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Telemetry Assignment

Apr 04, 2018



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    EI- H


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    A ( modulator-demodulator ) is a device thatmodulates an analog carrier signal to encode digitalinformation , and also demodulates such a carriersignal to decode the transmitted information. Thegoal is to produce a signal that can be transmittedeasily and decoded to reproduce the original digitaldata. Modems can be used over any means oftransmitting analog signals, from light emittingdiodes to radio . The most familiar example is a

    voice modem that turns the digital data ofa personal computer into modulated electricalsignals in the voice frequency range of a telephonechannel. These signals can be transmittedover telephone lines and demodulated by anothermodem at the receiver side to recover the digitaldata.

    Modems are generally classified by the amount ofdata they can send in a given unit of time , usuallyexpressed in bits per second (bit/s, or bps), orbytes (B/s). Modems can alternatively be classifiedby their symbol rate , measured in baud .The baud unit denotes symbols per second, or thenumber of times per second the modem sends a newsignal. For example, the ITU V.21 standardused audio frequency shift keying , that is to say,tones of different frequencies, with two possiblefrequencies corresponding to two distinct symbols
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    (or one bit per symbol), to carry 300 bits persecond using 300 baud. By contrast, the original ITUV.22 standard, which was able to transmit andreceive four distinct symbols (two bits per symbol),handled 1,200 bit/s by sending 600 symbols persecond (600 baud) using phase shift keying .

    ( ) is both an

    analog and a digital modulation scheme. It conveystwo analog message signals, or two digital bitstreams , by changing ( modulating ) the amplitudes oftwo carrier waves , using the amplitude-shiftkeying (ASK) digital modulation scheme or amplitudemodulation (AM) analog modulation scheme. The twocarrier waves, usually sinusoids , are out ofphase with each other by 90 and are thus calledquadrature carriers or quadrature components hence the name of the scheme. The modulated wavesare summed, and the resulting waveform is acombination of both phase-shift keying (PSK)and amplitude-shift keying (ASK), or (in the analog

    case) of phase modulation (PM) and amplitudemodulation. In the digital QAM case, a finite numberof at least two phases and at least two amplitudesare used. PSK modulators are often designed usingthe QAM principle, but are not considered as QAMsince the amplitude of the modulated carrier signal
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    is constant. QAM is used extensively as a modulationscheme for digital telecommunication systems.Arbitrarily high spectral efficiencies can beachieved with QAM by setting a suitableconstellation size, limited only by the noise leveland linearity of the communications channel. [1]

    QAM modulation is being used in optical fibersystems as bit rates increase; QAM16 and QAM64 canbe optically emulated with a 3-path interferometer .

    When you make a dialup connection, there are (at

    least) three separate components to the connection.Assuming you are dialing up from a PC, there is theconnection between your PC and your (originating)modem, the connection between the two modems, andthe connection between the "other" (answering) modemand whatever device it is attached to. Each of partof the connection can be running at a differentspeed:

    1.LOCAL INTERFACE SPEED: The speed used on theconnection between your PC (or terminal orworkstation) and your modem.
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    2.CONNECTION SPEED: The speed of the connectionbetween the two modems, based on the modulationtechnique that they negotiate with each other.

    3.REMOTE INTERFACE SPEED: The speed of theconnection between the remote (answering) modemand the terminal server.

    When originating a call, some modems change theirinterface speed to match the negotiated connectionspeed automatically. When that happens, your

    communications software must also change its speedat the same time. For example, if you dial at 9600bps, but the remote modem answers at 1200 bps, yourmodem will print a message like:

    CONNECT 1200which your communication software takes as a signalto change its interface speed to 1200 bps beforeattempting to go "online" with the remote computeror service.

    Most modern modems can be configured to fix theirinterface speed at a given value, rather than changeit according to the connection speed. This is

    desirable when using data compression. In this case,the CONNECTION SPEED (or MODULATION SPEED) betweenthe two modems is different from the INTERFACE SPEEDbetween the modem and the computer. The modemperforms the speed conversion between its telephoneside and its data side, and your communications

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    software must be configured to IGNORE the speedgiven in the CONNECT message.

    After the modems have agreed on a modulationtechnique, they might also try to negotiate anerror-detection and -correction method:MNP Level 1, 2, 3, or 4ITU-T V.42 = LAPM

    Telebit PEP (proprietary)US Robotics HST (proprietary)

    When modems' initial error-control methods do notagree, automatic fallback is usually as follows:

    V.42 ->. MNP 4 ->. MNP 3 ->. MNP 2 ->. MNP 1 ->.noneWhen PEP, HST, or other proprietary methods areinvolved, special configuration settings are neededon the modems to specify the fallback sequence.

