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114-632: KULA-LP (95.1 FM ) is a radio station licensed to serve Ili'ili, American Samoa . The station is owned by Pacific Islands Bible School. It airs a Religious radio format. The station was assigned the KULA-LP call letters by the Federal Communications Commission on September 9, 2002. This article about a radio station in American Samoa is a stub . You can help Misplaced Pages by expanding it . FM broadcasting Throughout

228-542: A density function multiplied by an infinitesimally small frequency interval, describing the energy contained in the signal at frequency f {\displaystyle f} in the frequency interval f + d f {\displaystyle f+df} . Therefore, the energy spectral density of x ( t ) {\displaystyle x(t)} is defined as: The function S ¯ x x ( f ) {\displaystyle {\bar {S}}_{xx}(f)} and

342-400: A dispersive prism is used to obtain a spectrum of light in a spectrograph , or when a sound is perceived through its effect on the auditory receptors of the inner ear, each of which is sensitive to a particular frequency. However this article concentrates on situations in which the time series is known (at least in a statistical sense) or directly measured (such as by a microphone sampled by

456-454: A transmission line of impedance Z {\displaystyle Z} , and suppose the line is terminated with a matched resistor (so that all of the pulse energy is delivered to the resistor and none is reflected back). By Ohm's law , the power delivered to the resistor at time t {\displaystyle t} is equal to V ( t ) 2 / Z {\displaystyle V(t)^{2}/Z} , so

570-456: A computer). The power spectrum is important in statistical signal processing and in the statistical study of stochastic processes , as well as in many other branches of physics and engineering . Typically the process is a function of time, but one can similarly discuss data in the spatial domain being decomposed in terms of spatial frequency . In physics , the signal might be a wave, such as an electromagnetic wave , an acoustic wave , or

684-1098: A discrete signal with a countably infinite number of values x n {\displaystyle x_{n}} such as a signal sampled at discrete times t n = t 0 + ( n Δ t ) {\displaystyle t_{n}=t_{0}+(n\,\Delta t)} : S ¯ x x ( f ) = lim N → ∞ ( Δ t ) 2 | ∑ n = − N N x n e − i 2 π f n Δ t | 2 ⏟ | x ^ d ( f ) | 2 , {\displaystyle {\bar {S}}_{xx}(f)=\lim _{N\to \infty }(\Delta t)^{2}\underbrace {\left|\sum _{n=-N}^{N}x_{n}e^{-i2\pi fn\,\Delta t}\right|^{2}} _{\left|{\hat {x}}_{d}(f)\right|^{2}},} where x ^ d ( f ) {\displaystyle {\hat {x}}_{d}(f)}

798-531: A measurement) that it could as well have been over an infinite time interval. The PSD then refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite. Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process), identical to what would be obtained by integrating x 2 ( t ) {\displaystyle x^{2}(t)} over

912-510: A monophonic broadcast, again the most common permitted maximum deviation is ±75 kHz. However, some countries specify a lower value for monophonic broadcasts, such as ±50 kHz. The bandwidth of an FM transmission is given by the Carson bandwidth rule which is the sum of twice the maximum deviation and twice the maximum modulating frequency. For a transmission that includes RDS this would be 2 × 75 kHz + 2 × 60 kHz  = 270 kHz . This

1026-403: A more accurate estimate of the theoretical PSD of the physical process underlying the individual measurements. This computed PSD is sometimes called a periodogram . This periodogram converges to the true PSD as the number of estimates as well as the averaging time interval T {\displaystyle T} approach infinity. If two signals both possess power spectral densities, then

1140-603: A periodic signal which is not simply sinusoidal. Or a continuous spectrum may show narrow frequency intervals which are strongly enhanced corresponding to resonances, or frequency intervals containing almost zero power as would be produced by a notch filter . The concept and use of the power spectrum of a signal is fundamental in electrical engineering , especially in electronic communication systems , including radio communications , radars , and related systems, plus passive remote sensing technology. Electronic instruments called spectrum analyzers are used to observe and measure

1254-557: A program feed for AM transmitters of AM/FM stations. SCA subcarriers are typically 67 kHz and 92 kHz. Initially the users of SCA services were private analog audio channels which could be used internally or leased, for example Muzak -type services. There were experiments with quadraphonic sound. If a station does not broadcast in stereo, everything from 23 kHz on up can be used for other services. The guard band around 19 kHz (±4 kHz) must still be maintained, so as not to trigger stereo decoders on receivers. If there

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1368-448: A single estimate of the PSD can be obtained through a finite number of samplings. As before, the actual PSD is achieved when N {\displaystyle N} (and thus T {\displaystyle T} ) approaches infinity and the expected value is formally applied. In a real-world application, one would typically average a finite-measurement PSD over many trials to obtain

1482-419: A single such time series, the estimated power spectrum will be very "noisy"; however this can be alleviated if it is possible to evaluate the expected value (in the above equation) using a large (or infinite) number of short-term spectra corresponding to statistical ensembles of realizations of x ( t ) {\displaystyle x(t)} evaluated over the specified time window. Just as with

1596-470: A studio-to-transmitter link system. In April 1935, the AM subcarriers were replaced by FM subcarriers, with much improved results. The first FM subcarrier transmissions emanating from Major Armstrong's experimental station KE2XCC at Alpine, New Jersey occurred in 1948. These transmissions consisted of two-channel audio programs, binaural audio programs and a fax program. The original subcarrier frequency used at KE2XCC

1710-480: A time-varying spectral density. In this case the time interval T {\displaystyle T} is finite rather than approaching infinity. This results in decreased spectral coverage and resolution since frequencies of less than 1 / T {\displaystyle 1/T} are not sampled, and results at frequencies which are not an integer multiple of 1 / T {\displaystyle 1/T} are not independent. Just using

1824-645: A total measurement period T = ( 2 N + 1 ) Δ t {\displaystyle T=(2N+1)\,\Delta t} . S x x ( f ) = lim N → ∞ ( Δ t ) 2 T | ∑ n = − N N x n e − i 2 π f n Δ t | 2 {\displaystyle S_{xx}(f)=\lim _{N\to \infty }{\frac {(\Delta t)^{2}}{T}}\left|\sum _{n=-N}^{N}x_{n}e^{-i2\pi fn\,\Delta t}\right|^{2}} Note that

