Misplaced Pages

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98-476: Reference implementations of FSK modems exist and are documented in detail. The demodulation of a binary FSK signal can be done using the Goertzel algorithm very efficiently, even on low-power microcontrollers. In principle FSK can be implemented by using completely independent free-running oscillators, and switching between them at the beginning of each symbol period. In general, independent oscillators will not be at

196-458: A Gaussian filter to make the transitions smoother to limit spectral width. Gaussian filtering is a standard way to reduce spectral width; it is called pulse shaping in this application. In ordinary non-filtered FSK, at a jump from −1 to +1 or +1 to −1, the modulated waveform changes rapidly, which introduces large out-of-band spectrum. If the pulse is changed going from −1 to +1 as −1, −0.98, −0.93, ..., +0.93, +0.98, +1, and this smoother pulse

294-440: A digital-to-analog converter , typically at a frequency less than the desired RF-output frequency. The analog signal must then be shifted in frequency and linearly amplified to the desired frequency and power level (linear amplification must be used to prevent modulation distortion). This low-level method for AM is used in many Amateur Radio transceivers. AM may also be generated at a low level, using analog methods described in

392-481: A software object that maintains the filter state between updates, with the final power result accessed after the other processing is done. The case of real-valued input data arises frequently, especially in embedded systems where the input streams result from direct measurements of physical processes. When the input data are real-valued, the filter internal state variables sprev and sprev2 can be observed also to be real-valued, consequently, no complex arithmetic

490-421: A DFT. A simple but inelegant expedient is to extend the input sequence x [ n ] {\displaystyle x[n]} with one more artificial value x [ N ] = 0 {\displaystyle x[N]=0} . We can see from equation (9) that the mathematical effect on the final result is the same as removing term x [ N ] {\displaystyle x[N]} from

588-505: A buzz in receivers. In effect they were already amplitude modulated. The first AM transmission was made by Canadian-born American researcher Reginald Fessenden on 23 December 1900 using a spark gap transmitter with a specially designed high frequency 10 kHz interrupter , over a distance of one mile (1.6 km) at Cobb Island, Maryland, US. His first transmitted words were, "Hello. One, two, three, four. Is it snowing where you are, Mr. Thiessen?". The words were barely intelligible above

686-436: A compromise in terms of bandwidth) in order to reduce the required channel spacing. Another improvement over standard AM is obtained through reduction or suppression of the carrier component of the modulated spectrum. In figure 2 this is the spike in between the sidebands; even with full (100%) sine wave modulation, the power in the carrier component is twice that in the sidebands, yet it carries no unique information. Thus there

784-478: A faithful reproduction of the original program, including its varying modulation levels, is expected. In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation: Amplitude modulation was used in experiments of multiplex telegraph and telephone transmission in the late 1800s. However, the practical development of this technology is identified with

882-455: A great increase in the number of radio stations experimenting with AM transmission of news or music. The vacuum tube was responsible for the rise of AM broadcasting around 1920, the first electronic mass communication medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting began after World War II. At the same time as AM radio began, telephone companies such as AT&T were developing

980-408: A human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted above the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times,

1078-468: A precise carrier frequency reference signal (usually as shifted to the intermediate frequency ) from a greatly reduced "pilot" carrier (in reduced-carrier transmission or DSB-RC) to use in the demodulation process. Even with the carrier eliminated in double-sideband suppressed-carrier transmission , carrier regeneration is possible using a Costas phase-locked loop . This does not work for single-sideband suppressed-carrier transmission (SSB-SC), leading to

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1176-665: A problem. Early experiments in AM radio transmission, conducted by Fessenden, Valdemar Poulsen , Ernst Ruhmer , Quirino Majorana , Charles Herrold , and Lee de Forest , were hampered by the lack of a technology for amplification . The first practical continuous wave AM transmitters were based on either the huge, expensive Alexanderson alternator , developed 1906–1910, or versions of the Poulsen arc transmitter (arc converter), invented in 1903. The modifications necessary to transmit AM were clumsy and resulted in very low quality audio. Modulation

