lecture 13
通信原理Lecture 13 Bandpass Modulation and Demodulation_1
Lecture 13Bandpass Modulation and DemodulationDr. Xin Zhang School of Electronics and Information EngineeringSouth China University of TechnologyReviews of Lecture 12Eye patternTransversal equalizerZero-forcingMSEModulation motivationDigital bandpass modulation Coherent modulationNoncoherent modulatione.g. A Zero-Forcing Three-Tap EqualizerConsider that the tap weights of an equalizing transversal filter are to be determined by transmitting a single impulse asa training signal. Let the equalizer circuit in Figure 3.26 bemade up of just three taps. Given a received distorted set of pulse samples {x(k)}, with voltage values 0.0, 0.2, 0.9, -0.3, 0.1, as shown in Figure 3.25, use a zero-forcing solution to find the weights {c-1, c0, c1} that reduce the ISI so that the equalized pulse samples {z(k)} have the values, {z(-1) = 0, z(0) = 1, z(1) = 0}. Using these weights, calculate the ISI values of theequalized pulse at the sample times k = ±2, ±3.What is the largest magnitude sample contributing to ISI, and what is the sum of all the ISI magnitudes?SolutionFor the channel impulse response specifiedz=x ce.g. A Zero-Forcing Three-Tap Equalizer (2)orSolving these three simultaneous equations results in the following weights:The values of the equalized pulse samples {z(k)} corresponding to sample times k =-3, -2, -1, 0, 1, 2, 3 are computed by using the preceding weights in Equation (3.89a),yielding0.0000 -0.0428 0.0000 1.0000 0.0000 0.1171 0.0345Introduction•4.2.1 Phasor Representation of a SinusoidPhasor representation of a sinusoid.•4.2.1 Phasor Representation of a Sinusoid (2)First, within this compact from, , is contained the two important quadrature components of any sinusoidal carrier wave, namely the inphase (real) and thequadrature (imaginary) components that are orthogonal to each other.Second, the unmodulated carrier wave is conveniently represented in a polar coordinate system as a unit vector or phasor rotating counterclockwise at the constant rate of radians/s.Third, when it comes time to modulate the carrier wave with information, we can view this modulation as amethodical perturbation of the rotating phasor.Figure 4.3 Amplitude modulation.•4.2.1 Phasor Representation of a Sinusoid (3)Figure Narrowband frequency modulation.•4.2.1 Phasor Representation of a Sinusoid (4)•4.2.2 Phase Shift KeyingThe general analytic expression for PSK is shown above.Phase shift keying (PSK) was developed during the early days of the deep-space program; PSK is now widely used in both military and commercial communicationssystems.•4.2.3 Frequency Shift KeyingAt the symbol transitions, the figure depicts a gentle shift from one frequency (tone) to another. This behavior is only true for a special class of FSK called continuous-phase FSK (CPFSK)•4.2.4 Amplitude Shift KeyingBinary ASK signaling (also called on–off keying) was one of the earliest forms of digital modulation used in radio telegraphy at the beginning of this century.•4.2.5 Amplutude Phase KeyingWhen the set of M symbols in the two-dimensional signal space are arranged in a rectangular constellation, thesignaling is referred to as quadrature amplitudemodulation(QAM).•4.2.6 Waveform Amplitude CoefficientThe waveform amplitude coefficient appearing in Equations (4.7) to (4.10) has the same general form for all modulation formats.Since the energy of a received signal is the key parameter in determining the error performance of the detectionprocess, it is often more convenient to use the amplitude notation in Equation above because it facilitates solving directly for the probability of error P E as a function of signal energy.4.3 DETECTION OF SIGNALS IN GAUSSIAN NOISE Equivalence theorem: Performing bandpass linear signal processing, followed by heterodyning the signal tobaseband yields the same results as heterodyning thebandpass signal to baseband, followed by baseband linear signal processing.The term “heterodyning” refers to a frequency conversion or mixing process that yields a spectral shift in the signal.As a result of this equivalence theorem, all linear signal-processing simulations can take place at baseband , withthe same results as at bandpass.