1938-457: Is S x y ( f ) = ∑ n = − ∞ ∞ R x y ( τ n ) e − i 2 π f τ n Δ τ {\displaystyle S_{xy}(f)=\sum _{n=-\infty }^{\infty }R_{xy}(\tau _{n})e^{-i2\pi f\tau _{n}}\,\Delta \tau } The goal of spectral density estimation

2052-525: Is added. VHF radio waves usually do not travel far beyond the visual horizon , so reception distances for FM stations are typically limited to 30–40 miles (50–60 km). They can also be blocked by hills and to a lesser extent by buildings. Individuals with more-sensitive receivers or specialized antenna systems, or who are located in areas with more favorable topography, may be able to receive useful FM broadcast signals at considerably greater distances. The knife edge effect can permit reception where there

2166-422: Is also known as the necessary bandwidth . Random noise has a triangular spectral distribution in an FM system, with the effect that noise occurs predominantly at the higher audio frequencies within the baseband . This can be offset, to a limited extent, by boosting the high frequencies before transmission and reducing them by a corresponding amount in the receiver. Reducing the high audio frequencies in

2280-408: Is amplitude modulated onto a 38 kHz double-sideband suppressed-carrier (DSB-SC) signal, thus occupying 23 kHz to 53 kHz. A 19 kHz ± 2 Hz pilot tone , at exactly half the 38 kHz sub-carrier frequency and with a precise phase relationship to it, as defined by the formula below, is also generated. The pilot is transmitted at 8–10% of overall modulation level and used by

2394-422: Is authorized for "hybrid" mode operation, wherein both the conventional analog FM carrier and digital sideband subcarriers are transmitted. The output power of an FM broadcasting transmitter is one of the parameters that governs how far a transmission will cover. The other important parameters are the height of the transmitting antenna and the antenna gain . Transmitter powers should be carefully chosen so that

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2508-408: Is called its spectrum . When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density . More commonly used is the power spectral density (PSD, or simply power spectrum ), which applies to signals existing over all time, or over a time period large enough (especially in relation to the duration of

2622-1399: Is denoted as R x x ( τ ) {\displaystyle R_{xx}(\tau )} , provided that x ( t ) {\displaystyle x(t)} is ergodic , which is true in most, but not all, practical cases. lim T → ∞ 1 T | x ^ T ( f ) | 2 = ∫ − ∞ ∞ [ lim T → ∞ 1 T ∫ − ∞ ∞ x T ∗ ( t − τ ) x T ( t ) d t ] e − i 2 π f τ   d τ = ∫ − ∞ ∞ R x x ( τ ) e − i 2 π f τ d τ {\displaystyle \lim _{T\to \infty }{\frac {1}{T}}\left|{\hat {x}}_{T}(f)\right|^{2}=\int _{-\infty }^{\infty }\left[\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }x_{T}^{*}(t-\tau )x_{T}(t)dt\right]e^{-i2\pi f\tau }\ d\tau =\int _{-\infty }^{\infty }R_{xx}(\tau )e^{-i2\pi f\tau }d\tau } From here we see, again assuming

2736-581: Is designed to be capable of use alongside ARI despite using identical subcarrier frequencies. In the United States and Canada , digital radio services are deployed within the FM band rather than using Eureka 147 or the Japanese standard ISDB . This in-band on-channel approach, as do all digital radio techniques, makes use of advanced compressed audio . The proprietary iBiquity system, branded as HD Radio ,

2850-454: Is determined by the spectrum of the electromagnetic wave's electric field E ( t ) {\displaystyle E(t)} as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform , and generalizations based on Fourier analysis. In many cases the time domain is not specifically employed in practice, such as when

2964-480: Is mainly the preserve of talk radio, news, sports, religious programming, ethnic (minority language) broadcasting and some types of minority interest music. This shift has transformed AM into the "alternative band" that FM once was. (Some AM stations have begun to simulcast on, or switch to, FM signals to attract younger listeners and aid reception problems in buildings, during thunderstorms, and near high-voltage wires. Some of these stations now emphasize their presence on

3078-975: Is most suitable for transients—that is, pulse-like signals—having a finite total energy. Finite or not, Parseval's theorem (or Plancherel's theorem) gives us an alternate expression for the energy of the signal: ∫ − ∞ ∞ | x ( t ) | 2 d t = ∫ − ∞ ∞ | x ^ ( f ) | 2 d f , {\displaystyle \int _{-\infty }^{\infty }|x(t)|^{2}\,dt=\int _{-\infty }^{\infty }\left|{\hat {x}}(f)\right|^{2}\,df,} where: x ^ ( f ) ≜ ∫ − ∞ ∞ e − i 2 π f t x ( t )   d t {\displaystyle {\hat {x}}(f)\triangleq \int _{-\infty }^{\infty }e^{-i2\pi ft}x(t)\ dt}

3192-671: Is no direct line of sight between broadcaster and receiver. The reception can vary considerably depending on the position. One example is the Učka mountain range, which makes constant reception of Italian signals from Veneto and Marche possible in a good portion of Rijeka , Croatia, despite the distance being over 200 km (125 miles). Other radio propagation effects such as tropospheric ducting and Sporadic E can occasionally allow distant stations to be intermittently received over very large distances (hundreds of miles), but cannot be relied on for commercial broadcast purposes. Good reception across

3306-487: Is only suitable for text. A few proprietary systems are used for private communications. A variant of RDS is the North American RBDS or "smart radio" system. In Germany the analog ARI system was used prior to RDS to alert motorists that traffic announcements were broadcast (without disturbing other listeners). Plans to use ARI for other European countries led to the development of RDS as a more powerful system. RDS

3420-424: Is open to anyone who does not carry a prohibition and can put up the appropriate licensing and royalty fees. In 2010 around 450 such licences were issued. Frequency spectrum In signal processing , the power spectrum S x x ( f ) {\displaystyle S_{xx}(f)} of a continuous time signal x ( t ) {\displaystyle x(t)} describes