1274-584: A rather small (or zero) remaining carrier amplitude. Modulation circuit designs may be classified as low- or high-level (depending on whether they modulate in a low-power domain—followed by amplification for transmission—or in the high-power domain of the transmitted signal). In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are converted to voltages with

1372-499: A single sine wave, as treated above. However, by the principle of Fourier decomposition , m(t) can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of 1 + m(t) with c(t) as above, the result consists of a sum of sine waves. Again, the carrier c(t) is present unchanged, but each frequency component of m at f i has two sidebands at frequencies f c + f i and f c – f i . The collection of

1470-468: A small number of selected frequency components, it is more numerically efficient. The simple structure of the Goertzel algorithm makes it well suited to small processors and embedded applications. The Goertzel algorithm can also be used "in reverse" as a sinusoid synthesis function, which requires only 1 multiplication and 1 subtraction per generated sample. The main calculation in the Goertzel algorithm has

1568-403: A special modulator produces such a waveform at a low level followed by a linear amplifier . What's more, a standard AM receiver using an envelope detector is incapable of properly demodulating such a signal. Rather, synchronous detection is required. Thus double-sideband transmission is generally not referred to as "AM" even though it generates an identical RF waveform as standard AM as long as

1666-443: A two-tone method of transmitting Morse code. Dots and dashes were replaced with different tones of equal length. The intent was to minimize transmission time. Some early Continuous Wave (CW) transmitters employed an arc converter that could not be conveniently keyed . Instead of turning the arc on and off, the key slightly changed the transmitter frequency in a technique known as the compensation-wave method . The compensation-wave

1764-518: Is marginally stable and vulnerable to numerical-error accumulation when computed using low-precision arithmetic and long input sequences. A numerically stable version was proposed by Christian Reinsch . For the important case of computing a DFT term, the following special restrictions are applied. Making these substitutions into equation (6) and observing that the term e + j 2 π k = 1 {\displaystyle e^{+j2\pi k}=1} , equation (6) then takes

1862-466: Is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave . In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to that of the message signal, such as an audio signal . This technique contrasts with angle modulation , in which either the frequency of the carrier wave is varied, as in frequency modulation , or its phase , as in phase modulation . AM

1960-429: Is a modulation technique by which digital data is represented by changes in the frequency ( pitch ) of an audio tone, yielding an encoded signal suitable for transmission via radio or telephone . Normally, the transmitted audio alternates between two tones: one, the "mark", represents a binary one; the other, the "space", represents a binary zero. AFSK differs from regular frequency-shift keying in performing

2058-400: Is a carrier with a frequency of 0 Hz. It is modulated by a microphone ( transmitter ) in the telephone set according to the acoustic signal from the speaker. The result is a varying amplitude direct current, whose AC-component is the speech signal extracted at the central office for transmission to another subscriber. An additional function provided by the carrier in standard AM, but which

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2156-448: Is a great advantage in efficiency in reducing or totally suppressing the carrier, either in conjunction with elimination of one sideband ( single-sideband suppressed-carrier transmission ) or with both sidebands remaining ( double sideband suppressed carrier ). While these suppressed carrier transmissions are efficient in terms of transmitter power, they require more sophisticated receivers employing synchronous detection and regeneration of

2254-451: Is always positive for undermodulation. If m > 1 then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss of original signal. Amplitude modulation results when the carrier c(t) is multiplied by the positive quantity (1 + m(t)/A) : In this simple case m is identical to the modulation index , discussed below. With m = 0.5 the amplitude modulated signal y ( t ) thus corresponds to

2352-451: Is based, heterodyning , and invented one of the first detectors able to rectify and receive AM, the electrolytic detector or "liquid baretter", in 1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal detector (1906) also proved able to rectify AM signals, so the technological hurdle was generating AM waves; receiving them was not

2450-454: Is equally valid to apply equation (11) and calculate the signal power from term y [ N ] {\displaystyle y[N]} or to apply equation (2) and calculate the signal power from term y [ N − 1 ] {\displaystyle y[N-1]} . Both cases lead to the following expression for the signal power represented by DFT term X [ k ] {\displaystyle X[k]} : In

2548-412: Is lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in the modulation, so

