Costas loop
A Costas loop is a phase-locked loop based circuit, used for carrier frequency recovery from suppressed-carrier modulation signals and phase modulation signals. It was invented by John P. Costas at General Electric in the 1950s, its invention was described as having had "a profound effect on modern digital communications". The primary application of Costas loops is in wireless receivers, its advantage over the PLL-based detectors is that at small deviations the Costas loop error voltage is sin as compared to sin . This translates to double the sensitivity and makes the Costas loop uniquely suited for tracking Doppler-shifted carriers in OFDM and GPS receivers. In the classical implementation of a Costas loop, a local voltage-controlled oscillator provides quadrature outputs, one to each of two phase detectors, e.g. product detectors. The same phase of the input signal is applied to both phase detectors and the output of each phase detector is passed through a low-pass filter; the outputs of these low-pass filters are inputs to another phase detector, the output of which passes through noise-reduction filter before being used to control the voltage-controlled oscillator.
The overall loop response is controlled by the two individual low-pass filters that precede the third phase detector while the third low-pass filter serves a trivial role in terms of gain and phase margin. The above figure of a Costas loop is drawn under the condition of the "locked" state, where the VCO frequency and the incoming carrier frequency have become the same as a result of the Costas loop process; the figure does not represent the "unlocked" state. In the simplest case m 2 = 1. Therefore, m 2 = 1 does not affect the input of noise-reduction filter. Carrier and voltage-controlled oscillator signals are periodic oscillations f r e f, v c o with high-frequencies θ ˙ r e f, v c o. Block ⨂ is an analog multiplier. From the mathematical point of view, a linear filter can be described by a system of linear differential equations x ˙ = A x + b u d, u L F = c ∗ x. Here, A is a constant matrix, x is a state vector of filter, b and c are constant vectors; the model of a VCO is assumed to be linear θ ˙ v c o = ω v c o f r e e + K v c o u L F, t ∈, where ω v c o f r e e is a free-running frequency of voltage-controlled oscillator and K v c o is an oscillator gain.
It is possible to consider various nonlinear models of VCO. Suppose that the frequency of master generator is constant θ ˙ r e f ≡ ω r e f. Equation of VCO and equation of filter yield x ˙ = A x + b f r e f ( θ r
Modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that contains information to be transmitted. Most radio systems in the 20th century used frequency modulation or amplitude modulation for radio broadcast. A modulator is a device. A demodulator is a device that performs the inverse of modulation. A modem can perform both operations; the aim of analog modulation is to transfer an analog baseband signal, for example an audio signal or TV signal, over an analog bandpass channel at a different frequency, for example over a limited radio frequency band or a cable TV network channel. The aim of digital modulation is to transfer a digital bit stream over an analog communication channel, for example over the public switched telephone network or over a limited radio frequency band. Analog and digital modulation facilitate frequency division multiplexing, where several low pass information signals are transferred over the same shared physical medium, using separate passband channels.
The aim of digital baseband modulation methods known as line coding, is to transfer a digital bit stream over a baseband channel a non-filtered copper wire such as a serial bus or a wired local area network. The aim of pulse modulation methods is to transfer a narrowband analog signal, for example, a phone call over a wideband baseband channel or, in some of the schemes, as a bit stream over another digital transmission system. In music synthesizers, modulation may be used to synthesize waveforms with an extensive overtone spectrum using a small number of oscillators. In this case, the carrier frequency is in the same order or much lower than the modulating waveform. In analog modulation, the modulation is applied continuously in response to the analog information signal. Common analog modulation techniques include: Amplitude modulation Double-sideband modulation Double-sideband modulation with carrier Double-sideband suppressed-carrier transmission Double-sideband reduced carrier transmission Single-sideband modulation Single-sideband modulation with carrier Single-sideband modulation suppressed carrier modulation Vestigial sideband modulation Quadrature amplitude modulation Angle modulation, constant envelope Frequency modulation Phase modulation Transpositional Modulation, in which the waveform inflection is modified resulting in a signal where each quarter cycle is transposed in the modulation process.