3534-504: Is performed by a decoder, built into stereo receivers. Again, the decoder can use a switching technique to recover the left and right channels. In addition, for a given RF level at the receiver, the signal-to-noise ratio and multipath distortion for the stereo signal will be worse than for the mono receiver. For this reason many stereo FM receivers include a stereo/mono switch to allow listening in mono when reception conditions are less than ideal, and most car radios are arranged to reduce

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3648-1362: Is possible to define a cross power spectral density ( CPSD ) or cross spectral density ( CSD ). To begin, let us consider the average power of such a combined signal. P = lim T → ∞ 1 T ∫ − ∞ ∞ [ x T ( t ) + y T ( t ) ] ∗ [ x T ( t ) + y T ( t ) ] d t = lim T → ∞ 1 T ∫ − ∞ ∞ | x T ( t ) | 2 + x T ∗ ( t ) y T ( t ) + y T ∗ ( t ) x T ( t ) + | y T ( t ) | 2 d t {\displaystyle {\begin{aligned}P&=\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }\left[x_{T}(t)+y_{T}(t)\right]^{*}\left[x_{T}(t)+y_{T}(t)\right]dt\\&=\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }|x_{T}(t)|^{2}+x_{T}^{*}(t)y_{T}(t)+y_{T}^{*}(t)x_{T}(t)+|y_{T}(t)|^{2}dt\\\end{aligned}}} Using

3762-554: Is related to the transmitter 's RF power, the antenna gain , and antenna height . Interference from other stations is also a factor in some places. In the U.S, the FCC publishes curves that aid in calculation of this maximum distance as a function of signal strength at the receiving location. Computer modelling is more commonly used for this around the world. Many FM stations, especially those located in severe multipath areas, use extra audio compression /processing to keep essential sound above

3876-412: Is simply reckoned in terms of the square of the signal, as this would always be proportional to the actual power delivered by that signal into a given impedance . So one might use units of V  Hz for the PSD. Energy spectral density (ESD) would have units of V  s Hz , since energy has units of power multiplied by time (e.g., watt-hour ). In the general case, the units of PSD will be

3990-626: Is stereo, there will typically be a guard band between the upper limit of the DSBSC stereo signal (53 kHz) and the lower limit of any other subcarrier. Digital data services are also available. A 57 kHz subcarrier ( phase locked to the third harmonic of the stereo pilot tone) is used to carry a low-bandwidth digital Radio Data System signal, providing extra features such as station name, alternative frequency (AF), traffic data for satellite navigation systems and radio text (RT). This narrowband signal runs at only 1,187.5 bits per second , thus

4104-446: Is the cross-correlation of x ( t ) {\displaystyle x(t)} with y ( t ) {\displaystyle y(t)} and R y x ( τ ) {\displaystyle R_{yx}(\tau )} is the cross-correlation of y ( t ) {\displaystyle y(t)} with x ( t ) {\displaystyle x(t)} . In light of this,

4218-418: Is the discrete-time Fourier transform of x n . {\displaystyle x_{n}.}   The sampling interval Δ t {\displaystyle \Delta t} is needed to keep the correct physical units and to ensure that we recover the continuous case in the limit Δ t → 0. {\displaystyle \Delta t\to 0.}   But in

4332-559: Is the periodogram . The spectral density is usually estimated using Fourier transform methods (such as the Welch method ), but other techniques such as the maximum entropy method can also be used. Any signal that can be represented as a variable that varies in time has a corresponding frequency spectrum. This includes familiar entities such as visible light (perceived as color ), musical notes (perceived as pitch ), radio/TV (specified by their frequency, or sometimes wavelength ) and even

4446-541: Is the value of the Fourier transform of x ( t ) {\displaystyle x(t)} at frequency f {\displaystyle f} (in Hz ). The theorem also holds true in the discrete-time cases. Since the integral on the left-hand side is the energy of the signal, the value of | x ^ ( f ) | 2 d f {\displaystyle \left|{\hat {x}}(f)\right|^{2}df} can be interpreted as

4560-402: Is then estimated to be E ( f ) / Δ f {\displaystyle E(f)/\Delta f} . In this example, since the power V ( t ) 2 / Z {\displaystyle V(t)^{2}/Z} has units of V Ω , the energy E ( f ) {\displaystyle E(f)} has units of V  s Ω  = J , and hence

4674-418: Is to estimate the spectral density of a random signal from a sequence of time samples. Depending on what is known about the signal, estimation techniques can involve parametric or non-parametric approaches, and may be based on time-domain or frequency-domain analysis. For example, a common parametric technique involves fitting the observations to an autoregressive model . A common non-parametric technique

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4788-430: Is unity within the arbitrary period and zero elsewhere. P = lim T → ∞ 1 T ∫ − ∞ ∞ | x T ( t ) | 2 d t . {\displaystyle P=\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }\left|x_{T}(t)\right|^{2}\,dt.} Clearly, in cases where

4902-427: Is used. This applies to both mono and stereo transmissions. For stereo, pre-emphasis is applied to the left and right channels before multiplexing . The use of pre-emphasis becomes a problem because many forms of contemporary music contain more high-frequency energy than the musical styles which prevailed at the birth of FM broadcasting. Pre-emphasizing these high-frequency sounds would cause excessive deviation of

5016-447: The power spectra of signals. The spectrum analyzer measures the magnitude of the short-time Fourier transform (STFT) of an input signal. If the signal being analyzed can be considered a stationary process, the STFT is a good smoothed estimate of its power spectral density. Primordial fluctuations , density variations in the early universe, are quantified by a power spectrum which gives

5130-580: The Light Programme , Third Programme and Home Service . These three networks used the sub-band 88.0–94.6 MHz. The sub-band 94.6–97.6 MHz was later used for BBC and local commercial services. However, only when commercial broadcasting was introduced to the UK in 1973 did the use of FM pick up in Britain. With the gradual clearance of other users (notably Public Services such as police, fire and ambulance) and

5244-498: The autocorrelation of x ( t ) {\displaystyle x(t)} form a Fourier transform pair, a result also known as the Wiener–Khinchin theorem (see also Periodogram ). As a physical example of how one might measure the energy spectral density of a signal, suppose V ( t ) {\displaystyle V(t)} represents the potential (in volts ) of an electrical pulse propagating along