2646-446: Is often larger for an FFT, and the practical advantage favours the Goertzel algorithm even for M {\displaystyle M} several times larger than log 2 ⁡ ( N ) {\displaystyle \log _{2}(N)} . As a rule-of-thumb for determining whether a radix-2 FFT or a Goertzel algorithm is more efficient, adjust the number of terms N {\displaystyle N} in

2744-516: Is often restricted to the range 0 to π (see Nyquist–Shannon sampling theorem ); using a value outside this range is not meaningless, but is equivalent to using an aliased frequency inside this range, since the exponential function is periodic with a period of 2π in ω 0 {\displaystyle \omega _{0}} . The second-stage filter can be observed to be a FIR filter , since its calculations do not use any of its past outputs. Z-transform methods can be applied to study

2842-592: Is required in the first IIR stage. Optimizing for real-valued arithmetic typically is as simple as applying appropriate real-valued data types for the variables. After the calculations using input term x [ N − 1 ] {\displaystyle x[N-1]} , and filter iterations are terminated, equation (11) must be applied to evaluate the DFT term. The final calculation uses complex-valued arithmetic, but this can be converted into real-valued arithmetic by separating real and imaginary terms: Comparing to

2940-404: Is shown in the first waveform, below. For m = 1.0 {\displaystyle m=1.0} , it varies by 100% as shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and this represents full modulation using standard AM and is often a target (in order to obtain the highest possible signal-to-noise ratio ) but mustn't be exceeded. Increasing

3038-417: Is strongly reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts (sports, news, talk radio etc.). AM is also inefficient in power usage; at least two-thirds of the power is concentrated in the carrier signal. The carrier signal contains none of

Frequency-shift keying - Misplaced Pages Continue

3136-418: Is that the receiver amplifies and detects noise and electromagnetic interference in equal proportion to the signal. Increasing the received signal-to-noise ratio , say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation (FM) and digital radio where the effect of such noise following demodulation

3234-478: Is used by Improved Layer 2 Protocol , DECT , Bluetooth , Cypress WirelessUSB , Nordic Semiconductor , Texas Instruments , IEEE 802.15.4 , Z-Wave and Wavenis devices. For basic data rate Bluetooth the minimum deviation is 115 kHz. A GFSK modulator differs from a simple frequency-shift keying modulator in that before the baseband waveform (with levels −1 and +1) goes into the FSK modulator, it passed through

3332-491: Is used for calculating the DFT, so calculations for all the other output terms are omitted. Since the FIR filter is not calculated, the IIR stage calculations s [ 0 ] , s [ 1 ] {\displaystyle s[0],s[1]} , etc. can be discarded immediately after updating the first stage's internal state. This seems to leave a paradox: to complete the algorithm,

3430-439: Is used to determine the carrier frequency , the out-of-band spectrum will be reduced. Minimum frequency-shift keying or minimum-shift keying (MSK) is a particular spectrally efficient form of coherent FSK. In MSK, the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms that represent a 0 and a 1 bit differ by exactly half a carrier period. The maximum frequency deviation

3528-408: Is useful in certain practical applications, such as recognition of dual-tone multi-frequency signaling (DTMF) tones produced by the push buttons of the keypad of a traditional analog telephone . The algorithm was first described by Gerald Goertzel in 1958. Like the DFT, the Goertzel algorithm analyses one selectable frequency component from a discrete signal . Unlike direct DFT calculations,

3626-448: Is δ = 0.25  f m , where f m is the maximum modulating frequency. As a result, the modulation index m is 0.5. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are orthogonal . A variant of MSK called Gaussian minimum-shift keying ( GMSK ) is used in the GSM mobile phone standard. Audio frequency-shift keying (AFSK)

3724-465: The envelope of the transmitted waveform. In the frequency domain , amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands . Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Standard AM is thus sometimes called "double-sideband amplitude modulation" (DSBAM). A disadvantage of all amplitude modulation techniques, not only standard AM,

3822-527: The Dual-tone multi-frequency (DTMF) system and a no-ring mode for meter-reading and the like. It's more of a recognition that the different types exist than an attempt to define a single "standard". The Telcordia Technologies (formerly Bellcore) standard is used in the United States , Canada (but see below), Australia , China , Hong Kong and Singapore . It sends the data after the first ring tone and uses