    Please note that no connection can ever be free oferrors. The error correction technique used betweenthe modems might be extremely effective, but it isnot foolproof. More to the point, the connectionsbetween the modems and the computers are not error-corrected, nor or the data paths within thecomputers. Thus it is still quite common toexperience data loss or corruption, even on an

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    error-corrected modem connection. Common causesinclude: buffer overflows (often due to a lack ofadequate flow control between the modem and thecomputer -- see below), interrupt conflicts, looseconnectors, and malfunctioning devices.

    They do NOT perform errorcorrection themselves, but rely on external softwareto do it. Most software does not. These modems areNOT SUPPORTED at Columbia University.

    Modems may incorporate data compression methods toincrease the effective throughput of your databeyond the actual connection speed. Compression ispossible only if (a) error correction is also beingdone, and (b) the interface speed between thecomputer and the modem is higher than the connectionspeed between the two modems.MNP Level 3

    108% efficiency by removing start & stop bits(synchronous)

    MNP Level 4120% efficiency by optimizing modem-to-modem

    protocolMNP Level 5True compression on top of Level 4, efficiencydepends on data

    V.42bisTrue compression, efficiency depends on data

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    Telebit PEPProprietary, characteristics unknown

    US Robotics HSTProprietary, characteristics unknown

    Effectiveness of MNP 5 and V.42bis compression varybetween 0% and 400% or higher, depending on thenature of the data. Compression fallback:

    V.42bis ->. MNP 5 ->. NoneWhen PEP or HST is involved, special configurationsettings are needed on the modem to specify how

    these fit into the fallback sequence. Again, bewareof RPI modems. They do not do compressionthemselves, but rely on external software to do it.

    "Flow control" is the method by which one device cancontrol the rate at which another device sends datato it. There are various methods of flow control.The two most commonly used in dialup datacommunication are:

    (Request To Send / Clear To Send)

    "hardware" flow control is the most effectivemethod. It uses special wires in the cable (or,in the case of an internal modem, specialsignals on the edge-connector), separate fromthe data wires, to control the flow of data. It

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    is used between two devices that are immediatelyconnected, such as a computer and a modem.

    "software" flow control is lesseffective and more risky because it mixes flowcontrol characters (Control-S and Control-Q)with the data. These characters are subject todelay, loss, and corruption, and also causetransparency problems with host applicationslike EMACS. Software flow control should be usedonly if hardware flow control is unavailable.

    When using error correction or compression, ormodems that are capable of retraining, it isessential to enable an effective form of flowcontrol between each modem and the computer (orterminal, or other device) it is immediatelyconnected to. Without effective flow control, datawill be lost when one device sends data faster than

    the other one can receive it.

    Flow control between the two modems is handled bythe underlying error modem-to-modem correctionprotocol: MNP or V.42. If there is no underlyingerror-correction protocol, then there can be no flowcontrol between the modems and therefore no

    protection against data loss EVEN IF there is flowcontrol between the modem and the computer. Thisapplies, in particular, to RPI modems.

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    Main article: space-division multiplexing In wired communication, space-division multiplexingsimply implies different point-to-point wires fordifferent channels. Examples include an analoguestereo audio cable, with one pair of wires for theleft channel and another for the right channel, and

    a multipart

    telephone cable . Another example is aswitched star network such as the analog telephoneaccess network (although inside the telephoneexchange or between the exchanges, othermultiplexing techniques are typically employed) or aswitched Ethernet network. A third example is a meshnetwork . Wired space-division multiplexing is

    typically not considered as multiplexing.In wireless communication, space-divisionmultiplexing is achieved by multiple antennaelements forming a phased array antenna . Examplesare multiple-input and multiple-output (MIMO),
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    single-input and multiple-output (SIMO) andmultiple-input and single-output (MISO)multiplexing. For example, a IEEE 802.11n wirelessrouter with N antennas makes it possible tocommunicate with M ultiplexed channels, each with apeak bit rate of 54 Mbit/s, thus increasing thetotal peak bit rate with a factor N . Differentantennas would give different multi-pathpropagation (echo) signatures, making it possiblefor digital signal processing techniques to separatedifferent signals from each other. These techniques

    may also be utilized for space diversity (improvedrobustness to fading) or beam forming (improvedselectivity) rather than multiplexing.

    [ edit ]

    Main article: Frequency-division multiplexing Frequency-division multiplexing (FDM): The spectrum

    of each input signal is shifted to a distinctfrequency range.