5358-443: The convolution theorem has been used when passing from the 3rd to the 4th line. Now, if we divide the time convolution above by the period T {\displaystyle T} and take the limit as T → ∞ {\displaystyle T\rightarrow \infty } , it becomes the autocorrelation function of the non-windowed signal x ( t ) {\displaystyle x(t)} , which

5472-593: The cross-spectral density can similarly be calculated; as the PSD is related to the autocorrelation, so is the cross-spectral density related to the cross-correlation . Some properties of the PSD include: Given two signals x ( t ) {\displaystyle x(t)} and y ( t ) {\displaystyle y(t)} , each of which possess power spectral densities S x x ( f ) {\displaystyle S_{xx}(f)} and S y y ( f ) {\displaystyle S_{yy}(f)} , it

5586-591: The energy of a signal or a time series is distributed with frequency. Here, the term energy is used in the generalized sense of signal processing; that is, the energy E {\displaystyle E} of a signal x ( t ) {\displaystyle x(t)} is: E ≜ ∫ − ∞ ∞ | x ( t ) | 2   d t . {\displaystyle E\triangleq \int _{-\infty }^{\infty }\left|x(t)\right|^{2}\ dt.} The energy spectral density

5700-400: The power spectral density (PSD) which exists for stationary processes ; this describes how the power of a signal or time series is distributed over frequency, as in the simple example given previously. Here, power can be the actual physical power, or more often, for convenience with abstract signals, is simply identified with the squared value of the signal. For example, statisticians study

5814-470: The variance of a function over time x ( t ) {\displaystyle x(t)} (or over another independent variable), and using an analogy with electrical signals (among other physical processes), it is customary to refer to it as the power spectrum even when there is no physical power involved. If one were to create a physical voltage source which followed x ( t ) {\displaystyle x(t)} and applied it to

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5928-492: The 1970s and 1980s: A commercially unsuccessful noise reduction system used with FM radio in some countries during the late 1970s, Dolby FM was similar to Dolby B but used a modified 25 μs pre-emphasis time constant and a frequency selective companding arrangement to reduce noise. The pre-emphasis change compensates for the excess treble response that otherwise would make listening difficult for those without Dolby decoders. A similar system named High Com FM

6042-638: The FCC announced the reassignment of the FM band to 90 channels from 88–106 MHz (which was soon expanded to 100 channels from 88–108 MHz). This shift, which the AM-broadcaster RCA had pushed for, made all the Armstrong-era FM receivers useless and delayed the expansion of FM. In 1961 WEFM (in the Chicago area) and WGFM (in Schenectady, New York ) were reported as the first stereo stations. By

6156-699: The FCC rules do not allow this mode of stereo operation. In 1969, Louis Dorren invented the Quadraplex system of single station, discrete, compatible four-channel FM broadcasting. There are two additional subcarriers in the Quadraplex system, supplementing the single one used in standard stereo FM. The baseband layout is as follows: The normal stereo signal can be considered as switching between left and right channels at 38 kHz, appropriately band-limited. The quadraphonic signal can be considered as cycling through LF, LR, RF, RR, at 76 kHz. Early efforts to transmit discrete four-channel quadraphonic music required

6270-567: The FCC. The original Dorren Quadraplex System outperformed all the others and was chosen as the national standard for Quadraphonic FM broadcasting in the United States. The first commercial FM station to broadcast quadraphonic program content was WIQB (now called WWWW-FM ) in Ann Arbor / Saline, Michigan under the guidance of Chief Engineer Brian Jeffrey Brown. Various attempts to add analog noise reduction to FM broadcasting were carried out in

6384-451: The FM carrier . Modulation control (limiter) devices are used to prevent this. Systems more modern than FM broadcasting tend to use either programme-dependent variable pre-emphasis; e.g., dbx in the BTSC TV sound system, or none at all. Pre-emphasis and de-emphasis was used in the earliest days of FM broadcasting. According to a BBC report from 1946, 100 μs was originally considered in

6498-511: The FM band.) The medium wave band (known as the AM band because most stations using it employ amplitude modulation) was overcrowded in western Europe, leading to interference problems and, as a result, many MW frequencies are suitable only for speech broadcasting. Belgium , the Netherlands , Denmark and particularly Germany were among the first countries to adopt FM on a widespread scale. Among

6612-969: The FM radio band from 87.5-108.0 MHz to 76.1-108.0 MHz to enable the migration of AM radio stations in Brazilian capitals and large cities. FM broadcasting began in the late 1930s, when it was initiated by a handful of early pioneer experimental stations, including W1XOJ/W43B/WGTR (shut down in 1953) and W1XTG/ WSRS , both transmitting from Paxton, Massachusetts (now listed as Worcester, Massachusetts ); W1XSL/W1XPW/W65H/WDRC-FM/WFMQ/WHCN , Meriden, Connecticut; and W2XMN , KE2XCC , and WFMN , Alpine, New Jersey (owned by Edwin Armstrong himself, closed down upon Armstrong's death in 1954). Also of note were General Electric stations W2XDA Schenectady and W2XOY New Scotland, New York—two experimental FM transmitters on 48.5 MHz—which signed on in 1939. The two began regular programming, as W2XOY, on November 20, 1940. Over

6726-564: The Fourier transform does not formally exist. Regardless, Parseval's theorem tells us that we can re-write the average power as follows. P = lim T → ∞ 1 T ∫ − ∞ ∞ | x ^ T ( f ) | 2 d f {\displaystyle P=\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }|{\hat {x}}_{T}(f)|^{2}\,df} Then

6840-460: The L+R signal so the listener will hear both channels through the single loudspeaker. A stereo receiver will add the difference signal to the sum signal to recover the left channel, and subtract the difference signal from the sum to recover the right channel. The (L+R) signal is limited to 30 Hz to 15 kHz to protect a 19 kHz pilot signal. The (L−R) signal, which is also limited to 15 kHz,