3920-639: The EXAR website. The Cable Communications Association (CCA) of the United Kingdom developed their own standard which sends the information after a short first ring, as either Bell 202 or V.23 tones. They developed a new standard rather than change some "street boxes" (multiplexors) which couldn't cope with the BT standard. The UK cable industry use a variety of switches: most are Nortel DMS-100; some are System X ; System Y ; and Nokia DX220. Note that some of these use

4018-506: The instantaneous phase deviation ϕ ( t ) {\displaystyle \phi (t)} . This description directly provides the two major groups of modulation, amplitude modulation and angle modulation . In angle modulation, the term A ( t ) is constant and the second term of the equation has a functional relationship to the modulating message signal. Angle modulation provides two methods of modulation, frequency modulation and phase modulation . In amplitude modulation,

Frequency-shift keying - Misplaced Pages Continue

4116-413: The poles of the filter's Z transform are located at e + j ω 0 {\displaystyle e^{+j\omega _{0}}} and e − j ω 0 {\displaystyle e^{-j\omega _{0}}} , on a circle of unit radius centered on the origin of the complex Z-transform plane. This property indicates that the filter process

4214-415: The pseudocode below, the real-valued input data is stored in the array x and the variables sprev and sprev2 temporarily store output history from the IIR filter. Nterms is the number of samples in the array, and Kterm corresponds to the frequency of interest, multiplied by the sampling period. It is possible to organise the computations so that incoming samples are delivered singly to

4312-573: The 1200 bits per second Bell 202 tone modulation. The data may be sent in SDMF – which includes the date, time and number – or in MDMF, which adds a NAME field. British Telecom (BT) in the United Kingdom developed their own standard, which wakes up the display with a line reversal, then sends the data as CCITT v.23 modem tones in a format similar to MDMF. It is used by BT, wireless networks like

4410-514: The AGC must respond to peaks of the transmitted power during peaks in the modulation. This typically involves a so-called fast attack, slow decay circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However it is absolutely undesired for music or normal broadcast programming, where

4508-462: The BT standard instead of the CCA one. The data format is similar to the BT one, but the transport layer is more like Telcordia Technologies, so North American or European equipment is more likely to detect it. Goertzel algorithm The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of the individual terms of the discrete Fourier transform (DFT). It

4606-410: The FIR filter stage must be evaluated once using the final two outputs from the IIR filter stage, while for computational efficiency the IIR filter iteration discards its output values. This is where the properties of the direct-form filter structure are applied. The two internal state variables of the IIR filter provide the last two values of the IIR filter output, which are the terms required to evaluate

4704-616: The FIR filter stage. Examining equation (6), a final IIR filter pass to calculate term y [ N ] {\displaystyle y[N]} using a supplemental input value x [ N ] = 0 {\displaystyle x[N]=0} applies a complex multiplier of magnitude 1 to the previous term y [ N − 1 ] {\displaystyle y[N-1]} . Consequently, y [ N ] {\displaystyle y[N]} and y [ N − 1 ] {\displaystyle y[N-1]} represent equivalent signal power. It

4802-472: The Goertzel algorithm applies a single real-valued coefficient at each iteration, using real-valued arithmetic for real-valued input sequences. For covering a full spectrum (except when using for continuous stream of data where coefficients are reused for subsequent calculations, which has computational complexity equivalent of sliding DFT ), the Goertzel algorithm has a higher order of complexity than fast Fourier transform (FFT) algorithms, but for computing

4900-919: The U.S. The CHU shortwave radio station in Ottawa, Ontario , Canada broadcasts an exclusive digital time signal encoded using AFSK modulation. Frequency-shift keying (FSK) is commonly used over telephone lines for caller ID (displaying callers' numbers) and remote metering applications. There are several variations of this technology. In some countries of Europe , the European Telecommunications Standards Institute (ETSI) standards 200 778-1 and -2 – replacing 300 778-1 & -2 – allow 3 physical transport layers ( Telcordia Technologies (formerly Bellcore), British Telecom (BT) and Cable Communications Association (CCA)), combined with 2 data formats Multiple Data Message Format (MDMF) & Single Data Message Format (SDMF), plus