•4.3.1 Decision RegionsM = 2AWGNd(r, s i) = ||r –s i|| The detector’s task after receiving r is to decide which of the signals (s1or s2,) was actually transmitted. The method is usually to decide on the signal classification that yields the minimum expected P E.•4.3.2 Correlation ReceiverThe received signal is the sum of the transmitted prototype signal plus the random noise:Detection process:1. the received waveform, r(t), is reduced to a singlerandom variable z(T), or to a set of random variables z i(T) (i= 1, . . . , M), formed at the output of the demodulator and sampler at time t = T, where T is the symbolduration.2.a symbol decision is made on the basis of comparingz(T) to a threshold or on the basis of choosing themaximum z i(T).•4.3.2 Correlation Receiver (2)Step 1 can be thought of as transforming the waveform into a point in the decision space. This point can bereferred to as the predetection point, the most criticalreference point in the receiver. Step 2 can be thought of as determining in which decision region the point islocated.For the detector to be optimized (in the sense of minimizing the error probability), it is necessary tooptimize the waveform-to-random-variabletransformation, by using matched filters or correlators in step 1, and by also optimizing the decision criterion instep 2.•4.3.2 Correlation Receiver (3)The verb “to correlate” means “to match.” The correlators attempt to match the incoming receivedsignal, r(t), with each of the candidate prototypewaveforms, s i(t), known a priori to the receiver. Areasonable decision rule is to choose the waveform, s i(t), that matches best or has the largest correlation with r(t).In other words, the decision rule isChoose the s i(t )whose index corresponds to the max z i(T)•4.3.2 Correlation Receiver (4)Figure Correlator receiver with reference signals {s(t)}.iFigure Correlator receiver with reference signals {}.•4.3.2 Correlation Receiver (5)•4.3.2 Correlation Receiver (6)In the case of binary detection, the correlation receiver can be configured as a single matched filter or product integrator with the reference signal being the difference between the binary prototype signals, s1(t)-s2(t). Theoutput of the correlator, z(T), is fed directly to thedecision stage.•4.3.2 Correlation Receiver (7)For binary detection, the correlation receiver can also be drawn as two matched filters or product integrators, one of which is matched to s2(t), and the other is matched to s2(t). In the decision stage ,the correlator outputs z i(T) (i = 1, 2) can be differenced to form Z(T) =z1(T) -z2(T).•Binary Decision ThresholdConditional probability density functions: p(z/s1), p(z/s2).The abscissa z (T ) represents the full range of possible sample output values from the correlation receiver shown in Figure above.With regard to optimizing the binary decision threshold for deciding in which region a received signal is located, we found in Section 3.2.1 that the minimum errorcriterionfor equally likely binary signals corrupted by Gaussian noise can be stated as•Binary Decision Threshold (2)4.4 COHERENT DETECTIONConsider the following binary PSK (BPSK) example:Let •4.4.1 Coherent Detection of PSKAssume that s1(t) was transmitted. Then the expectedvalues of the product integrators in Figure above, with reference signal ,are found as•4.4.1 Coherent Detection of PSK (2)where E{} denotes the ensemble average, referred to as the expected value .The decision stage must decide which signal wastransmitted by determining its location within the signalspace.•4.4.1 Coherent Detection of PSK (3)•4.4.2 Sampled Matched FilterThe impulse response of the matched filter is a delayed version of the mirror image (rotated on the t = 0 axis) of the input signal waveform. Therefore, if the signalwaveform is s(t), its mirror image is s(-t), and the mirror image delayed by T seconds is s(T -t).The impulseresponse h(t) of a filter matched to s(t) is then described by•4.4.2 Sampled Matched Filter (2)Figure above shows how an MF can be implemented using digital hardware.•4.4.2 Sampled Matched Filter (3)Sampledmatchedfilterdetectionexample,neglectingnoise.•4.4.2 Sampled Matched Filter (4)Note that a correlator only computes an output once per symbol time, such as the value of the peak signal at time T.If there are timing errors in the correlator, then the sampled output fed to the detector may be badlydegraded.。