TM is a pseudo-analog modulation. Where an AM carrier carries a phase variable phase f. TM is f. Digital modulation methods can be considered as digital-to-analog conversion and the corresponding demodulation or detection as analog-to-digital conversion; the changes in the carrier signal are chosen from a finite number of M alternative symbols. A simple example: A telephone line is designed for transferring audible sounds, for example and not digital bits. Computers may, communicate over a telephone line by means of modems, which are representing the digital bits by tones, called symbols. If there are four alternative symbols, the first symbol may represent the bit sequence 00, the second 01, the third 10 and the fourth 11. If the modem plays a melody consisting of 1000 tones per second, the symbol rate is 1000 symbols/second, or 1000 baud. Since each tone represents a message consisting of two digital bits in this example, the bit rate is twice the symbol rate, i.e. 2000 bits per second. This is similar to the technique used by dial-up modems as opposed to DSL modems.
According to one definition of digital signal, the modulated signal is a digital signal. According to another definition, the modulation is a form of digital-to-analog conversion. Most textbooks would consider digital modulation schemes as a form of digital transmission, synonymous to data transmission; the most fundamental digital modulation techniques are based on keying: PSK: a finite number of phases are used. FSK: a finite number of frequencies are used. ASK: a finite number of amplitudes are used. QAM: a finite number of at least two phases and at least two amplitudes are used. In QAM, an in-phase signal and a quadrature phase signal are amplitude modulated with a finite number of amplitudes and summed, it can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK. In all of the above methods, each of these phases, frequencies or amplitudes are assigned a u
Single-sideband modulation
In radio communications, single-sideband modulation or single-sideband suppressed-carrier modulation is a type of modulation, used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude modulation, it uses transmitter bandwidth more efficiently. Amplitude modulation produces an output signal the bandwidth of, twice the maximum frequency of the original baseband signal. Single-sideband modulation avoids this bandwidth increase, the power wasted on a carrier, at the cost of increased device complexity and more difficult tuning at the receiver. Radio transmitters work by mixing a radio frequency signal of a specific frequency, the carrier wave, with the audio signal to be broadcast. In AM transmitters this mixing takes place in the final RF amplifier, it is less common and much less efficient to do the mixing at low power and amplify it in a linear amplifier. Either method produces a set of frequencies with a strong signal at the carrier frequency and with weaker signals at frequencies extending above and below the carrier frequency by the maximum frequency of the input signal.
Thus the resulting signal has a spectrum whose bandwidth is twice the maximum frequency of the original input audio signal. SSB takes advantage of the fact that the entire original signal is encoded in each of these "sidebands", it is not necessary to transmit both sidebands plus the carrier, as a suitable receiver can extract the entire original signal from either the upper or lower sideband. There are several methods for eliminating the one sideband from the transmitted signal. Producing this single sideband signal is too complicated to be done in the final amplifier stage as with AM. SSB Modulation must be done at a low level and amplified in a linear amplifier where lower efficiency offsets the power advantage gained by eliminating the carrier and one sideband. SSB transmissions use the available amplifier energy more efficiently, providing longer-range transmission for the same power output. In addition, the occupied spectrum is less than half that of a full carrier AM signal. SSB reception requires frequency stability and selectivity well beyond that of inexpensive AM receivers, why broadcasters have used it.
In point to point communications where expensive receivers are in common use they can be adjusted to receive whichever sideband is being transmitted. The first U. S. patent application for SSB modulation was filed on December 1915 by John Renshaw Carson. The U. S. Navy experimented with SSB over its radio circuits before World War I. SSB first entered commercial service on January 7, 1927 on the longwave transatlantic public radiotelephone circuit between New York and London; the high power SSB transmitters were located at New York and Rugby, England. The receivers were in quiet locations in Houlton and Cupar Scotland. SSB was used over long distance telephone lines, as part of a technique known as frequency-division multiplexing. FDM was pioneered by telephone companies in the 1930s. With this technology, many simultaneous voice channels could be transmitted on a single physical circuit, for example in L-carrier. With SSB, channels could to be spaced only 4,000 Hz apart, while offering a speech bandwidth of nominally 300 Hz to 3,400 Hz.
