected **Key** Terms Sine wave Alternating current Period (T) Frequency (f) Hertz A type of waveform that follows a cyclic sinusoidal pattern defined by the **formula** y = A/

general carrier wave may be written: Modulation methods based on varying the **amplitude**, A, frequency, f and phase, to transmit digital data is known as **Amplitude** **Shift** **Keying** (ASK), Frequency **Shift** **Keying** (FSK) and Phase **Shift** **Keying** (PSK) respectively. Example – Tx of digital data over telephone / and 0s are occuring. Therefore, Where fa = highest fund freq (hz) fb = input bit rate (bps) The **formula** used for modulation index in FM is also valid for FSK, thus (unitless) Where h = FM modulation index called h/

Cisco Systems, Inc. All rights reserved. FWL 1.0—3-8 Calculating dB The **formula** for calculating dB is as follows: dB = 10 log10 (Pfinal/Pref) dB = /**Amplitude** –Frequency –Phase or angle The three corresponding techniques are as follows: –**Amplitude** modulation (AM) –Frequency modulation (FM) –Phase modulation (PM) Other modulation techniques –**Amplitude** **shift** **keying** (ASK) — Turning the **amplitude** all the way off –Frequency **shift** **keying** (FSK) — Hopping to an extreme frequency –Phase **shift** **keying** (PSK) — **Shifting**/

s bandwidth theorem Bandwidth efficiency B = R / B bps/Hz R=Data rate in bits/second B=Bandwidth of modulated RF signal Shannons **formula**: Bmax = C/B = channel capacity (bits/s) RF bandwidth = log2(1 + S/N) S/N = Signal to Noise/ period EB – Energy/bit, N0 – Noise spectral density QPSK BW = RB = 1 / TB Nonlinear or envelope modulation Frequency **shift** **keying** The frequency of a constant **amplitude** carrier signal is switched between 2 values ( 1 and 0) Properties of FSK Transmission Bandwidth BT = 2f + 2B B /

used. Refer to previous section for discussion and **formulas**. A digitized signal will always need more bandwidth /**Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency ◦ Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency ◦ Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** ◦ Quadrature **Amplitude** Modulation (QAM). Hierarchy Types of digital-to-analog modulation **Amplitude**-**Shift** **Keying** One binary digit represented by presence of carrier, at constant **amplitude**/

**amplitude**, frequency and phase **Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** Basic Encoding Techniques **Amplitude**-**Shift** **Keying** One binary digit represented by presence of carrier, at constant **amplitude**/ signal elements Angle Modulation Carson’s rule where The **formula** for FM becomes **Amplitude** Modulation Transmitted power P t = total transmitted power /

of an analog signal based on the information in digital data. Aspects of Digital-to-Analog Conversion **Amplitude** **Shift** **Keying** Frequency **Shift** **Keying** Phase **Shift** **Keying** Quadrature **Amplitude** Modulation Topics discussed in this section: 3 Kyung Hee University 5.1 Digital-to-Analog Conversion Figure /located at 250 kHz. This means that our carrier frequency can be at f c = 250 kHz. We can use the **formula** for bandwidth to find the bit rate (with d = 1 and r = 1). Digital-to-Analog Conversion - ASK 12/

62 Figure 6.1 Illustrative waveforms for the three basic forms of signaling binary information. (a) **Amplitude**-**shift** **keying**. (b) Phase-**shift** **keying**. (c) Frequency-**shift** **keying** with continuous phase. Chapter 6: Pass-band Data Transmission Digital Communication Systems 2012 R.Sokullu6/62 /e is calculated –for simple binary coherent methods as coherent binary PSK and coherent binary FSK, there are exact **formulas** for P e –for coherent M-ary PSK and coherent M-ary FSK approximate solutions are sought. Chapter /