Lecture-13 GPS单点定位
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GPS原理及其应用
第十三讲 单点定位
张小红 武汉大学测绘学院
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GPS单点定位的几何原理
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GPS单点定位的几何原理
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lecture13
2) Immediate Constituent Analysis----an approach adopted by structural ling to the analysis of sentence structure.Traditionally sens---individual words in a linear direction.Structural view---not only…but also composed of hierarchies of construction.Ole men and women were killedOld men and old women / old men and womenJohn saw Mary on the bus…..when she was on the bus----when they were on the busIn IC analysis a sentence is cut into two(or more) segments. This kind of pure segmentation is simply dividing a sentence into its constituent elements without even knowing what they really are . What remain of the first cut are called "immediate constituents", and what are left at the final cut are called "ultimate constituents". For example, "The man left yesterday" can be thus segmented: "the | | man| left | | yesterday". We get two immediate constituents for the first cut (|), and they are "The man" and "left yesterday". Further split(||) this sentence generates three "ultimate constituents": "The", “man”,"left " and "yesterday".immediate constituent----the two parts that are produced after each division. It can be further devided until smallest gram unit is observed.ultimate constituent----the smallest gram unit obtained through division.Advantages of IC:a)It avoids some weakpoints of traditional approach to syntaxMy sister lives next door.He is afraid of darkness.The film is worth seeing.b)It helps to account for the ambiguity of certain constructionsChinese fur coatDisadvantages:a)Some strings of ling forms cannot readily becut into two parts.He look the word up in the dictionary.Is he coming tonight?b)It cannot indicate the ambiguity of some constructionsFlying planes can be dangerous.The man was good to leave.c)It cannot account for the difference between the sens which are similar in structure.John is easy to teach.John is eager to teach.3）Deep StructureEvery sen has two levels of structures. One is obvious on the surface and the other is deep and abstract. Chomsky called them surface stru and deep stru respectively.SS----the syntactic stru of the sen as it is pronounced or written.DS----all the units and relationships that are necessary for interpreting the meaning of the sen. It is much more abstruct and is considered to be in the speaker’s mind.e.g. The newspaper was not delivered today-------SS(Negative) Someone (Past tense) deliver newspaper today (Passive)---DSAccording to Chomsky, the SS comes from the DS through transformationsTransformations----the syntactic rules, which convert the abstract/deep stru into the actual/surface stru.Be quiet---Y ou will be quietT-imperativeThe significance:1)paraphrase----the ling phenomenon that two or more sens have the same meaning.a) It snowed yesterdayb) Y esterday it snowed.DS--- it (past tense) snow yesterdaySen a)-----T-tense Sen b) ---- T-tense; T-adverb prepossing2)ambiguity----the ling phenomenon that a single sen has more than one meaning.John is too far away to see.DS1---- John is too far away Anyone see JohnDS2----John is too far away John see anyone3)similar structures with different meaningsa) John promised Mary to come.b) John persuaded Mary to come.The above two sens are very similar in structure but their meanings are different. That is, their DS are different:DS of sen a)----John (past tense) promise Mary John comeDS of sen b)----John (past tense) persade Mary Mary come4. Syntax beyond the sens----the investigation of the syntactic relation between sens in a paragraph or text.1）我们不知道李峰住的房间，问了问护士才找到了。
地球物理流体力学课件：Lecture 13 Rossby Wave and Topographic
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Ending 文章结尾形式
2-1 concise conclusion 结论性--------- 通过对文 章前面的讨论 ,引出或重申文章的中心思想及观 点. [1]. From what has been discussed above, we may safely draw the conclusion that .....
[3]. The great challenge today is ...... There is much difficulty , but ........
2--6 significance 意义性的结尾方式 --------> 文章结尾的时候,从更高的更 新的角度指出所讨论的问题的重要 性以及其深远的意义!