6954-701: The PSD is seen to be a special case of the CSD for x ( t ) = y ( t ) {\displaystyle x(t)=y(t)} . If x ( t ) {\displaystyle x(t)} and y ( t ) {\displaystyle y(t)} are real signals (e.g. voltage or current), their Fourier transforms x ^ ( f ) {\displaystyle {\hat {x}}(f)} and y ^ ( f ) {\displaystyle {\hat {y}}(f)} are usually restricted to positive frequencies by convention. Therefore, in typical signal processing,

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7068-674: The US, but 75 μs subsequently adopted. Long before FM stereo transmission was considered, FM multiplexing of other types of audio-level information was experimented with. Edwin Armstrong, who invented FM, was the first to experiment with multiplexing, at his experimental 41 MHz station W2XDG located on the 85th floor of the Empire State Building in New York City . These FM multiplex transmissions started in November 1934 and consisted of

7182-526: The above expression for P is non-zero, the integral must grow without bound as T grows without bound. That is the reason why we cannot use the energy of the signal, which is that diverging integral, in such cases. In analyzing the frequency content of the signal x ( t ) {\displaystyle x(t)} , one might like to compute the ordinary Fourier transform x ^ ( f ) {\displaystyle {\hat {x}}(f)} ; however, for many signals of interest

7296-454: The assigned frequency. There are other unusual and obsolete FM broadcasting standards in some countries, with non-standard spacings of 1, 10, 30, 74, 500, and 300 kHz. To minimise inter-channel interference, stations operating from the same or nearby transmitter sites tend to keep to at least a 500 kHz frequency separation even when closer frequency spacing is technically permitted. The ITU publishes Protection Ratio graphs, which give

7410-511: The background noise for listeners, often at the expense of overall perceived sound quality. In such instances, however, this technique is often surprisingly effective in increasing the station's useful range. The first radio station to broadcast in FM in Brazil was Rádio Imprensa, which began broadcasting in Rio de Janeiro in 1955, on the 102.1 MHz frequency, founded by businesswoman Anna Khoury. Due to

7524-402: The carrier, with its frequency remaining constant. With FM, frequency deviation from the assigned carrier frequency at any instant is directly proportional to the amplitude of the (audio) input signal, determining the instantaneous frequency of the transmitted signal. Because transmitted FM signals use significantly more bandwidth than AM signals, this form of modulation is commonly used with

7638-4010: The complex conjugate. Taking into account that F { x T ∗ ( − t ) } = ∫ − ∞ ∞ x T ∗ ( − t ) e − i 2 π f t d t = ∫ − ∞ ∞ x T ∗ ( t ) e i 2 π f t d t = ∫ − ∞ ∞ x T ∗ ( t ) [ e − i 2 π f t ] ∗ d t = [ ∫ − ∞ ∞ x T ( t ) e − i 2 π f t d t ] ∗ = [ F { x T ( t ) } ] ∗ = [ x ^ T ( f ) ] ∗ {\displaystyle {\begin{aligned}{\mathcal {F}}\left\{x_{T}^{*}(-t)\right\}&=\int _{-\infty }^{\infty }x_{T}^{*}(-t)e^{-i2\pi ft}dt\\&=\int _{-\infty }^{\infty }x_{T}^{*}(t)e^{i2\pi ft}dt\\&=\int _{-\infty }^{\infty }x_{T}^{*}(t)[e^{-i2\pi ft}]^{*}dt\\&=\left[\int _{-\infty }^{\infty }x_{T}(t)e^{-i2\pi ft}dt\right]^{*}\\&=\left[{\mathcal {F}}\left\{x_{T}(t)\right\}\right]^{*}\\&=\left[{\hat {x}}_{T}(f)\right]^{*}\end{aligned}}} and making, u ( t ) = x T ∗ ( − t ) {\displaystyle u(t)=x_{T}^{*}(-t)} , we have: | x ^ T ( f ) | 2 = [ x ^ T ( f ) ] ∗ ⋅ x ^ T ( f ) = F { x T ∗ ( − t ) } ⋅ F { x T ( t ) } = F { u ( t ) } ⋅ F { x T ( t ) } = F { u ( t ) ∗ x T ( t ) } = ∫ − ∞ ∞ [ ∫ − ∞ ∞ u ( τ − t ) x T ( t ) d t ] e − i 2 π f τ d τ = ∫ − ∞ ∞ [ ∫ − ∞ ∞ x T ∗ ( t − τ ) x T ( t ) d t ] e − i 2 π f τ   d τ , {\displaystyle {\begin{aligned}\left|{\hat {x}}_{T}(f)\right|^{2}&=[{\hat {x}}_{T}(f)]^{*}\cdot {\hat {x}}_{T}(f)\\&={\mathcal {F}}\left\{x_{T}^{*}(-t)\right\}\cdot {\mathcal {F}}\left\{x_{T}(t)\right\}\\&={\mathcal {F}}\left\{u(t)\right\}\cdot {\mathcal {F}}\left\{x_{T}(t)\right\}\\&={\mathcal {F}}\left\{u(t)\mathbin {\mathbf {*} } x_{T}(t)\right\}\\&=\int _{-\infty }^{\infty }\left[\int _{-\infty }^{\infty }u(\tau -t)x_{T}(t)dt\right]e^{-i2\pi f\tau }d\tau \\&=\int _{-\infty }^{\infty }\left[\int _{-\infty }^{\infty }x_{T}^{*}(t-\tau )x_{T}(t)dt\right]e^{-i2\pi f\tau }\ d\tau ,\end{aligned}}} where

7752-423: The contributions of S x x ( f ) {\displaystyle S_{xx}(f)} and S y y ( f ) {\displaystyle S_{yy}(f)} are already understood. Note that S x y ∗ ( f ) = S y x ( f ) {\displaystyle S_{xy}^{*}(f)=S_{yx}(f)} , so the full contribution to

7866-431: The country is one of the main advantages over DAB/+ radio . This is still less than the range of AM radio waves, which because of their lower frequencies can travel as ground waves or reflect off the ionosphere , so AM radio stations can be received at hundreds (sometimes thousands) of miles. This is a property of the carrier wave's typical frequency (and power), not its mode of modulation. The range of FM transmission