4998-513: The advantage that encoded signals will pass through AC-coupled links, including most equipment originally designed to carry music or speech. AFSK is used in the U.S.-based Emergency Alert System to notify stations of the type of emergency, locations affected, and the time of issue without actually hearing the text of the alert. Phase 1 radios in the Project 25 system use 4-level frequency-shift keying (4FSK). In 1910, Reginald Fessenden invented

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5096-487: The angle term is held constant and the first term, A ( t ), of the equation has a functional relationship to the modulating message signal. The modulating message signal may be analog in nature, or it may be a digital signal, in which case the technique is generally called amplitude-shift keying . For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission. The message signal determines

5194-411: The background buzz of the spark. Fessenden was a significant figure in the development of AM radio. He was one of the first researchers to realize, from experiments like the above, that the existing technology for producing radio waves, the spark transmitter, was not usable for amplitude modulation, and that a new kind of transmitter, one that produced sinusoidal continuous waves , was needed. This

5292-401: The bandwidth of an AM signal is narrower than one using frequency modulation (FM), it is twice as wide as single-sideband techniques; it thus may be viewed as spectrally inefficient. Within a frequency band, only half as many transmissions (or "channels") can thus be accommodated. For this reason analog television employs a variant of single-sideband (known as vestigial sideband , somewhat of

5390-549: The carrier frequency. Single-sideband modulation uses bandpass filters to eliminate one of the sidebands and possibly the carrier signal, which improves the ratio of message power to total transmission power , reduces power handling requirements of line repeaters, and permits better bandwidth utilization of the transmission medium. AM remains in use in many forms of communication in addition to AM broadcasting : shortwave radio , amateur radio , two-way radios , VHF aircraft radio , citizens band radio , and in computer modems in

5488-451: The carrier frequency. For that reason, standard AM continues to be widely used, especially in broadcast transmission, to allow for the use of inexpensive receivers using envelope detection . Even (analog) television, with a (largely) suppressed lower sideband, includes sufficient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of both one sideband and

5586-454: The carrier frequency. Passing the modulated signal through another nonlinear device can extract the original baseband signal. His analysis also showed that only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915. This advanced variant of amplitude modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After WW-II, it

5684-400: The carrier itself remains constant, and of greater power than the total sideband power. The RF bandwidth of an AM transmission (refer to figure 2, but only considering positive frequencies) is twice the bandwidth of the modulating (or " baseband ") signal, since the upper and lower sidebands around the carrier frequency each have a bandwidth as wide as the highest modulating frequency. Although

5782-468: The carrier represent a net advantage and are frequently employed. A technique used widely in broadcast AM transmitters is an application of the Hapburg carrier, first proposed in the 1930s but impractical with the technology then available. During periods of low modulation the carrier power would be reduced and would return to full power during periods of high modulation levels. This has the effect of reducing

5880-504: The characteristic "Donald Duck" sound from such receivers when slightly detuned. Single-sideband AM is nevertheless used widely in amateur radio and other voice communications because it has power and bandwidth efficiency (cutting the RF bandwidth in half compared to standard AM). On the other hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers. The broadcaster absorbs

5978-708: The data set upward to the nearest exact power of 2, calling this N 2 {\displaystyle N_{2}} , and the Goertzel algorithm is likely to be faster if FFT implementations and processing platforms have a significant impact on the relative performance. Some FFT implementations perform internal complex-number calculations to generate coefficients on-the-fly, significantly increasing their "cost K per unit of work." FFT and DFT algorithms can use tables of pre-computed coefficient values for better numerical efficiency, but this requires more accesses to coefficient values buffered in external memory, which can lead to increased cache contention that counters some of

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6076-444: The extra power cost to greatly increase potential audience. A simple form of digital amplitude modulation which can be used for transmitting binary data is on–off keying , the simplest form of amplitude-shift keying, in which ones and zeros are represented by the presence or absence of a carrier. On–off keying is likewise used by radio amateurs to transmit Morse code where it is known as continuous wave (CW) operation, even though