50. 所以¸ 我们应该了解…。 Therefore, we should realize (that)子句 例︰所以¸ 我们应该了解学英文不能没有字典。 Therefore, we should realize that in learning English we cannot do without a dictionary. 51. 因此¸ 由上列的讨论我们可以明了…。 We, therefore, can make clear from the above discussion (that)子句 例︰因此¸ 由上列的讨论我们可以明了毅力可以克服任何 困难。 We, therefore, can make clear from the above discussion that perseverance can overcome any difficulty. 52. 1. 从～观点来看¸…。 From the ～ point of view, …. 2. 根据～的看法¸…。 According to ～ point of view, …. 例︰从政治的观点来看¸ 这是一个很复杂的问题。 From the political point
lecture 13-14 中式英语
will always think as a Chinese and speak Chinglish.
When you learn your mother tongue, you also
acquire the „mental set‟ that goes with it.
中式英语抑或中国英语： ① 欢迎你到... ② welcome you to ... ③ welcome to ... ① 永远记住你 ② remember you forever ③ always remember you
（没有人能活到forever） ① 给你 ② give you ③ here you are ① 很喜欢... ② very like ... ③ like ... very much ① 黄头发 ② yellow hair ③ blond/blonde（西方人没有yellow hair的说 法） ① 厕所 ② WC ③ men's room/women's room/restroom ① 入口 ② way in ③ entrance ① 出口 ② way out ③ exit（way out在口语中是crazy的意思） ① 马马虎虎 ② so-so ③ average/fair/all right/not too bad/OK（西方 人很少使用so-so） ① 有名 ② famous ③ well-known/renowned/legendary/popular （famous在中国被滥用） ① 玩 ② play ③ go to/do（play在中国被滥用） ① 农民 ② peasant ③ farmer 第一部分是汉语说法，第二部分是Chinglish说法，第三部分则是英语的 标准说法。
Lecture-13-FundamentalMatrix
Fundamental Matrix
• • • • Longuet Higgins (1981) Hartley (1992) Faugeras (1992) Zhang (1995)
Fundamental Matrix
Preliminaries
• • • • • • Linear Independence Rank of a Matrix Matrix Norm Singular Value Decomposition Vector Cross product to Matrix Multiplication RANSAC
Copyright Mubarak Shah 2003
Example (Row Echelon)
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Alper Yilmaz, Mubarak Shah, Fall 2011 UCF
Line Fitting
Epipolar Geometry
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重要课件 Lecture-13
LECTURE 13LEARNING OUTCOMESBy the end of this lecture, students will be able to:∙Understand what is meant by Perfect Bayesian Equilibrium (PBE)∙Understand how a PBE relates to the other equilibrium concepts studied so far∙Understand how to find a PBEINTRODUCTIONSo far we have studied three equilibrium concepts:-Nash equilibrium in static games of complete information.-SPNE in dynamic games of complete information.-Bayesian Nash Equilibrium in static games of incomplete information.In this lecture, we will introduce a new equilibrium concept:-Perfect Bayesian Equilibrium (PBE) in dynamic games of incomplete information.Why do we require a “new” equilibrium concept for each class of games?The equilibrium concepts above are closely related – they are not new per se. We also need to strengthen our equilibrium concept, as we consider progressively richer games. For example, a SPNE eliminates Nash equilibria that involve non-credible threats. Similarly, a Perfect Bayesian Equilibrium can be thought of as a refinement of a Bayesian Nash EquilibriumAlso, a Perfect Bayesian Equilibrium strengthens the requirements of SPNE (see example below) by considering explicitly the players’ beliefs. (Recall that beliefs are important in the context of games characterized by incomplete information.)MOTIVATION FOR THE USE OF A PBEConsider the following dynamic game (characterized by complete but imperfect information).2,1Normal form Representation:2L’R’1 LM RIt is easy to see that, in the normal form game above, there are 2 (pure strategy) Nash equilibria: (L, L’) and(R, R’).Are these Nash equilibria subgame-perfect?The answer is yes. The reason is that the only subgame is the entire game. (Recall that a SPNE is a Nash equilibrium in every subgame.)However, there is a problem with the equilibrium (R, R’), as it involves a non-credible threat: For player 2, L’ dominates R’ (so player 2 would not play R’).Thus, we need to strengthen our equilibrium concept to eliminate the SPNE (R, R’). This is the reason why we need to consider a PBE – not just a SPNE.REFINING OUR EQUILIBRIUM PREDICTIONSA PBE imposes 3 requirements on our equilibrium predictions, 2 of which a presented below:Requirement 1 (“Beliefs”)At each information set, the player with the move must have a belief about which node in the information set has been reached.∙Non-singleton information set: belief = probability distribution.