2012/2013 Communications and Signals Processing 1 Dr. Ahmed Masri 7.1 Some Preliminaries 7.2 Binary **Amplitude**-**Shift** **Keying** 7.3 Phase-**Shift** **Keying** 7.4 Frequency-**Shift** **Keying** Chapter 7 - Outlines 2 Dr. Ahmed Masri Section 7.1 – Some Preliminaries 3 Dr. Ahmed/this basis, we may express the average transmitted signal energy as For this **formula** to hold, however, the two binary symbols must be equiprobable. Section 7.2 – Binary **Amplitude**-**Shift** **Keying** 17 Dr. Ahmed Masri Generation Of Ask Signals From Eqs. (7.9)/

observation interval of length To Linear modulation with sinc pulse uses all available degrees of freedom (interpolation **formula**) Bandwidth efficiency for a modulation scheme Signal space description of modulation formats Modulation degrees of freedom, II/symbols can now take complex values, typically from a fixed constellation Some example constellations PSK: phase **shift** **keying** QAM: quadrature **amplitude** modulation Bandwidth of linearly modulated signals Model as random process We give an outline of the /

vector is called a phasor. Phasors are useful for showing the phase relationships in ac circuits. Phase **Shift** The phase of a sine wave is an angular measurement that specifies the position of a sine wave relative/ **amplitude**). Oscilloscope The oscilloscope is divided into four main sections. © Copyright 2007 Prentice-Hall Oscilloscope © Copyright 2007 Prentice-Hall Oscilloscopes Display Trigger Horizontal Vertical Selected **Key** Terms A type of waveform that follows a cyclic sinusoidal pattern defined by the **formula** /

Strength (continued) Data Communications and Computer Networks: A Business Users Approach, Sixth Edition Loss of Signal Strength **Formula** for decibel (dB): dB = 10 x log10 (P2 / P1) where P1 is the beginning power / using analog signals, digital data must first undergo a process called **shift** **keying** or modulation Three basic techniques of **shift** **keying** are **amplitude** **shift** **keying**, frequency **shift** **keying**, and phase **shift** **keying** Data Communications and Computer Networks: A Business Users Approach, Sixth Edition/

analogue and digital signals Transmission impairments – attenuation and noise affect signal quality Shannon’s **formula** provides a theoretical estimate of maximum channel capacity Topic 15 – Data Communication Fundamentals Learning/of Modulation **Amplitude** modulation (AM) or **amplitude** **shift** **keying** (ASK) Frequency modulation (FM) or frequency **shift** **keying** (FSK) Phase modulation or phase **shift** **keying** (PSK) **Amplitude** **Shift** **Keying** (ASK) In radio transmission, known as **amplitude** modulation (AM) The **amplitude** (or /

also to the S/N ratio; specifically he showed that: Bit Rate = Bandwidth * log 2 (1 + S/N) bps The **formula** states that a higher BW and S/N ratio allow higher bit rate Hence, for the telephone system, which has a frequency of /3.13 – FSK (Two Frequencies), One Bit per Baud – Analog signal for 01001 21 D igital-to-Analog- Conversion **Amplitude** Modulation (AM) Also known as **Amplitude** **Shift** **Keying** (ASK) Each bit group is assigned to an analog signal of given magnitude The signal is transmitted for a/

. 5.10 5.11 5.5.2 **Amplitude** **Shift** **Keying** In **amplitude** **shift** **keying**, the **amplitude** of the carrier signal is varied to create signal elements. Both frequency and phase remain constant while the **amplitude** changes. 5.12 Figure 5.3: Binary **amplitude** **shift** **keying** 5.13 Figure 5.4: Implementation of /bandwidth is located at 250 kHz. This means that our carrier frequency can be at fc = 250 kHz. We can use the **formula** for bandwidth to find the bit rate (with d = 1 and r = 1). 5.14 In data communications, we normally /

: A Business Users Approach, Eighth Edition © 2016. Cengage Learning. All Rights Reserved. 25 Loss of Signal Strength **Formula** for decibel (dB): dB = 10 x log 10 (P 2 / P 1 ) where P 1 is the/to be transmitted using analog signals, digital data must first undergo a process called **shift** **keying** or modulation –Three basic techniques of **shift** **keying** are **amplitude** **shift** **keying**, frequency **shift** **keying**, and phase **shift** **keying** Data Communications and Computer Networks: A Business Users Approach, Eighth Edition © 2016/