Amateur radio operators began serious experimentation with SSB after World War II. The Strategic Air Command established SSB as the radio standard for its aircraft in 1957, it has become a de facto standard for long-distance voice radio transmissions since then. Single-sideband has the mathematical form of quadrature amplitude modulation in the special case where one of the baseband waveforms is derived from the other, instead of being independent messages: where s is the message, s ^ is its Hilbert transform, f 0 is the radio carrier frequency. To understand this formula, we may express s as the real part of a complex-valued function, with no loss of information: s = Re = Re , where j represents the imaginary unit. S a is the analytic representation of s, which means that it comprises only the positive-frequency components of s: 1 2 S a = { S, for f > 0, 0, for f < 0, {\displaystyle S_{\
Envelope detector
An envelope detector is an electronic circuit that takes a high-frequency amplitude modulated signal as input and provides an output, the envelope of the original signal. The capacitor in the circuit above stores charge on the rising edge and releases it through the resistor when the input signal amplitude falls; the diode in series rectifies the incoming signal, allowing current flow only when the positive input terminal is at a higher potential than the negative input terminal. Most practical envelope detectors use either half-wave or full-wave rectification of the signal to convert the AC audio input into a pulsed DC signal. Filtering is used to smooth the final result; this filtering is perfect and some "ripple" is to remain on the envelope follower output for low frequency inputs such as notes from a bass instrument. Reducing the filter cutoff frequency gives a smoother output, but decreases the high frequency response. Therefore, practical designs must reach a compromise. Any AM FM signal x can be written in the following form x = R cos In the case of AM, φ is constant and can be ignored.
In AM, the carrier frequency ω is constant. Thus, all the information in the AM signal is. Hence an AM signal is given by the function x = cos with m representing the original audio frequency message, C the carrier amplitude and R equal to C + m. So, if the envelope of the AM signal can be extracted, the original message can be recovered. In the case of FM, the transmitted x can be ignored. However, many FM receivers measure the envelope anyway for received signal strength indication; the simplest form of envelope detector is the diode detector, shown above. A diode detector is a diode between the input and output of a circuit, connected to a resistor and capacitor in parallel from the output of the circuit to the ground. If the resistor and capacitor are chosen, the output of this circuit should approximate a voltage-shifted version of the original signal. A simple filter can be applied to filter out the DC component. An envelope detector can be constructed using a precision rectifier feeding into a low-pass filter.
The envelope detector has several drawbacks: The input to the detector must be band-pass filtered around the desired signal, or else the detector will demodulate several signals. The filtering can be done with a tunable filter or, more a superheterodyne receiver It is more susceptible to noise than a product detector If the signal is overmodulated, distortion will occurMost of these drawbacks are minor and are acceptable tradeoffs for the simplicity and low cost of using an envelope detector. An envelope detector can be used to demodulate a modulated signal by removing all high frequency components of the signal; the capacitor and resistor form a low-pass filter to filter out the carrier frequency. Such a device is used to demodulate AM radio signals because the envelope of the modulated signal is equivalent to the baseband signal. An envelope detector is sometimes referred to as an envelope follower in musical environments, it is still used to detect the amplitude variations of an incoming signal to produce a control signal that resembles those variations.
However, in this case the input signal is made up of audible frequencies. Envelope detectors are a component of other circuits, such as a compressor or an auto-wah or envelope-followed filter. In these circuits, the envelope follower is part of what is known as the "side chain", a circuit which describes some characteristic of the input, in this case its volume. Both expanders and compressors use the envelope's output voltage to control the gain of an amplifier. Auto-wah uses the voltage to control the cutoff frequency of a filter; the voltage-controlled filter of an analog synthesizer is a similar circuit. Modern envelope followers can be implemented: directly as electronic hardware, or as software using either a digital signal processor or on a general purpose CPU. Analytic signal Attack-decay-sustain-release envelope Envelope detector Envelope and envelope recovery
Spectrogram
A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams; when the data is represented in a 3D plot they may be called waterfalls. Spectrograms are used extensively in the fields of music, sonar and speech processing and others. Spectrograms of audio can be used to identify spoken words phonetically, to analyse the various calls of animals. A spectrogram can be generated by an optical spectrometer, a bank of band-pass filters, by Fourier transform or by a wavelet transform. A spectrogram is depicted as a heat map, i.e. as an image with the intensity shown by varying the colour or brightness. A common format is a graph with two geometric dimensions: one axis represents time or RPM, the other axis is frequency. There are many variations of format: sometimes the vertical and horizontal axes are switched, so time runs up and down; the frequency and amplitude axes can be either linear or logarithmic, depending on what the graph is being used for.