    Frequency-division multiplexing (FDM) is inherentlyan analog technology. FDM achieves the combining ofseveral digital signals into one medium by sendingsignals in several distinct frequency ranges overthat medium.

    One of FDM's most common applications is cabletelevision. Only one cable reaches a customer's homebut the service provider can send multipletelevision channels or signals simultaneously overthat cable to all subscribers. Receivers must tune
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    to the appropriate frequency (channel) to access thedesired signal. [1]

    A variant technology, called wavelength-divisionmultiplexing (WDM) is used in optical

    communications .

    Main article: Time-division multiplexing Time-division multiplexing (TDM).

    Time-division multiplexing (TDM) is a digital (or inrare cases, analog) technology. TDM involves

    sequencing groups of a few bits or bytes from eachindividual input stream, one after the other, and insuch a way that they can be associated with theappropriate receiver. If done sufficiently quickly,the receiving devices will not detect that some ofthe circuit time was used to serve another logicalcommunication path.

    Consider an application requiring four terminals atan airport to reach a central computer. Eachterminal communicated at 2400 bit/s, so rather thanacquire four individual circuits to carry such alow-speed transmission, the airline has installed apair of multiplexers. A pair of 9600 bit/s modems

    and one dedicated analog communications circuit fromthe airport ticket desk back to the airline datacenter are also installed. [1]

    Main article: Polarization-division multiplexing
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    Polarization-division multiplexing usesthe polarization of electromagnetic radiation toseparate orthogonal channels. It is in practical usein both radio and optical communications,particularly in 100 Gbit/s per channel fiber optictransmission systems .

    Main article: Orbital angular momentum multiplexing Orbital angular momentum multiplexing is arelatively new and experimental technique formultiplexing multiple channels of signals carriedusing electromagnetic radiation over a singlepath. [2] It can potentially be used in addition toother physical multiplexing methods to greatlyexpand the transmission capacity of such systems. Asof 2012 it is still in its early research phase,with small-scale laboratory demonstrations of

    bandwidths of up to 2.5 Tbit/s over a single lightpath. [3]

    Main articles: Spread spectrum and Code division multiplexing

    Code division multiplexing (CDM) or spreadspectrum is a class of techniques where severalchannels simultaneously share the same frequencyspectrum, and this spectral bandwidth is much higherthan the bit rate or symbol rate . One form isfrequency hopping, another is direct sequence spread
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    spectrum. In the latter case, each channel transmitsits bits as a coded channel-specific sequence ofpulses called chips. Number of chips per bit, orchips per symbol, is the spreading factor . Thiscoded transmission typically is accomplished bytransmitting a unique time-dependent series of shortpulses, which are placed within chip times withinthe larger bit time. All channels, each with adifferent code, can be transmitted on the same fiberor radio channel or other medium, and asynchronouslydemultiplexed. Advantages over conventional

    techniques are that variable bandwidth is possible(just as in statistical multiplexing ), that the widebandwidth allows poor signal-to-noise ratioaccording to Shannon-Hartley theorem , and thatmulti-path propagation in wireless communication canbe combated by rake receivers .

    Code Division Multiplex techniques are used asan channel access scheme, namely Code DivisionMultiple Access (CDMA), e.g. for mobilephone service and in wireless networks, with theadvantage of spreading intercell interference amongmany users. Confusingly, the generic term Code Division Multiple access sometimes refers to aspecific CDMA based cellular system definedby Qualcomm.

    Another important application of CDMA is the GlobalPositioning System (GPS).
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    In telecommunications , ( ) is a technique by which the

    total bandwidth available in a communicationmedium is divided into a series of non-overlapping frequency sub-bands, each of which isused to carry a separate signal. This allows asingle transmission medium such as a cable oroptical to be shared by many signals. An example ofa system using FDM is cable television , in whichmany television channels are carried simultaneouslyon a single cable. FDM is also used by telephone

    systems to transmit multiple telephone calls throughhigh capacity trunk lines, communicationssatellites to transmit multiple channels of data onuplink and downlink radio beams, and broadband DSLmodems to transmit large amounts of computer datathrough twisted pair telephone lines, among manyother uses.
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    In conventional PCM, the analog signal may beprocessed (e.g., by amplitude compression ) beforebeing digitized. Once the signal is digitized, thePCM signal is usually subjected to furtherprocessing (e.g., digital data compression ).

    PCM with linear quantization is known as LinearPCM (LPCM). [9]

    Some forms of PCM combine signal processing withcoding. Older versions of these systems applied theprocessing in the analog domain as part ofthe analog-to-digital process; newer implementationsdo so in the digital domain. These simple techniqueshave been largely rendered obsolete by moderntransform-based audio compression techniques.