two types of conversions. Contents: 1.Digital-to-analog conversion 1.**Amplitude** **Shift** **Keying** 2.Frequency **Shift** **Keying** 3.Phase **Shift** **Keying** 4.Quadrature **Amplitude** Modulation 2.Analog-to-Analog Conversion 1.**Amplitude** Modulation 2.Frequency Modulation 3.Phase Modulation 1.Digital-to-Analog Conversion / B is the bandwidth. The **formula** shows that the required bandwidth has a minimum value of S and a maximum value of 2 S. Multilevel ASK The above discussion uses only two **amplitude** levels. We can have multilevel /

of a circles part that encloses a circumference of length equal to the radius **Key** equation to convert: 2 π = 360 degrees Convert degrees to radians: /Also written as: n=c θoθo 31 Complex Numbers Convert polar rectangular via Euler’s **Formula**: e jθ = cos θ + j sin θ Conjugate of a complex number is simply formed/( ωt - 26 o ), yet ω cannot be derived from the phasor Phasor only expresses **amplitude** and phase **shift** Phasor doe NOT include frequency or ω Goal to transform Phasor to time domain is finding the /

**Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** Basic Encoding Techniques **Amplitude**-**Shift** **Keying** One binary digit represented by presence of carrier, at constant **amplitude**/FM and PM require greater bandwidth than AM Angle Modulation Carson’s rule where The **formula** for FM becomes Basic Encoding Techniques Analog data to digital signal Pulse code modulation (/

sin (q + 45o) …and the equation has a positive phase **shift** Phase **shift** An important application of phase-**shifted** sine waves is in electrical power systems. Electrical utilities generate ac with /dc and the ac sources produce the same power to the bulb: The power **formulas** are: 120 Vdc 0 V 170 Vp = 120 Vrms 0 V Power in/for root mean square. Selected **Key** Terms A unit of angular measurement. There are 2p radians in one complete 360o revolution. Radian Phase **Amplitude** Pulse Harmonics The relative angular /

totally replaced analog Rev.5;Page. 4 ©1996-2005 R.Levine Data Communication in 1960 Modulator-demodulators (MODEMs) using frequency- **shift**-**keying** (FSK) modulation were in limited use via dial-up PSTN connections –Data rates up to 110 bit/second typically used with /5;Page. 41 ©1996-2005 R.Levine Approx. Square Wave Using 3 Odd Harmonics Proper **amplitude** of each “harmonic” sine wave was found from a product integral **formula** (same as statistical cross correlation). Rev.5;Page. 42 ©1996-2005 R.Levine Approx. /

Basic Encoding Techniques Digital data to analog signal **Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** The case of transmitting digital data using analog /most cases, infinite bandwidth is required to transmit FM and PM signals. Angle Modulation Carson’s rule The **formula** for FM becomes where Am is the maximum value of m(t). F is the peak derivation F/

Encoding Techniques Digital data to analog signal **Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** Basic Encoding Techniques Stallings, Wireless Communications &/ Inc. All rights reserved. 0-13-191835-4 Angle Modulation Carson’s rule where The **formula** for FM becomes Stallings, Wireless Communications & Networks, Second Edition, © 2005 Pearson Education, Inc/

5.13 5.14 5.5.2 **Amplitude** **Shift** **Keying** In **amplitude** **shift** **keying**, the **amplitude** of the carrier signal is varied to create signal elements. ( Both frequency and phase remain constant while the **amplitude** changes. ) 5.15 Figure 5.3: Binary **amplitude** **shift** **keying** 5.16 Figure 5.4: Implementation of / is located at 250 kHz. This means that our carrier frequency can be at fc = 250 kHz. We can use the **formula** for bandwidth to find the bit rate (with d = 1 and r = 1). 5.21 In data communications, we normally/

(**keying**!) examples Use data to modify the **amplitude** of a carrier frequency ! **Amplitude** **Shift** **Keying** Use data to modify the frequency of a carrier frequency ! Frequency **Shift** **Keying** Use data to modify the phase of a carrier frequency ! Phase **Shift** **Keying** ©/ a multi-path environment Brighter color = stronger signal Obviously, simple (quadratic) free space attenuation **formula** is not sufficient to capture these effects © Jochen Schiller, FU Berlin University of Freiburg Institute of Computer Science/