7980-2372: The cross power is, generally, from twice the real part of either individual CPSD . Just as before, from here we recast these products as the Fourier transform of a time convolution, which when divided by the period and taken to the limit T → ∞ {\displaystyle T\to \infty } becomes the Fourier transform of a cross-correlation function. S x y ( f ) = ∫ − ∞ ∞ [ lim T → ∞ 1 T ∫ − ∞ ∞ x T ∗ ( t − τ ) y T ( t ) d t ] e − i 2 π f τ d τ = ∫ − ∞ ∞ R x y ( τ ) e − i 2 π f τ d τ S y x ( f ) = ∫ − ∞ ∞ [ lim T → ∞ 1 T ∫ − ∞ ∞ y T ∗ ( t − τ ) x T ( t ) d t ] e − i 2 π f τ d τ = ∫ − ∞ ∞ R y x ( τ ) e − i 2 π f τ d τ , {\displaystyle {\begin{aligned}S_{xy}(f)&=\int _{-\infty }^{\infty }\left[\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }x_{T}^{*}(t-\tau )y_{T}(t)dt\right]e^{-i2\pi f\tau }d\tau =\int _{-\infty }^{\infty }R_{xy}(\tau )e^{-i2\pi f\tau }d\tau \\S_{yx}(f)&=\int _{-\infty }^{\infty }\left[\lim _{T\to \infty }{\frac {1}{T}}\int _{-\infty }^{\infty }y_{T}^{*}(t-\tau )x_{T}(t)dt\right]e^{-i2\pi f\tau }d\tau =\int _{-\infty }^{\infty }R_{yx}(\tau )e^{-i2\pi f\tau }d\tau ,\end{aligned}}} where R x y ( τ ) {\displaystyle R_{xy}(\tau )}

8094-401: The distribution of power into frequency components f {\displaystyle f} composing that signal. According to Fourier analysis , any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of any sort of signal (including noise ) as analyzed in terms of its frequency content,

8208-524: The energy spectral density, the definition of the power spectral density can be generalized to discrete time variables x n {\displaystyle x_{n}} . As before, we can consider a window of − N ≤ n ≤ N {\displaystyle -N\leq n\leq N} with the signal sampled at discrete times t n = t 0 + ( n Δ t ) {\displaystyle t_{n}=t_{0}+(n\,\Delta t)} for

8322-891: The ergodicity of x ( t ) {\displaystyle x(t)} , that the power spectral density can be found as the Fourier transform of the autocorrelation function ( Wiener–Khinchin theorem ). Many authors use this equality to actually define the power spectral density. The power of the signal in a given frequency band [ f 1 , f 2 ] {\displaystyle [f_{1},f_{2}]} , where 0 < f 1 < f 2 {\displaystyle 0<f_{1}<f_{2}} , can be calculated by integrating over frequency. Since S x x ( − f ) = S x x ( f ) {\displaystyle S_{xx}(-f)=S_{xx}(f)} , an equal amount of power can be attributed to positive and negative frequency bands, which accounts for

8436-425: The estimate E ( f ) / Δ f {\displaystyle E(f)/\Delta f} of the energy spectral density has units of J Hz , as required. In many situations, it is common to forget the step of dividing by Z {\displaystyle Z} so that the energy spectral density instead has units of V  Hz . This definition generalizes in a straightforward manner to

8550-553: The extension of the FM band to 108.0 MHz between 1980 and 1995, FM expanded rapidly throughout the British Isles and effectively took over from LW and MW as the delivery platform of choice for fixed and portable domestic and vehicle-based receivers. In addition, Ofcom (previously the Radio Authority) in the UK issues on demand Restricted Service Licences on FM and also on AM (MW) for short-term local-coverage broadcasting which

8664-404: The factor of 2 in the following form (such trivial factors depend on the conventions used): P bandlimited = 2 ∫ f 1 f 2 S x x ( f ) d f {\displaystyle P_{\textsf {bandlimited}}=2\int _{f_{1}}^{f_{2}}S_{xx}(f)\,df} More generally, similar techniques may be used to estimate

8778-458: The full CPSD is just one of the CPSD s scaled by a factor of two. CPSD Full = 2 S x y ( f ) = 2 S y x ( f ) {\displaystyle \operatorname {CPSD} _{\text{Full}}=2S_{xy}(f)=2S_{yx}(f)} For discrete signals x n and y n , the relationship between the cross-spectral density and the cross-covariance

8892-505: The high import costs of FM radio receivers, transmissions were carried out in circuit closed to businesses and stores, which played ambient music offered by radio. Until 1976, Rádio Imprensa was the only station operating in FM in Brazil. From the second half of the 1970s onwards, FM radio stations began to become popular in Brazil, causing AM radio to gradually lose popularity. In 2021, the Brazilian Ministry of Communications expanded

9006-467: The higher ( VHF or UHF ) frequencies used by TV , the FM broadcast band , and land mobile radio systems . The maximum frequency deviation of the carrier is usually specified and regulated by the licensing authorities in each country. For a stereo broadcast, the maximum permitted carrier deviation is invariably ±75 kHz, although a little higher is permitted in the United States when SCA systems are used. For

9120-496: The import of vehicles, principally from the United States, with radios that can only tune to these frequencies. In some parts of Europe , Greenland , and Africa , only even multiples are used. In the United Kingdom , both odd and even are used. In Italy , multiples of 50 kHz are used. In most countries the maximum permitted frequency error of the unmodulated carrier is specified, which typically should be within 2 kHz of

9234-517: The late 1960s, FM had been adopted for broadcast of stereo "A.O.R.—' Album Oriented Rock ' Format", but it was not until 1978 that listenership to FM stations exceeded that of AM stations in North America. In most of the 70s FM was seen as highbrow radio associated with educational programming and classical music, which changed during the 1980s and 1990s when Top 40 music stations and later even country music stations largely abandoned AM for FM. Today AM

9348-516: The main channel audio program and three subcarriers : a fax program, a synchronizing signal for the fax program and a telegraph order channel. These original FM multiplex subcarriers were amplitude modulated. Two musical programs, consisting of both the Red and Blue Network program feeds of the NBC Radio Network, were simultaneously transmitted using the same system of subcarrier modulation as part of