    DPCM encodes the PCM values as differencesbetween the current and the predicted value. Analgorithm predicts the next sample based on theprevious samples, and the encoder stores only thedifference between this prediction and the actualvalue. If the prediction is reasonable, fewerbits can be used to represent the sameinformation. For audio, this type of encodingreduces the number of bits required per sample by

    about 25% compared to PCM. Adaptive DPCM (ADPCM) is a variant of DPCM that

    varies the size of the quantization step, toallow further reduction of the required bandwidthfor a given signal-to-noise ratio .
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    Delta modulation is a form of DPCM which uses onebit per sample.

    In telephony, a standard audio signal for a singlephone call is encoded as 8,000 analog samples per

    second, of 8 bits each, giving a 64 kbit/s digitalsignal known as DS0. The default signalcompression encoding on a DS0 is either -law (mu-law) PCM (North America and Japan) or A-law PCM(Europe and most of the rest of the world). Theseare logarithmic compression systems where a 12 or13-bit linear PCM sample number is mapped into an 8-

    bit value. This system is described by internationalstandard G.711 . An alternative proposal fora floating point representation, with 5-bit mantissaand 3-bit radix, was abandoned.

    Where circuit costs are high and loss of voicequality is acceptable, it sometimes makes sense to

    compress the voice signal even further. An ADPCMalgorithm is used to map a series of 8-bit -law orA-law PCM samples into a series of 4-bit ADPCMsamples. In this way, the capacity of the line isdoubled. The technique is detailed inthe G.726 standard.

    Later it was found that even further compression waspossible and additional standards were published.Some of these international standards describesystems and ideas which are covered by privatelyowned patents and thus use of these standardsrequires payments to the patent holders.
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    Some ADPCM techniques are used in Voice overIP communications.

    PCM can be either return-to-zero (RZ) or non-return-to-zero (NRZ). For a NRZ system to be synchronized

    using in-band information, there must not be longsequences of identical symbols, such as ones orzeroes. For binary PCM systems, the density of 1-symbols is called ones-density . [10]

    Ones-density is often controlled using precodingtechniques such as Run Length Limited encoding,where the PCM code is expanded into a slightlylonger code with a guaranteed bound on ones-densitybefore modulation into the channel. In other cases,extra framing bits are added into the stream whichguarantee at least occasional symbol transitions.

    Another technique used to control ones-density isthe use of a scrambler polynomial on the rawdata which will tend to turn the raw data streaminto a stream that looks pseudo-random , but wherethe raw stream can be recovered exactly by reversingthe effect of the polynomial. In this case, longruns of zeroes or ones are still possible on theoutput, but are considered unlikely enough to be

    within normal engineering tolerance.In other cases, the long term DC value of themodulated signal is important, as building up a DCoffset will tend to bias detector circuits out oftheir operating range. In this case special measuresare taken to keep a count of the cumulative DC
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    offset, and to modify the codes if necessary to makethe DC offset always tend back to zero.

    Many of these codes are bipolar codes , where thepulses can be positive, negative or absent. In the

    typical alternate mark inversion code, non-zeropulses alternate between being positive andnegative. These rules may be violated to generatespecial symbols used for framing or other specialpurposes.

    ( ) is a technique used inelectronic communication, most commonly fortransmitting information via a radio carrier wave .AM works by varying the strength of the transmittedsignal in relation to the information being sent.For example, changes in signal strength may be usedto specify the sounds to be reproduced bya loudspeaker , or the light intensity of televisionpixels. Contrast this with frequency modulation , in

    which the frequency is varied, and phase modulation ,in which the phase is varied.

    In the mid-1870s, a form of amplitude modulation initially called "undulatory currents" was thefirst method to successfully produce quality audio
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    over telephone lines. Beginning with ReginaldFessenden 's audio demonstrations in 1906, it wasalso the original method used for audio radiotransmissions, and remains in use today by manyforms of communication "AM" is often used to referto the mediumwave broadcast band (see AM radio ).

    Modulation methods
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    High-power AM transmitters (such as those usedfor AM broadcasting ) are based on high-efficiencyclass-D and class-E power amplifier stages, modulatedby varying the supply voltage. [4]

    Older designs (for broadcast and amateur radio) alsogenerate AM by controlling the transmitters finalamplifier (generally a class-C, for efficiency)gain. The following types are for vacuum tubetransmitters (but similar options are available withtransistors): [5]

    In plate modulation, the platevoltage of the RF amplifier is modulated with theaudio signal. The audio power requirement is 50percent of the RF-carrier power.