(II) oUse data to modify the **amplitude** of a carrier frequency - **Amplitude** **Shift** **Keying** (ASK) oUse data to modify the frequency of a carrier frequency - Frequency **Shift** **Keying** (FSK) oUse data to modify the phase of a carrier frequency - Phase **Shift** **Keying** (PSK) © Tanenbaum, Computer Networks 10/by default the gain of an the gain of an isotropic antennaisotropic antenna A linear number is converted into dB, using the following **formula**: X(dB) = 10log 10 (X) X(dBm) = 10log 10 (X/1mW) E.g. 1W = 0dBW = +/

**amplitude** modulation can be described as follows: the **amplitude** of s c (t) is varied according to the modulating signal, s m (t). To simplify the analysis, assume that the two signals are in phase (φ m = φ c = 0) and thus, Equation (5.17) reduces to: applying Euler’s **formula**/ 5.12) it requires a mixer with an excessive bandwidth - expensive to afford Figure 5.12 **Amplitude** **shift**-**keying** technique using an on – off switch 52 Fundamentals of Wireless Sensor Networks: Theory and Practice Waltenegus Dargie /

of making an erroneous decision. The risk levels are typically = 10%, 5%, 2%, 1%, or 0.5%. The **key** is whether or not the sample mean falls among the least likely of all possible sample means for a given risk level. Hypothesis/and minimum; estimate the midline. 3.Estimate the **amplitude**. 4.What is the frequency? 5.Estimate the phase **shift** for a cosine or sine function. 6.Write a **formula** to model the phenomenon. Write a possible **formula** for each of the following trigonometric functions: Dallas Temperatures/

**Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** 14 Basic Encoding Techniques 15 **Amplitude**-**Shift** **Keying** One binary digit represented by presence of carrier, at constant **amplitude**/PM require greater bandwidth than AM 40 Angle Modulation Carson ’ s rule where The **formula** for FM becomes 41 Basic Encoding Techniques Analog data to digital signal Pulse code /

DSB, SSB r Digital modulation m **Amplitude** **shift** **keying** (ASK) m Frequency **shift** **keying**: FSK m Phase **shift** **keying**: BPSK, QPSK, MSK m Quadrature **amplitude** modulation (QAM) 16 Outline r Recap r Frequency domain examples r Basic concepts of modulation r **Amplitude** modulation 17 Example: **Amplitude** Modulation (AM) r Block diagram/ contains both cos() and sin(). r Using Euler’s **formula**: 113 Implementing Wireless: From Hardware to Software 114 Making Sense of the Transform 115 Relating the Two Representations

—Use modem (modulator-demodulator) **Amplitude** **shift** **keying** (ASK) Frequency **shift** **keying** (FSK) Phase **shift** **keying** (PK) TUNALIData Communication34 Modulation Techniques TUNALIData Communication35 **Amplitude** **Shift** **Keying** (1) Two binary values represented by different **amplitudes** of carrier frequency Usually, one **amplitude** is zero —i.e. presence/B T ) dB From Figure 5.4, for FSK and ASK, E b /N 0 = 14.2 dB And substitution to above **formula** yields 14.2 dB = 12 dB – (R/B T ) dB yielding R/B T = 0.6. For PSK, from /

Digital data to analog signal **Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** ECEN 621, Mobile Wireless Networks Prof. Xi/ AM ECEN 621, Mobile Wireless Networks Prof. Xi Zhang Angle Modulation Carson’s rule where The **formula** for FM becomes ECEN 621, Mobile Wireless Networks Prof. Xi Zhang Basic Encoding Techniques Analog data to /

**Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** Basic Encoding Techniques **Amplitude**-**Shift** **Keying** One binary digit represented by presence of carrier, at constant **amplitude**/PM require greater bandwidth than AM Angle Modulation Carson’s rule where The **formula** for FM becomes Basic Encoding Techniques Analog data to digital signal Pulse code /

levels. How many bits are needed per level? We calculate the number of bits from the **formula** Each signal level is represented by 3 bits. A digital signal has 9 levels. How many / Analog Signals Three basic techniques: **Amplitude** **shift** **keying** Frequency **shift** **keying** Phase **shift** **keying** 29 **Amplitude** **Shift** **Keying** One **amplitude** encodes a 0 while another **amplitude** encodes a 1 (a form of **amplitude** modulation) 30 **Amplitude** **Shift** **Keying** 31 **Amplitude** **Shift** **Keying** 32 Frequency **Shift** **Keying** One frequency encodes a 0 while/