6174-451: The filter updates at term N − 1 {\displaystyle N-1} and immediately applying equation (2) rather than equation (11) misses the final filter state updates, yielding a result with incorrect phase. The particular filtering structure chosen for the Goertzel algorithm is the key to its efficient DFT calculations. We can observe that only one output value y [ N ] {\displaystyle y[N]}

6272-596: The following filter to s [ n ] {\displaystyle s[n]} , producing output sequence y [ n ] {\displaystyle y[n]} : The first filter stage can be observed to be a second-order IIR filter with a direct-form structure. This particular structure has the property that its internal state variables equal the past output values from that stage. Input values x [ n ] {\displaystyle x[n]} for n < 0 {\displaystyle n<0} are presumed all equal to 0. To establish

6370-511: The following form: We can observe that the right side of equation (9) is extremely similar to the defining formula for DFT term X [ k ] {\displaystyle X[k]} , the DFT term for index number k {\displaystyle k} , but not exactly the same. The summation shown in equation (9) requires N + 1 {\displaystyle N+1} input terms, but only N {\displaystyle N} input terms are available when evaluating

6468-400: The form of QAM . In electronics , telecommunications and mechanics , modulation means varying some aspect of a continuous wave carrier signal with an information-bearing modulation waveform, such as an audio signal which represents sound, or a video signal which represents images. In this sense, the carrier wave, which has a much higher frequency than the message signal, carries

6566-549: The form of a digital filter , and for this reason the algorithm is often called a Goertzel filter . The filter operates on an input sequence x [ n ] {\displaystyle x[n]} in a cascade of two stages with a parameter ω 0 {\displaystyle \omega _{0}} , giving the frequency to be analysed, normalised to radians per sample. The first stage calculates an intermediate sequence, s [ n ] {\displaystyle s[n]} : The second stage applies

6664-626: The form of the Bell 202 standard. Some early microcomputers used a specific form of AFSK modulation, the Kansas City standard , to store data on audio cassettes . AFSK is still widely used in amateur radio , as it allows data transmission through unmodified voiceband equipment. AFSK is also used in the United States' Emergency Alert System to transmit warning information. It is used at higher bitrates for Weathercopy used on Weatheradio by NOAA in

6762-493: The former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation m(t) may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation m(t) having simply been shifted in frequency by f c as depicted at the bottom right of figure 2. The short-term spectrum of modulation, changing as it would for

6860-417: The frequency with the digital data symbols, "instantaneously" changing the frequency at the beginning of each symbol period, Gaussian frequency-shift keying ( GFSK ) filters the data pulses with a Gaussian filter to make the transitions smoother. This filter has the advantage of reducing sideband power, reducing interference with neighboring channels, at the cost of increasing intersymbol interference . It

6958-441: The information. At the receiving station, the message signal is extracted from the modulated carrier by demodulation . In general form, a modulation process of a sinusoidal carrier wave may be described by the following equation: A(t) represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its angular frequency ω {\displaystyle \omega } , and

7056-417: The initial filter state so that evaluation can begin at sample x [ 0 ] {\displaystyle x[0]} , the filter states are assigned initial values s [ − 2 ] = s [ − 1 ] = 0 {\displaystyle s[-2]=s[-1]=0} . To avoid aliasing hazards, frequency ω 0 {\displaystyle \omega _{0}}

7154-455: The inverse tangent function. Since complex signals decompose linearly into real and imaginary parts, the Goertzel algorithm can be computed in real arithmetic separately over the sequence of real parts, yielding y r [ n ] {\displaystyle y_{\text{r}}[n]} , and over the sequence of imaginary parts, yielding y i [ n ] {\displaystyle y_{\text{i}}[n]} . After that,

7252-535: The late Ionica , and some cable companies. Details are to be found in BT Supplier Information Notes (SINs) 227 Archived 2014-07-26 at the Wayback Machine (link broken 28/7/21) and 242 Archived 2014-07-26 at the Wayback Machine (link broken 28/7/21); another useful document is Designing Caller Identification Delivery Using XR-2211 for BT Archived 2016-03-06 at the Wayback Machine from