Audio would be represented with a logarithmic amplitude axis, frequency would be linear to emphasize harmonic relationships, or logarithmic to emphasize musical, tonal relationships. Spectrograms of light may be created directly using an optical spectrometer over time. Spectrograms may be created from a time-domain signal in one of two ways: approximated as a filterbank that results from a series of band-pass filters, or calculated from the time signal using the Fourier transform; these two methods form two different time–frequency representations, but are equivalent under some conditions. The bandpass filters method uses analog processing to divide the input signal into frequency bands. Creating a spectrogram using the FFT is a digital process. Digitally sampled data, in the time domain, is broken up into chunks, which overlap, Fourier transformed to calculate the magnitude of the frequency spectrum for each chunk; each chunk corresponds to a vertical line in the image. These spectrums or time plots are "laid side by side" to form the image or a three-dimensional surface, or overlapped in various ways, i.e. windowing.
This process corresponds to computing the squared magnitude of the short-time Fourier transform of the signal s — that is, for a window width ω, s p e c t r o g r a m = | S T F T | 2. From the formula above, it appears that a spectrogram contains no information about the exact, or approximate, phase of the signal that it represents. For this reason, it is not possible to reverse the process and generate a copy of the original signal from a spectrogram, though in situations where the exact initial phase is unimportant it may be possible to generate a useful approximation of the original signal; the Analysis & Resynthesis Sound Spectrograph is an example of a computer program that attempts to do this. The Pattern Playback was an early speech synthesizer, designed at Haskins Laboratories in the late 1940s, that converted pictures of the acoustic patterns of speech back into sound. In fact, there is some phase information in the spectrogram, but it appears in another form, as time delay, the dual of the Instantaneous Frequency.
The size and shape of the analysis window can be varied. A smaller window will produce more accurate results in timing, at the expense of precision of frequency representation. A larger window will provide a more precise frequency representation, at the expense of precision in timing representation; this is an instance of the Heisenberg uncertainty principle, that the product of the precision in two conjugate variables is less than or equal to a constant. Early analog spectrograms were applied to a wide range of areas including the study of bird calls, with current research continuing using modern digital equipment and applied to all animal sounds. Contemporary use of the digital spectrogram is useful for studying frequency modulation in animal calls; the distinguishing characteristics of FM chirps, broadband clicks, social harmonizing are most visualized with the spectrogram. Spectrograms are useful in assisting in overcoming speech deficits and in speech training for the portion of the population, profoundly deaf The studies of phonetics and speech synthesis are facilitated through the use of spectrograms.
By reversing the process of producing a spectrogram, it is possible to create a
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency; the period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals, radio waves, light. For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics and radio, frequency is denoted by a Latin letter f or by the Greek letter ν or ν; the relation between the frequency and the period T of a repeating event or oscillation is given by f = 1 T.
The SI derived unit of frequency is the hertz, named after the German physicist Heinrich Hertz. One hertz means. If a TV has a refresh rate of 1 hertz the TV's screen will change its picture once a second. A previous name for this unit was cycles per second; the SI unit for period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 rpm equals one hertz. As a matter of convenience and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are described by their frequency instead of period; these used conversions are listed below: Angular frequency denoted by the Greek letter ω, is defined as the rate of change of angular displacement, θ, or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument to the sine function: y = sin = sin = sin d θ d t = ω = 2 π f Angular frequency is measured in radians per second but, for discrete-time signals, can be expressed as radians per sampling interval, a dimensionless quantity.
Angular frequency is larger than regular frequency by a factor of 2π. Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. E.g.: y = sin = sin d θ d x = k Wavenumber, k, is the spatial frequency analogue of angular temporal frequency and is measured in radians per meter. In the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has an inverse relationship to the wavelength, λ. In dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: f = v λ. In the special case of electromagnetic waves moving through a vacuum v = c, where c is the speed of light in a vacuum, this expression becomes: f = c λ; when waves from a monochrome source travel from one medium to another, their frequency remains the same—only their wavelength and speed change. Measurement of frequency can done in the following ways, Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period dividing the count by the length of the time period.