    RFamplifier plate voltage is fed througha choke (high-value inductor). The AMmodulation tube plate is fed through the sameinductor, so the modulator tube diverts currentfrom the RF amplifier. The choke acts as aconstant current source in the audio range. Thissystem has a low power efficiency.

    The operating bias and

    gain of the final RF amplifier can be controlledby varying the voltage of the control grid. Thismethod requires little audio power, but care mustbe taken to reduce distortion.

    The screen-grid bias may be controlled through a clamp
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    tube, which reduces voltage according to themodulation signal. It is difficult to approach100-percent modulation while maintaining lowdistortion with this system.

    In electronics , a ( , also"follow-and-hold" [1] ) circuit is an analogdevice that samples (captures, grabs) the voltage ofa continuously varying analog signal and holds(locks, freezes) its value at a constant level for aspecified minimal period of time. Sample and holdcircuits and related peak detectors are theelementary analog memory devices. They are typically

    used in analog-to-digital converters to eliminatevariations in input signal that can corrupt theconversion process. [2]

    A typical sample and hold circuit stores electriccharge in a capacitor and contains at least onefast FET switch and at least one operational

    amplifier .[1]

    To sample the input signal the switchconnects the capacitor to the output of a bufferamplifier . The buffer amplifier charges ordischarges the capacitor so that the voltage acrossthe capacitor is practically equal, or proportionalto, input voltage. In hold mode the switch
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    disconnects the capacitor from the buffer. Thecapacitor is invariably discharged by itsown leakage currents and useful load currents, whichmakes the circuit inherently volatile , but the lossof voltage ( voltage drop ) within a specified holdtime remains within an acceptable error margin.

    In the context of LCD screens, it is used todescribe when a screen samples the input signal, andthe frame is held there without redrawing it. Thisdoes not allow the eye to refresh and leads toblurring during motion sequences, also thetransition is visible between frames because thebacklight is constantly illuminated, addingto display motion blur

    ( ) is a method usedto digitally represent sampled analog signals . It isthe standard form for digital audio in computers andvarious Blu-ray , DVD and Disc formats, as well as
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    other uses such as digital telephone systems. A PCMstream is a digital representation of an analogsignal, in which the magnitude of the analog signalis sampled regularly at uniform intervals, with eachsample being quantized to the nearest value within arange of digital steps.

    PCM streams have two basic properties that determinetheir fidelity to the original analog signal:the sampling rate , which is the number of times persecond that samples are taken; and the bit depth ,which determines the number of possible digitalvalues that each sample can take.
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    Differential pulse-code modulation (DPCM) is a

    signal encoder that uses the baseline of pulse-codemodulation (PCM) but adds some functionalities basedon the prediction of the samples of the signal. Theinput can be an analog signal or a digital signal .

    If the input is a continuous-time analog signal, itneeds to be sampled first so that a discrete-time

    signal is the input to the DPCM encoder. Option 1: take the values of two consecutive

    samples; if they are analogsamples, quantize them; calculate the differencebetween the first one and the next; the output is
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    the difference, and it can be further entropycoded .

    Option 2: instead of taking a difference relativeto a previous input sample, take the differencerelative to the output of a local model of thedecoder process; in this option, the differencecan be quantized, which allows a good way toincorporate a controlled loss in the encoding.

    Applying one of these two processes, short-termredundancy (positive correlation of nearby values)of the signal is eliminated; compression ratios onthe order of 2 to 4 can be achieved if differencesare subsequently entropy coded, because the entropyof the difference signal is much smaller than thatof the original discrete signal treated asindependent samples.

    DPCM was invented by C. Chapin Cutler at Bell

    Labs in 1950; his patent includes both methods.
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    (DM or -modulation)is an analog-to- digital and digital-to- analog signal conversiontechnique used for transmission of voice informationwhere quality is not of primary importance. DM isthe simplest form of differential pulse-codemodulation (DPCM) where the difference betweensuccessive samples are encoded into n-bit datastreams. In delta modulation, the transmitted datais reduced to a 1-bit data stream. Its main featuresare:

    the analog signal is approximated with a seriesof segments

    each segment of the approximated signal iscompared to the original analog wave to determinethe increase or decrease in relative amplitude

    the decision process for establishing the stateof successive bits is determined by thiscomparison

    only the change of information is sent, that is,only an increase or decrease of the signalamplitude from the previous sample is sentwhereas a no-change condition causes the
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    modulated signal to remain at the same 0 or 1state of the previous sample.

    To achieve high signal-to-noise ratio , deltamodulation must use oversampling techniques, that

    is, the analog signal is sampled at a rate severaltimes higher than the Nyquist rate .