∙Singleton information set: probability 1 is assigned to the single decision node.Based on our example above, requirement 1 is represented by the probabilities p and l-p(see Figure).Requirement 2 (“Sequential Rationality”)Players act optimally given their beliefs and the other players’ strategy.Based on our example aboveThus, Requirement 2 pre vents player 2 from choosing R’ becauseIn consequence, requiring that each player has a belief and acts optimally given this belief suffices to eliminate (R, R’).That is, player 2 won't play R’, so player 1 won’t be induced to play R. Thus, we are left with (L, L’) as our unique SPNE outcome.ANOTHER EXAMPLE TO ILLUSTRATE “SEQUENTIAL RATIONALITY”3, 01∙ Suppose that player 2 assigns probability 2/3 to history C ∙ Suppose that player 2 assigns probability 1/3 to history DSequential rationality requires that player 2’s strategy be optimal, given the subsequent behavior specified by player 1's strategy: i.e.Thus, Sequential Rationality requires that player 2 chooses G.Sequential rationality also requires that player 1’s strategy is optimal at her two information sets, given player 2’s strategy: i.e. ∙ after history (C, F) J optimal∙ at the beginning of the gameD, E optimal, given GThus, there are 2 optimal strategies for player 1: DJ, EJ; given G. (Recall that a strategy is complete plan of action, specifying what the player is going to do at each decision node she may be called upon to decide –so we need to specify an action at each of player 1’s decision nodes.)REQUIREMENT 3Requirement 3 says: Each player’s belief is consistent with the equilibrium strategy profile (“consistency of beliefs with equilibrium strategies”).Based on our initial example, requirement 3 simply says that, in the SPNE (L, L’), player 2's belief is p=1.This completes our analysis of the 3 requirements related to a PBE.CALCULATING BELIEFS – A GENERAL APPROACHExample: Entry GameConsider the following entry game:Suppose that the Challenger attaches probability P R, P U and P O to “Ready”, “Unready” and “Out”, respectively. The Incumbent’s probabilities that “Ready” and “Unready” will occur are p and 1-p, respectively.We have the following possibilities:∙ If , then Requirement 3 does not restrict the Incumbent’s belief.∙ If , then Requirement 3 says that the Incumbent assigns probabilityto “Ready” and probabilityto “Unready”.Both of the last 2 probabilities are consistent with Bayes’ rule.Thus we have arrived at the following definition of a PBE:EXAMPLEConsider the game tree below. Find the PBE.subgameThe subgame identified above can be translated into the following normal form game:L’R’LMIt is easy to see that this game has a unique Nash equilibrium: (L, R’).Using backward induction, we can now identify the optimal action of player 1, given (L, R’). Thus, it is optimal for player 1 to choose D. In consequence, there is a unique SPNE in this game: (D, L, R’).What is the PBE of the game?Requirement 1: Implies beliefs p and 1-p for player 3.Requirement 2: It is fulfilled because the strategies (D, L, R’) have been chosen optimally.Requirement 3: It is fulfilled because p=1 for player 3 is consistent with L chosen by player 2.Thus we can state that: According to the definition of a PBE, the strategies (D, L, R’) and belief p=1 for player 3 satisfy requirements 1-3 – and therefore constitute a PBE.SUMMARYIn this lecture, we saw that all equilibrium concepts studied so far are closely related. We noted that, as we progressively consider richer game, we need to strengthen our equilibrium concept. For example, a Perfect Bayesian Equilibrium can be thought of as a refinement of a Bayesian Nash Equilibrium in the sense that it considers explicitly the players’ beliefs.We examined 3 requirements implied by a Perfect Bayesian Equilibrium: in brief, (i) beliefs, (ii) sequential rationality and (iii) consistency of beliefs with equilibrium strategies. We defined a PBE as strategies and beliefs satisfying requirements 1-3. Through a series of examples, we studied how the 3 requirements can be applied so as to obtain a PBE.。
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Step 4: The offering
• The underwriter buys the shares from the company at a fixed price and immediately sells it to investors at the IPO price • “Green Shoe” option: • Clause in the underwriter agreement specifying that in case of exceptional public demand the issuer will authorize additional shares for distribution by the underwriter at the offering price (usual is overallotment option of 15%)
Evidence - Formal theories of IPO difficult to test. We observe only the firms that go public. There is no “control” group. - Pagano, Panetta, and Zingales (1998) with a unique data set of Italian firms find that larger companies and with high MB ratio are more likely to go public. They also find, IPOs reduce cost of credit. IPO follows high investment and growth (not viceversa). - Lerner (1994) studies U.S. biotech IPOs. MB ratio has a significant effect on IPO decisions. - Baker and Wurgler (2000) find that when investors are optimistic (higher previous returns), IPOs happen. - Lowry (2002) finds that investor sentiment (measured by the discount on closed-end funds), growth opportunities, and adverse selection considerations all are determinants of aggregate IPO volume.