9462-564: The main channel signal-to-noise ratio. The GE and Zenith systems, so similar that they were considered theoretically identical, were formally approved by the FCC in April 1961 as the standard stereo FM broadcasting method in the United States and later adopted by most other countries. It is important that stereo broadcasts be compatible with mono receivers. For this reason, the left (L) and right (R) channels are algebraically encoded into sum (L+R) and difference (L−R) signals. A mono receiver will use just

9576-422: The mathematical sciences the interval is often set to 1, which simplifies the results at the expense of generality. (also see normalized frequency ) The above definition of energy spectral density is suitable for transients (pulse-like signals) whose energy is concentrated around one time window; then the Fourier transforms of the signals generally exist. For continuous signals over all time, one must rather define

9690-405: The minimum spacing between frequencies based on their relative strengths. Only broadcast stations with large enough geographic separations between their coverage areas can operate on the same or close frequencies. Frequency modulation or FM is a form of modulation which conveys information by varying the frequency of a carrier wave ; the older amplitude modulation or AM varies the amplitude of

9804-536: The next few years this station operated under the call signs W57A, W87A and WGFM, and moved to 99.5 MHz when the FM band was relocated to the 88–108 MHz portion of the radio spectrum. General Electric sold the station in the 1980s. Today this station is WRVE . Other pioneers included W2XQR/W59NY/WQXQ/WQXR-FM , New York; W47NV/WSM-FM Nashville, Tennessee (signed off in 1951); W1XER/W39B/WMNE , with studios in Boston and later Portland, Maine, but whose transmitter

9918-433: The originating station. The Crosby system was rejected by the FCC because it was incompatible with existing subsidiary communications authorization (SCA) services which used various subcarrier frequencies including 41 and 67 kHz. Many revenue-starved FM stations used SCAs for "storecasting" and other non-broadcast purposes. The Halstead system was rejected due to lack of high frequency stereo separation and reduction in

10032-568: The period T {\displaystyle T} is centered about some arbitrary time t = t 0 {\displaystyle t=t_{0}} : P = lim T → ∞ 1 T ∫ t 0 − T / 2 t 0 + T / 2 | x ( t ) | 2 d t {\displaystyle P=\lim _{T\to \infty }{\frac {1}{T}}\int _{t_{0}-T/2}^{t_{0}+T/2}\left|x(t)\right|^{2}\,dt} However, for

10146-563: The power spectral density is simply defined as the integrand above. From here, due to the convolution theorem , we can also view | x ^ T ( f ) | 2 {\displaystyle |{\hat {x}}_{T}(f)|^{2}} as the Fourier transform of the time convolution of x T ∗ ( − t ) {\displaystyle x_{T}^{*}(-t)} and x T ( t ) {\displaystyle x_{T}(t)} , where * represents

10260-415: The ratio of units of variance per unit of frequency; so, for example, a series of displacement values (in meters) over time (in seconds) will have PSD in units of meters squared per hertz, m /Hz. In the analysis of random vibrations , units of g  Hz are frequently used for the PSD of acceleration , where g denotes the g-force . Mathematically, it is not necessary to assign physical dimensions to

10374-551: The reasons for this were: Public service broadcasters in Ireland and Australia were far slower at adopting FM radio than those in either North America or continental Europe . Hans Idzerda operated a broadcasting station, PCGG , at The Hague from 1919 to 1924, which employed narrow-band FM transmissions. In the United Kingdom the BBC conducted tests during the 1940s, then began FM broadcasting in 1955, with three national networks:

10488-451: The receiver also reduces the high-frequency noise. These processes of boosting and then reducing certain frequencies are known as pre-emphasis and de-emphasis , respectively. The amount of pre-emphasis and de-emphasis used is defined by the time constant of a simple RC filter circuit. In most of the world a 50  μs time constant is used. In the Americas and South Korea , 75 μs

10602-515: The receiver to identify a stereo transmission and to regenerate the 38 kHz sub-carrier with the correct phase. The composite stereo multiplex signal contains the Main Channel (L+R), the pilot tone, and the (L−R) difference signal. This composite signal, along with any other sub-carriers, modulates the FM transmitter. The terms composite , multiplex and even MPX are used interchangeably to describe this signal. The instantaneous deviation of

10716-404: The regular rotation of the earth. When these signals are viewed in the form of a frequency spectrum, certain aspects of the received signals or the underlying processes producing them are revealed. In some cases the frequency spectrum may include a distinct peak corresponding to a sine wave component. And additionally there may be peaks corresponding to harmonics of a fundamental peak, indicating

10830-570: The required area is covered without causing interference to other stations further away. Practical transmitter powers range from a few milliwatts to 80 kW. As transmitter powers increase above a few kilowatts, the operating costs become high and only viable for large stations. The efficiency of larger transmitters is now better than 70% (AC power in to RF power out) for FM-only transmission. This compares to 50% before high efficiency switch-mode power supplies and LDMOS amplifiers were used. Efficiency drops dramatically if any digital HD Radio service

10944-400: The resulting signal is that it alternates between left and right at 38 kHz, with the phase determined by the 19 kHz pilot signal. Most stereo encoders use this switching technique to generate the 38 kHz subcarrier, but practical encoder designs need to incorporate circuitry to deal with the switching harmonics. Converting the multiplex signal back into left and right audio signals

11058-475: The sake of dealing with the math that follows, it is more convenient to deal with time limits in the signal itself rather than time limits in the bounds of the integral. As such, we have an alternative representation of the average power, where x T ( t ) = x ( t ) w T ( t ) {\displaystyle x_{T}(t)=x(t)w_{T}(t)} and w T ( t ) {\displaystyle w_{T}(t)}

11172-961: The same notation and methods as used for the power spectral density derivation, we exploit Parseval's theorem and obtain S x y ( f ) = lim T → ∞ 1 T [ x ^ T ∗ ( f ) y ^ T ( f ) ] S y x ( f ) = lim T → ∞ 1 T [ y ^ T ∗ ( f ) x ^ T ( f ) ] {\displaystyle {\begin{aligned}S_{xy}(f)&=\lim _{T\to \infty }{\frac {1}{T}}\left[{\hat {x}}_{T}^{*}(f){\hat {y}}_{T}(f)\right]&S_{yx}(f)&=\lim _{T\to \infty }{\frac {1}{T}}\left[{\hat {y}}_{T}^{*}(f){\hat {x}}_{T}(f)\right]\end{aligned}}} where, again,