    Derived forms of delta modulation are continuouslyvariable slope delta modulation , delta-sigmamodulation , and differential modulation . Differentialpulse-code modulation is the super set of DM.
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    A band-pass filter is a device thatpasses frequencies within a certain range andrejects ( attenuates ) frequencies outside that range.

    Optical band-pass filters are of common usage.

    An example of an analogue electronic band-

    pass filter is an RLC circuit (a resistor inductor capacitor circuit ). These filters can alsobe created by combining a low-pass filter witha high-pass filter . [1]

    Bandpass is an adjective that describes a type offilter or filtering process; it is frequently

    confused with passband , which refers to the actualportion of affected spectrum. Hence, one might say"A dual bandpass filter has two passbands."A bandpass signal is a signal containing a band offrequencies away from zero frequency, such as asignal that comes out of a bandpass filter. [2]

    An ideal bandpass filter would have a completelyflat passband (e.g. with no gain/attenuationthroughout) and would completely attenuate allfrequencies outside the passband. Additionally, thetransition out of the passband would beinstantaneous in frequency. In practice, no bandpass
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    filter is ideal. The filter does not attenuate allfrequencies outside the desired frequency rangecompletely; in particular, there is a region justoutside the intended passband where frequencies areattenuated, but not rejected. This is known as thefilter roll-off , and it is usually expressedin dB of attenuation per octave or decade offrequency. Generally, the design of a filter seeksto make the roll-off as narrow as possible, thusallowing the filter to perform as close as possibleto its intended design. Often, this is achieved at

    the expense of pass-band or stop-band ripple .The bandwidth of the filter is simply the differencebetween the upper and lower cutoff frequencies . Theshape factor is the ratio of bandwidths measuredusing two different attenuation values to determinethe cutoff frequency, e.g., a shape factor of 2:1 at

    30/3 dB means the bandwidth measured betweenfrequencies at 30 dB attenuation is twice thatmeasured between frequencies at 3 dB attenuation.

    Outside of electronics and signal processing, oneexample of the use of band-pass filters is inthe atmospheric sciences . It is common to band-passfilter recent meteorological data witha period range of, for example, 3 to 10 days, sothat only cyclones remain as fluctuations in thedata fields.

    In neuroscience , visual cortical simple cells werefirst shown by David Hubel and Torsten Wiesel to
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    have response properties that resemble Gaborfilters , which are band-pass.
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    In electronics , a isan electronic circuit that generates anoutput signal whose output frequency is

    a harmonic (multiple) of its input frequency.Frequency multipliers consist of a nonlinear circuitthat distorts the input signal and consequentlygenerates harmonics of the input signal. Asubsequent bandpass filter selects the desiredharmonic frequency and removes the unwantedfundamental and other harmonics from the output.

    Frequency multipliers are often used in frequencysynthesizers and communications circuits. It can bemore economical to develop a lower frequency signalwith lower power and less expensive devices, andthen use a frequency multiplier chain to generate an
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    output frequency in the microwave or millimeterwave range. Some modulation schemes, suchas frequency modulation , survive the nonlineardistortion without ill effect (but schemes suchas amplitude modulation do not).

    Frequency multiplication is also used in nonlinearoptics . The nonlinear distortion in crystals can beused to generate harmonics of laser light.

    A pure sinewave at frequency f has no harmonics. Ifit goes through a linear amplifier, the resultcontinues to be pure (but may acquire a phaseshift).

    If the sinewave is run through a stateless nonlinearcircuit (transcribing function), the resultingdistortion creates harmonics. The distorted signalcan be described by a Fourier series in f .

    The nonzero c k represent the generated harmonics.The Fourier coefficients are given by integratingover the fundamental period T :

    These harmonics can be selected by a bandpassfilter.

    The power in the distorted signal is spreadacross all the resulting harmonics. [1] An idealhalfwave rectifier, for example, has all
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    nonzero coefficients. An approximate circuitcould use a diode.

    From a conversion efficiency standpoint, thenonlinear circuit should maximize the

    coefficient for the desired harmonic andminimize the others. Consequently, thetranscribing function is often speciallychosen. Easy choices are to use an evenfunction to generate even harmonics or an oddfunction to for odd harmonics. See Even and oddfunctions#Harmonics . A full wave rectifier, forexample, is good for making a doubler. Toproduce a times-3 multiplier, the originalsignal may be input to an amplifier that isover driven to produce nearly a square wave.This signal is high in 3rd order harmonics andcan be filtered to produce the desired x3

    outcome.YIG multipliers often want to select anarbitrary harmonic, so they use a statefuldistortion circuit that converts the input sinewave into an approximate impulse train . Theideal (but impractical) impulse train generatesan infinite number of (weak) harmonics. Inpractice, an impulse train generated by amonostable circuit will have many usableharmonics. YIG multipliers using step recoverydiodes may, for example, take an inputfrequency of 1 to 2 GHz and produce outputs up
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    to 18 GHz.[2] Sometimes the frequency multipliercircuit will adjust the width of the impulsesto improve conversion efficiency for a specificharmonic.
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    An electronic circuit or device producing frequencymodulation. This device changes the frequency of anoscillator in accordance with the amplitude of amodulating signal. If the modulation is linear, thefrequency change is proportional to the amplitude ofthe modulating voltage.