**Amplitude**-**shift** **keying** (ASK) **Amplitude** difference of carrier frequency Frequency-**shift** **keying** (FSK) Frequency difference near carrier frequency Phase-**shift** **keying** (PSK) Phase of carrier signal **shifted** Basic Encoding Techniques **Amplitude**-**Shift** **Keying** One binary digit represented by presence of carrier, at constant **amplitude**/FM and PM require greater bandwidth than AM Angle Modulation Carson’s rule where The **formula** for FM becomes Basic Encoding Techniques Analog data to digital signal Pulse code modulation (/

of a channel between 3 MHz and 4 MHz ; SNR dB = 24 dB Using Shannon’s **formula**, Channel capacity 35 Example of Nyquist and Shannon Formulations How many signaling levels are required? Classifications of / 52 Digital modulation Modulation of digital signals known as **Shift** **Keying** **Amplitude** **Shift** **Keying** (ASK): –very simple –low bandwidth requirements –very susceptible to interference Frequency **Shift** **Keying** (FSK): –needs larger bandwidth Phase **Shift** **Keying** (PSK): –more complex –robust against interference 101 /

channel dictates the information carrying capacity of the channel This is calculated using Shannon’s channel capacity **formula** Increasing bandwidth Shannon’s Theorem (Shannon’s Limit for Information Capacity) Claude Shannon at Bell / transmit information in analog form using **Amplitude** or Frequency modulation Digital communication systems also employ modulation techniques, some of which include: **Amplitude** **Shift** **Keying** Frequency **Shift** **Keying** Phase **Shift** **Keying** Basic digital communications system Transmitter EM /

. 4.D Body Wave direction L To drive the animation use PageUp- and PageDown-**keys** in SlideShow-state (F5). Gravitational wave contains transverse and longitudinal component. A wave is/the field and an **amplitude** of cyclic wave. Thus the speed ve must be added to the relative speeds vr of all bodies parallel the radius of the field. The **formula** to add the / faster it seems to fly away on grounds of the light trace (red **shift**). The red **shift** is caused, when the time of the bodies at inner orbits passes slower./

Physics Energy Efficiency The energy efficiency of a device can be calculated using this **formula**: energy efficiency = useful output energy total input energy Useful energy is measured in/of direction when they are refracted at an interface. i) The terms frequency, wavelength and **amplitude**. j) All waves obey the wave equation: v = f x k) Radio waves/ Boardworks GCSE Science: Physics The Universe Red **Shift** and the Big Bang Theory The observation of red **shift** is a **key** piece of evidence for the Big Bang theory/

by solving bx – c = 0 and bx – c = 2π The vertical **shift** up is d. 4.5: Sketching Sine and Cosine by **Key** Points Find the **amplitude**, frequency, period, vertical **shift**, and endpoints of a one-cycle interval, and then sketch the graph of each function/simple harmonic motion for a spring whose period is 6 seconds and whose **amplitude** is 4 cm. Chapter 4 Review Trigonometry **Formulas** Definitions Laws and Identities Textbook Site Animated Precalculus Study Guides by Section Practice Quizzes Khan Academy Brightstorm /

to another constant level. Time domain function of a signal: s(t) Specifies the **amplitude** (in volts) of the signal at each instant in time. Analogue & Digital Signals /of a signal will arrive at the receiver at different times, resulting in phase **shifts** between the different frequencies. Delay distortion is particularly critical for digital data Some of/levels are required at least? By Nyquist’s **formula**: C = 2Blog2M We have 8 x 106 = 2 x 106 x log2M M = 16. **KEY** POINTS All of the forms of information can be/

based on the information in digital data. Topics discussed in this section: Aspects of Digital-to-Analog Conversion **Amplitude** **Shift** **Keying** Frequency **Shift** **Keying** Phase **Shift** **Keying** Quadrature **Amplitude** Modulation Figure 5.1 Digital-to-analog conversion Figure 5.2 Types of digital-to-analog conversion Bit /is located at 250 kHz. This means that our carrier frequency can be at fc = 250 kHz. We can use the **formula** for bandwidth to find the bit rate (with d = 1 and r = 1). Example 5.4 In data communications, we/

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