7350-489: The modulating signal beyond that point, known as overmodulation , causes a standard AM modulator (see below) to fail, as the negative excursions of the wave envelope cannot become less than zero, resulting in distortion ("clipping") of the received modulation. Transmitters typically incorporate a limiter circuit to avoid overmodulation, and/or a compressor circuit (especially for voice communications) in order to still approach 100% modulation for maximum intelligibility above

7448-443: The modulation amplitude and carrier amplitude, respectively; the modulation amplitude is the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is normally expressed as a percentage, and may be displayed on a meter connected to an AM transmitter. So if m = 0.5 {\displaystyle m=0.5} , carrier amplitude varies by 50% above (and below) its unmodulated level, as

7546-479: The modulation at baseband frequencies. In radio applications, the AFSK-modulated signal normally is being used to modulate an RF carrier (using a conventional technique, such as AM or FM ) for transmission. AFSK is not always used for high-speed data communications, since it is far less efficient in both power and bandwidth than most other modulation modes. In addition to its simplicity, however, AFSK has

7644-409: The modulation index is below 100%. Such systems more often attempt a radical reduction of the carrier level compared to the sidebands (where the useful information is present) to the point of double-sideband suppressed-carrier transmission where the carrier is (ideally) reduced to zero. In all such cases the term "modulation index" loses its value as it refers to the ratio of the modulation amplitude to

7742-534: The next section. High-power AM transmitters (such as those used for AM broadcasting ) are based on high-efficiency class-D and class-E power amplifier stages, modulated by varying the supply voltage. Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitter's final amplifier (generally class-C, for efficiency). The following types are for vacuum tube transmitters (but similar options are available with transistors): The simplest form of AM demodulator consists of

7840-542: The noise. Such circuits are sometimes referred to as a vogad . However it is possible to talk about a modulation index exceeding 100%, without introducing distortion, in the case of double-sideband reduced-carrier transmission . In that case, negative excursions beyond zero entail a reversal of the carrier phase, as shown in the third waveform below. This cannot be produced using the efficient high-level (output stage) modulation techniques (see below) which are widely used especially in high power broadcast transmitters. Rather,

7938-448: The numerical advantage. Both algorithms gain approximately a factor of 2 efficiency when using real-valued rather than complex-valued input data. However, these gains are natural for the Goertzel algorithm but will not be achieved for the FFT without using certain algorithm variants specialised for transforming real-valued data . Amplitude modulation Amplitude modulation ( AM )

8036-467: The original information being transmitted (voice, video, data, etc.). However its presence provides a simple means of demodulation using envelope detection , providing a frequency and phase reference to extract the modulation from the sidebands. In some modulation systems based on AM, a lower transmitter power is required through partial or total elimination of the carrier component, however receivers for these signals are more complex because they must provide

8134-404: The other large application for AM: sending multiple telephone calls through a single wire by modulating them on separate carrier frequencies, called frequency division multiplexing . In 1915, John Renshaw Carson formulated the first mathematical description of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device creates a sideband on both sides of

8232-489: The overall power demand of the transmitter and is most effective on speech type programmes. Various trade names are used for its implementation by the transmitter manufacturers from the late 80's onwards. The AM modulation index is a measure based on the ratio of the modulation excursions of the RF signal to the level of the unmodulated carrier. It is thus defined as: where M {\displaystyle M\,} and A {\displaystyle A\,} are

8330-514: The period between 1900 and 1920 of radiotelephone transmission, that is, the effort to send audio signals by radio waves. The first radio transmitters, called spark gap transmitters , transmitted information by wireless telegraphy , using pulses of the carrier wave to spell out text messages in Morse code . They could not transmit audio because the carrier consisted of strings of damped waves , pulses of radio waves that declined to zero, and sounded like

8428-435: The power-spectrum application, the only difference are the calculation used to finish: This application requires the same evaluation of DFT term X [ k ] {\displaystyle X[k]} , as discussed in the previous section, using a real-valued or complex-valued input stream. Then the signal phase can be evaluated as taking appropriate precautions for singularities, quadrant, and so forth when computing

8526-474: The properties of the filter cascade. The Z transform of the first filter stage given in equation (1) is The Z transform of the second filter stage given in equation (2) is The combined transfer function of the cascade of the two filter stages is then This can be transformed back to an equivalent time-domain sequence, and the terms unrolled back to the first input term at index n = 0 {\displaystyle n=0} : It can be observed that