11286-415: The separation as the signal-to-noise ratio worsens, eventually going to mono while still indicating a stereo signal is received. As with monaural transmission, it is normal practice to apply pre-emphasis to the left and right channels before encoding and to apply de-emphasis at the receiver after decoding. In the U.S. around 2010, using single-sideband modulation for the stereo subcarrier was proposed. It

11400-479: The signal or to the independent variable. In the following discussion the meaning of x ( t ) will remain unspecified, but the independent variable will be assumed to be that of time. A PSD can be either a one-sided function of only positive frequencies or a two-sided function of both positive and negative frequencies but with only half the amplitude. Noise PSDs are generally one-sided in engineering and two-sided in physics. Energy spectral density describes how

11514-424: The terminals of a one ohm resistor , then indeed the instantaneous power dissipated in that resistor would be given by x 2 ( t ) {\displaystyle x^{2}(t)} watts . The average power P {\displaystyle P} of a signal x ( t ) {\displaystyle x(t)} over all time is therefore given by the following time average, where

11628-406: The time domain, as dictated by Parseval's theorem . The spectrum of a physical process x ( t ) {\displaystyle x(t)} often contains essential information about the nature of x {\displaystyle x} . For instance, the pitch and timbre of a musical instrument are immediately determined from a spectral analysis. The color of a light source

11742-516: The top 25 U.S. radio markets to transmit in Quadraplex. The test results hopefully would prove to the FCC that the system was compatible with existing two-channel stereo transmission and reception and that it did not interfere with adjacent stations. There were several variations on this system submitted by GE, Zenith, RCA, and Denon for testing and consideration during the National Quadraphonic Radio Committee field trials for

11856-445: The total energy is found by integrating V ( t ) 2 / Z {\displaystyle V(t)^{2}/Z} with respect to time over the duration of the pulse. To find the value of the energy spectral density S ¯ x x ( f ) {\displaystyle {\bar {S}}_{xx}(f)} at frequency f {\displaystyle f} , one could insert between

11970-422: The transmission line and the resistor a bandpass filter which passes only a narrow range of frequencies ( Δ f {\displaystyle \Delta f} , say) near the frequency of interest and then measure the total energy E ( f ) {\displaystyle E(f)} dissipated across the resistor. The value of the energy spectral density at f {\displaystyle f}

12084-423: The transmitter carrier frequency due to the stereo audio and pilot tone (at 10% modulation) is where A and B are the pre-emphasized left and right audio signals and f p {\displaystyle f_{p}} =19 kHz is the frequency of the pilot tone. Slight variations in the peak deviation may occur in the presence of other subcarriers or because of local regulations. Another way to look at

12198-527: The use of two FM stations; one transmitting the front audio channels, the other the rear channels. A breakthrough came in 1970 when KIOI ( K-101 ) in San Francisco successfully transmitted true quadraphonic sound from a single FM station using the Quadraplex system under Special Temporary Authority from the FCC . Following this experiment, a long-term test period was proposed that would permit one FM station in each of

12312-475: The vibration of a mechanism. The power spectral density (PSD) of the signal describes the power present in the signal as a function of frequency, per unit frequency. Power spectral density is commonly expressed in SI units of watts per hertz (abbreviated as W/Hz). When a signal is defined in terms only of a voltage , for instance, there is no unique power associated with the stated amplitude. In this case "power"

12426-615: The world, the FM broadcast band falls within the VHF part of the radio spectrum . Usually 87.5 to 108.0 MHz is used, or some portion of it, with few exceptions: The frequency of an FM broadcast station (more strictly its assigned nominal center frequency) is usually a multiple of 100 kHz. In most of South Korea , the Americas , the Philippines , and the Caribbean , only odd multiples are used. Some other countries follow this plan because of

12540-755: Was 27.5 kHz. The IF bandwidth was ±5 kHz, as the only goal at the time was to relay AM radio-quality audio. This transmission system used 75 μs audio pre-emphasis like the main monaural audio and subsequently the multiplexed stereo audio. In the late 1950s, several systems to add stereo to FM radio were considered by the FCC . Included were systems from 14 proponents including Crosby, Halstead, Electrical and Musical Industries, Ltd ( EMI ), Zenith, and General Electric. The individual systems were evaluated for their strengths and weaknesses during field tests in Uniontown, Pennsylvania , using KDKA-FM in Pittsburgh as

12654-616: Was atop the highest mountain in the northeast United States, Mount Washington , New Hampshire (shut down in 1948); and W9XAO/W55M/WTMJ-FM Milwaukee, Wisconsin (went off air in 1950). A commercial FM broadcasting band was formally established in the United States as of January 1, 1941, with the first fifteen construction permits announced on October 31, 1940. These stations primarily simulcast their AM sister stations, in addition to broadcasting lush orchestral music for stores and offices, classical music to an upmarket listenership in urban areas, and educational programming. On June 27, 1945

12768-565: Was seen as another service which licensees could use to create additional income. Use of SCAs was particularly popular in the US, but much less so elsewhere. Uses for such subcarriers include radio reading services for the blind , which became common and remain so, private data transmission services (for example sending stock market information to stockbrokers or stolen credit card number denial lists to stores, ) subscription commercial-free background music services for shops, paging ("beeper") services, alternative-language programming, and providing

12882-639: Was tested in Germany between July 1979 and December 1981 by IRT . It was based on the Telefunken High ;Com broadband compander system, but was never introduced commercially in FM broadcasting. Yet another system was the CX -based noise reduction system FMX implemented in some radio broadcasting stations in the United States in the 1980s. FM broadcasting has included subsidiary communications authorization (SCA) services capability since its inception, as it

12996-424: Was theorized to be more spectrum-efficient and to produce a 4 dB s/n improvement at the receiver, and it was claimed that multipath distortion would be reduced as well. A handful of radio stations around the country broadcast stereo in this way, under FCC experimental authority. It may not be compatible with very old receivers, but it is claimed that no difference can be heard with most newer receivers. At present,

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