For example, if 71 events occur within 15 seconds the frequency is: f = 71 15 s ≈ 4.73 Hz If the number of counts is not large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time. The latter method introduces a random error into the count of between zero and one count, so on average half a count; this is called gating error and causes an average error in the calculated frequency of Δ f = 1 2 T
Analog television
Analog television or analogue television is the original television technology that uses analog signals to transmit video and audio. In an analog television broadcast, the brightness and sound are represented by rapid variations of either the amplitude, frequency or phase of the signal. Analog signals vary over a continuous range of possible values which means that electronic noise and interference becomes reproduced by the receiver, thus with analog, a moderately weak signal becomes subject to interference. In contrast, a moderately weak digital signal and a strong digital signal transmit equal picture quality. Analog television can be distributed over a cable network using cable converters. All broadcast. Motivated by the lower bandwidth requirements of compressed digital signals, since the 2000s a digital television transition is proceeding in most countries of the world, with different deadlines for cessation of analog broadcasts; the earliest systems of analog television were mechanical television systems, which used spinning disks with patterns of holes punched into the disc to scan an image.
A similar disk reconstructed the image at the receiver. Synchronization of the receiver disc rotation was handled through sync pulses broadcast with the image information; however these mechanical systems were slow, the images were dim and flickered and the image resolution low. Camera systems used similar spinning discs and required intensely bright illumination of the subject for the light detector to work. Analog television did not begin as an industry until the development of the cathode-ray tube, which uses a focused electron beam to trace lines across a phosphor coated surface; the electron beam could be swept across the screen much faster than any mechanical disc system, allowing for more spaced scan lines and much higher image resolution. Far less maintenance was required of an all-electronic system compared to a spinning disc system. All-electronic systems became popular with households after the Second World War. Broadcasters of analog television encode their signal using different systems.
The official systems of transmission are named: A, B, C, D, E, F, G, H, I, K, K1, L, M and N. These systems determine the number of scan lines, frame rate, channel width, video bandwidth, video-audio separation, so on; the colors in those systems are encoded with one of three color coding schemes: NTSC, PAL, or SECAM, use RF modulation to modulate this signal onto a high frequency or ultra high frequency carrier. Each frame of a television image is composed of lines drawn on the screen; the lines are of varying brightness. The next sequential frame is displayed; the analog television signal contains timing and synchronization information, so that the receiver can reconstruct a two-dimensional moving image from a one-dimensional time-varying signal. The first commercial television systems were black-and-white. A practical television system needs to take luminance, chrominance and audio signals, broadcast them over a radio transmission; the transmission system must include a means of television channel selection.
Analog broadcast television systems come in a variety of frame resolutions. Further differences exist in the modulation of the audio carrier; the monochrome combinations still existing in the 1950s are standardized by the International Telecommunication Union as capital letters A through N. When color television was introduced, the hue and saturation information was added to the monochrome signals in a way that black and white televisions ignore. In this way backwards compatibility was achieved; that concept is true for all analog television standards. There were three standards for the way the additional color information can be encoded and transmitted; the first was the American NTSC color television system. The European/Australian PAL and the French-former Soviet Union SECAM standard were developed and attempt to cure certain defects of the NTSC system. PAL's color encoding is similar to the NTSC systems. SECAM, uses a different modulation approach than PAL or NTSC. In principle, all three color encoding systems can be combined with any scan line/frame rate combination.
Therefore, in order to describe a given signal it's necessary to quote the color system and the broadcast standard as a capital letter. For example, the United States, Canada and South Korea use NTSC-M, Japan uses NTSC-J, the UK uses PAL-I, France uses SECAM-L, much of Western Europe and Australia use PAL-B/G, most of Eastern Europe uses SECAM-D/K or PAL-D/K and so on. However, not all of these possible combinations exist. NTSC is only used with system M though there were experiments with NTSC-A in the UK and NTSC-N in part of South America. PAL is used with a variety of 625-line standards but with the North American 525-line standard, accordingly n
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188).
This article incorporates 