8624-530: The same phase and therefore the same amplitude at the switch-over instant, causing sudden discontinuities in the transmitted signal. In practice, many FSK transmitters use only a single oscillator, and the process of switching to a different frequency at the beginning of each symbol period preserves the phase. The elimination of discontinuities in the phase (and therefore elimination of sudden changes in amplitude) reduces sideband power, reducing interference with neighboring channels. Rather than directly modulating

8722-461: The summation, thus delivering the intended DFT value. However, there is a more elegant approach that avoids the extra filter pass. From equation (1), we can note that when the extended input term x [ N ] = 0 {\displaystyle x[N]=0} is used in the final step, Thus, the algorithm can be completed as follows: The last two mathematical operations are simplified by combining them algebraically: Note that stopping

8820-422: The top graph (labelled "50% Modulation") in figure 4. Using prosthaphaeresis identities , y ( t ) can be shown to be the sum of three sine waves: Therefore, the modulated signal has three components: the carrier wave c(t) which is unchanged in frequency, and two sidebands with frequencies slightly above and below the carrier frequency f c . A useful modulation signal m(t) is usually more complex than

8918-425: The transmission is not strictly "continuous". A more complex form of AM, quadrature amplitude modulation is now more commonly used with digital data, while making more efficient use of the available bandwidth. A simple form of amplitude modulation is the transmission of speech signals from a traditional analog telephone set using a common battery local loop. The direct current provided by the central office battery

9016-437: The two complex-valued partial results can be recombined: In the complexity order expressions, when the number of calculated terms M {\displaystyle M} is smaller than log ⁡ N {\displaystyle \log N} , the advantage of the Goertzel algorithm is clear. But because FFT code is comparatively complex, the "cost per unit of work" factor K {\displaystyle K}

9114-427: Was a cheap source of continuous waves and could be easily modulated to make an AM transmitter. Modulation did not have to be done at the output but could be applied to the signal before the final amplifier tube, so the microphone or other audio source didn't have to modulate a high-power radio signal. Wartime research greatly advanced the art of AM modulation, and after the war the availability of cheap tubes sparked

9212-469: Was a radical idea at the time, because experts believed the impulsive spark was necessary to produce radio frequency waves, and Fessenden was ridiculed. He invented and helped develop one of the first continuous wave transmitters – the Alexanderson alternator , with which he made what is considered the first AM public entertainment broadcast on Christmas Eve, 1906. He also discovered the principle on which AM

9310-402: Was developed for military aircraft communication. The carrier wave ( sine wave ) of frequency f c and amplitude A is expressed by The message signal, such as an audio signal that is used for modulating the carrier, is m ( t ), and has a frequency f m , much lower than f c : where m is the amplitude sensitivity, M is the amplitude of modulation. If m < 1, (1 + m(t)/A)

9408-431: Was not used at the receiver. Spark transmitters used for this method consumed a lot of bandwidth and caused interference, so it was discouraged by 1921. Most early telephone-line modems used audio frequency-shift keying (AFSK) to send and receive data at rates up to about 1200 bits per second. The Bell 103 and Bell 202 modems used this technique. Even today, North American caller ID uses 1200 baud AFSK in

9506-415: Was the earliest modulation method used for transmitting audio in radio broadcasting. It was developed during the first quarter of the 20th century beginning with Roberto Landell de Moura and Reginald Fessenden 's radiotelephone experiments in 1900. This original form of AM is sometimes called double-sideband amplitude modulation ( DSBAM ), because the standard method produces sidebands on either side of

9604-643: Was usually accomplished by a carbon microphone inserted directly in the antenna or ground wire; its varying resistance varied the current to the antenna. The limited power handling ability of the microphone severely limited the power of the first radiotelephones; many of the microphones were water-cooled. The 1912 discovery of the amplifying ability of the Audion tube , invented in 1906 by Lee de Forest , solved these problems. The vacuum tube feedback oscillator , invented in 1912 by Edwin Armstrong and Alexander Meissner ,

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