    High-frequency oscillators usually employeither LC (inductance-capacitance) tuned circuits orpiezoelectric crystals to establish the frequency ofoscillation. This frequency can be controlled bychanging the effective capacitance or inductance ofthe tuned circuit in accordance with the modulatingsignal. Practical circuits usually employ a varactordiode to change the oscillator in accordance with amodulating voltage.

    The oscillators in high-frequency electronicsystems, such as frequency-modulating (FM)transmitters, usually employ piezoelectric crystalsfor precise control of the carrier frequency. Thesecrystals are equivalent to a series LC tuned circuitwith an extremely high Q . The crystal holder has asmall capacitance which is in parallel with thecrystal and therefore causes parallel resonance at a

    slightly higher frequency than the series resonantfrequency of the crystal. The actual oscillatorfrequency is between these two resonant frequenciesand is controllable by the parallel capacitance.

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    The junction capacitance of a semiconductor diodevaries with the diode voltage, and a reverse-biaseddiode may be used to control the oscillatorfrequency to produce frequency modulation. Low-lossdiodes designed for this service are known asvaractor diodes and have trade names such asVaricaps or Epicaps. A basic varactor modulatingscheme is shown in the illustration. In thiscircuit, the transistor that drives the varactormodulator provides reverse bias as well as themodulating voltage v m . The radio-frequency (rf)

    choke provides very high impedance at the oscillatorfrequency to isolate the transistor amplifier outputimpedance from the oscillator circuit but to allowthe modulating signal to pass through withnegligible attenuation. Only the frequency-determining part of the oscillator is shown. Thesymbols C c , Lc , and R represent the electricalequivalents of the compliance, mass, and loss,respectively, of the crystal; C h is the crystal-holder capacitance and C b is a dc blocking capacitor

    The capacitance of D 1, of course, is controlled by

    two factors: a fixed dc bias and the modulatingsignal. In Fig b, the bias on D 1 is set by thevoltage divider which is made up of R 1 and R 2.Usually either R 1 or R 2 is made variable so that thecenter carrier frequency can be adjusted over a

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    narrow range. The modulating signal is applied

    through C 3 and the RFC. The C 3 is a blockingcapacitor that keeps the DC bias out of the

    modulating signal circuits. The RFC is a radio

    frequency choke whose reactance is high at thecarrier frequency to prevent the carrier signal from

    getting into the modulating signal circuits. The

    modulating signal derived from the microphone is

    amplified and applied to the modulator. As themodulating signal varies, it adds to or subtracts

    from the fixed bias voltage. Thus the effective

    voltage applied to D 1 causes its capacitance tovary. This, in turn, produces a deviation of thecarrier frequency as desired. A positive-going

    signal at point A adds to the reverse bias,

    decreasing the capacitance and increasing thecarrier frequency. A negative-going signal at A

    subtracts from the bias, increasing the capacitance

    and decreasing the carrier frequency.

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    There are several ways of demodulation depending onhow parameters of the base-band signal aretransmitted in the carrier signal, such asamplitude, frequency or phase. For example, for asignal modulated with a linear modulation, like AM( Amplitude Modulation ), we can use a synchronousdetector. On the other hand, for a signal modulatedwith an angular modulation, we must use an FM( Frequency Modulation ) demodulator or a PM ( PhaseModulation ) demodulator. Different kinds of circuits

    perform these functions.Many techniques such as carrier recovery , clockrecovery , bit slip , frame synchronization , rakereceiver , pulse compression , Received SignalStrength Indication , error detection and correction ,etc. -- are only performed by demodulators, althoughany specific demodulator may perform only some ornone of these techniques.

    There are several common types of FM demodulator:

    The quadrature detector , which phase shifts thesignal by 90 degrees and multiplies it with the
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    unshifted version. One of the terms that dropsout from this operation is the originalinformation signal, which is selected andamplified.

    The signal is fed into a PLL and the error signalis used as the demodulated signal.