Direct and Indirect Costs of IPOs
Step 1: Selecting an underwriter
• Criteria: – Reputation of the analyst covering the firm – Performance of past IPOs – Not a criteria: fees! (7% of capital raised) • Hi-Tech IPOs are often underwritten by a consortium – Technology specialist plus large underwriter, “bulge bracket”
Step 2: Tasks of the underwriter
• • • • Due Diligence Determine the offering size Prepare the marketing material Prepare regulatory filings (S-1) together with the legal representation of the firm
Valuation theories • Holmstrom and Tirole (1993) and Bolton and Von Thadden (1998): public companies subject themselves to monitoring by outsiders (for example , investment banks, auditors, analysts, investors, SEC), activities which might enhance the value of the firm. • Amihud and Mendelson (1988): IPOs make firm shares more liquid, which also increases firm value. • Firms can learn from the information contained in stock prices. – “Information spillovers” to managers/investors. High prices may signal increased growth opportunities. Subramanyam and Titman (1999), Schultz (2000). • Signals stability and dependability to customers and suppliers – Maksimovic and Pichler (2001): a high public price can attract product market competition.
Costs of going public
• IPO creates substantial fees – Legal, accounting, investment banking fees are often 10% of funds raised in the offering • Greater degree of disclosure and scrutiny • First day under-pricing (usual result) • Market cycles in IPOs valuations
Estimation Technique - Event studies + regression of CARs on firm characteristics: CARi,t = f(Xi,t + FF factorsi,t) + εi,t, where f(.) is usually a linear function, and Xi,t are firm characteristics. - The usual issues apply: - CAR or BAR? - Endogeneity. - Misspecification (functional form, omitted variables) - Measurement error.
Lecture 13
IPOs
Why do firms go public?
Life cycle theories • It is easier for a potential acquiror to spot a potential takeover target when it is public. Zingales (1995). • Entrepreneurs regain control from venture capitalists (VC) at IPO. Black and Gilson (1998). A different angle in Chemmanur and Fulghieri (1999). – Pre-IPO “angel” investors or VC hold undiversified portfolios. – Since it is expensive to go public and proprietary data may be revealed, early on a firm will be private. – Then, diversified investors, who value more the firm than the undiverisified owners, take control of firm. (Leland and Lyle (1977).
Market-Timing Theories • Firms issue equity when it is “convenient” –when equity is overvalued. – Bayless and Chaplinsky (1996): When cost of equity is low, firms have a “window of opportunity.” – Choe, Masulis, and Nanda (1993): During good economic times, firms projects have high expected CFs. Asymmetry of information is reduced. Thus, firms avoid issuing in periods where few other good-quality firms issue. (A signaling story).
Step 5: Aftermarket activities
• Short covering: • Underwriter shorts the stock prior to the IPO. If the share price rises after the IPO, underwriter uses over-allotment option to cover the short, if the price falls it buys stocks in the market • “Pure” stabilization bids • Underwriter posts bid in the open market not exceeding the offer price. • Penalty bids. • Revoke selling concession if shares are “flipped.”