    The most common is a Foster-Seeley discriminator .This is composed of an electronic filter whichdecreases the amplitude of some frequenciesrelative to others, followed by an AMdemodulator. If the filter response changes

    linearly with frequency, the final analog outputwill be proportional to the input frequency, asdesired.

    A variant of the Foster-Seeley discriminatorcalled the ratio detector [2]

    Another method uses two AM demodulators, onetuned to the high end of the band and the otherto the low end, and feed the outputs into adifference amp.

    Using a digital signal processor , as usedin software-defined radio .
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    In an FM signal, the modulation is the deviation ofa carrier from its nominal frequency. Theconventional method to demodulate this signal is toconvert frequency deviation to phase and detect the

    change of phase. In the quadrature demodulator, themodulated carrier is passed through an LC tankcircuit that shifts the signal by 90 at the center frequency. This phase shift is either greater orless than 90 depending on the direction ofdeviation. A phase detector compares the phase-shifted signal to the original to give thedemodulated baseband signal. You use quadraturedemodulators not only for frequency modulation, butalso with digital modulation schemes such as FSK(frequency shift keying) and GFSK (Gaussianfrequency shift keying).

    FM Quadrature Demodulator Block DiagramThe conventional method of FM demodulation forintegrated circuits is Bilotti's quadraturedemodulator that uses a phase shift network and aphase detector . shows the block diagram

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    of this quadrature demodulator. The phase detectorcompares the phase of the IF signal ( v 1) to v 2, thesignal generated by passing v 1 through a phase shiftnetwork. This phase shift network includes an LCtank (L, R p , and C p ) and a series reactance (C s ). Thenetwork gives a frequency- sensitive 90 phase shift at the center frequency. The phase detectordiscussed here is the bipolar double-balancedmultiplier popularized by Bilotti . The output ofthe multiplier ( I o ) is filtered, which results in aDC level that changes as the input frequency


    Quadrature demodulator block diagram

    Quadrature Demodulator Transfer FunctionTo derive the transfer function of the quadraturedemodulator, the phase shift network is first drawnas a small-signal circuit model ( ). Theimpedance (Z p ) of the parallel combination of L, R p ,

    and C p is:

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    Small-signal model of the quadraturephase-shift networkThe ratio of v 2 over v 1 is the ratio ofimpedances Z p (s) over (Z p(s) + 1/ sC s ). Simplifyingthis ratio,

    The resonant frequency n of this filter is:

    The quality factor Q of the phase shift networkis R p /( n L). Next, is used to solve forthe transfer function from v 1 to v 2. The variables n and Q are substituted into and v 2/ v 1 iswritten in terms of s =j where n :

    In , is the deviation from the carrierfrequency, and 2 Q / n is the normalized deviation.Defining:

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    can be written as:

    Writing v 2 in terms of v 1,

    describes the signal at one multiplierinput in terms of the signal at the other input. Thesignal v 1 is applied to the first input and is inlimiting (a square wave). The signal at the secondinput ( v 2) is a linear signal. By integrating overhalf of the period, you get the average value of themultiplier output current:

    For a bipolar differential

    amplifier, g m is I o /V T where 2 I o is the multiplierbias current. Substituting for v 2 and g m ,

    where V 1 is the peak voltage of the signal v 1.Simplifying yields the transfer functionfor the quadrature demodulator:

    In , the term a /(1+ a ) from isplotted versus the normalized frequencydeviation (a). This plot is the quadrature

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    demodulator s-curve. As the frequency of the signalapplied to the demodulator becomes more positivethan the natural frequency of the phase shiftnetwork, the filtered output of the multiplierincreases. Likewise, the filtered output decreasesas the frequency of the input signal decreases.

    Plot of normalized demodulator outputvs. normalized frequency deviation

    Integrated Circuit Implementation shows an integrated circuit implementation

    of the quadrature demodulator. The inputsignal v in is supplied from a limiting amplifier andis a square wave of known amplitude. The inputsignal v in is level shifted, and v 1 is applied totransistors Q 1 and Q 2. The amplitude of v 1 is largeenough such that Q 1 and Q 2 are switched completely onor off during each cycle. Capacitor C s is typically

    integrated while C p , L, and R p are externalcomponents. The component values are chosen suchthat the amplitude of v 2 is less than that of v 1 asgiven by . This causes transistors Q 3-Q 6 to operate as linear devices rather thanswitches. The output of the multiplier is converted

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    from a differential current to a single-endedvoltage v o . The output is filtered bycomponents R f and C f .

    Integrated circuit implementation of thequadrature demodulatorThe authors gratefully acknowledge Mark Randol.