In telecommunications and signal processing, frequency modulation is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. In analog frequency modulation, such as FM radio broadcasting of an audio signal representing voice or music, the instantaneous frequency deviation, the difference between the frequency of the carrier and its center frequency, is proportional to the modulating signal. Digital data can be encoded and transmitted via FM by shifting the carrier's frequency among a predefined set of frequencies representing digits – for example one frequency can represent a binary 1 and a second can represent binary 0; this modulation technique is known as frequency-shift keying. FSK is used in modems such as fax modems, can be used to send Morse code. Radioteletype uses FSK. Frequency modulation is used for FM radio broadcasting, it is used in telemetry, seismic prospecting, monitoring newborns for seizures via EEG, two-way radio systems, music synthesis, magnetic tape-recording systems and some video-transmission systems.
In radio transmission, an advantage of frequency modulation is that it has a larger signal-to-noise ratio and therefore rejects radio frequency interference better than an equal power amplitude modulation signal. For this reason, most music is broadcast over FM radio. Frequency modulation and phase modulation are the two complementary principal methods of angle modulation; these methods contrast with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency and phase remain constant. If the information to be transmitted is x m and the sinusoidal carrier is x c = A c cos , where fc is the carrier's base frequency, Ac is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal: y = A c cos = A c cos = A c cos where f Δ = K f A m, K f being the sensitivity of the frequency modulator and A m being the amplitude of the modulating signal or baseband signal. In this equation, f is the instantaneous frequency of the oscillator and f Δ is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm is limited to the range ±1.
While most of the energy of the signal is contained within fc ± fΔ, it can be shown by Fourier analysis that a wider range of frequencies is required to represent an FM signal. The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are neglected in practical design problems. Mathematically, a baseband modulating signal may be approximated by a sinusoidal continuous wave signal with a frequency fm; this method is named as single-tone modulation. The integral of such a signal is: ∫ 0 t x m d τ = A m sin
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to certain equations. For example, the equation 2 = − 9 has no real solution, since the square of a real number cannot be negative. Complex numbers provide a solution to this problem; the idea is to extend the real numbers with an indeterminate i, taken to satisfy the relation i2 = −1, so that solutions to equations like the preceding one can be found. In this case the solutions are −1 + 3i and −1 − 3i, as can be verified using the fact that i2 = −1: 2 = 2 = = 9 = − 9, 2 = 2 = 2 = 9 = − 9.
According to the fundamental theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. In contrast, some polynomial equations with real coefficients have no solution in real numbers; the 16th century Italian mathematician Gerolamo Cardano is credited with introducing complex numbers in his attempts to find solutions to cubic equations. Formally, the complex number system can be defined as the algebraic extension of the ordinary real numbers by an imaginary number i; this means that complex numbers can be added and multiplied, as polynomials in the variable i, with the rule i2 = −1 imposed. Furthermore, complex numbers can be divided by nonzero complex numbers. Overall, the complex number system is a field. Geometrically, complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part.
The complex number a + bi can be identified with the point in the complex plane. A complex number whose real part is zero is said to be purely imaginary. A complex number whose imaginary part is zero can be viewed as a real number. Complex numbers can be represented in polar form, which associates each complex number with its distance from the origin and with a particular angle known as the argument of this complex number; the geometric identification of the complex numbers with the complex plane, a Euclidean plane, makes their structure as a real 2-dimensional vector space evident. Real and imaginary parts of a complex number may be taken as components of a vector with respect to the canonical standard basis; the addition of complex numbers is thus depicted as the usual component-wise addition of vectors. However, the complex numbers allow for a richer algebraic structure, comprising additional operations, that are not available in a vector space. Based on the concept of real numbers, a complex number is a number of the form a + bi, where a and b are real numbers and i is an indeterminate satisfying i2 = −1.
For example, 2 + 3i is a complex number. This way, a complex number is defined as a polynomial with real coefficients in the single indeterminate i, for which the relation i2 + 1 = 0 is imposed. Based on this definition, complex numbers can be added and multiplied, using the addition and multiplication for polynomials; the relation i2 + 1 = 0 induces the equalities i4k = 1, i4k+1 = i, i4k+2 = −1, i4k+3 = −i, which hold for all integers k. The real number a is called the real part of the complex number a + bi. To emphasize, the imaginary part does not include a factor i and b, not bi, is the imaginary part. Formally, the complex numbers are defined as the quotient ring of the polynomia
Signal processing is a subfield of mathematics and electrical engineering that concerns the analysis and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound and biological measurements. For example, signal processing techniques are used to improve signal transmission fidelity, storage efficiency, subjective quality, to emphasize or detect components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. Oppenheim and Schafer further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. Analog signal processing is for signals that have not been digitized, as in legacy radio, telephone and television systems; this involves linear electronic circuits as well as non-linear ones. The former are, for instance, passive filters, active filters, additive mixers and delay lines.
Non-linear circuits include compandors, voltage-controlled filters, voltage-controlled oscillators and phase-locked loops. Continuous-time signal processing is for signals; the methods of signal processing include time domain, frequency domain, complex frequency domain. This technology discusses the modeling of linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals Discrete-time signal processing is for sampled signals, defined only at discrete points in time, as such are quantized in time, but not in magnitude. Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers; this technology was a predecessor of digital signal processing, is still used in advanced processing of gigahertz signals. The concept of discrete-time signal processing refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.
Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors. Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued and addition. Other typical operations supported by the hardware are circular buffers and lookup tables. Examples of algorithms are the Fast Fourier transform, finite impulse response filter, Infinite impulse response filter, adaptive filters such as the Wiener and Kalman filters. Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatio-temporal domains. Nonlinear systems can produce complex behaviors including bifurcations, chaos and subharmonics which cannot be produced or analyzed using linear methods. Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks.
Statistical techniques are used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image, construct techniques based on this model to reduce the noise in the resulting image. Audio signal processing – for electrical signals representing sound, such as speech or music Speech signal processing – for processing and interpreting spoken words Image processing – in digital cameras and various imaging systems Video processing – for interpreting moving pictures Wireless communication – waveform generations, filtering, equalization Control systems Array processing – for processing signals from arrays of sensors Process control – a variety of signals are used, including the industry standard 4-20 mA current loop Seismology Financial signal processing – analyzing financial data using signal processing techniques for prediction purposes. Feature extraction, such as image understanding and speech recognition. Quality improvement, such as noise reduction, image enhancement, echo cancellation.
Including audio compression, image compression, video compression. Genomics, Genomic signal processing In communication systems, signal processing may occur at: OSI layer 1 in the seven layer OSI model, the Physical Layer. Filters – for example analog or digital Samplers and analog-to-digital converters for signal acquisition and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, later rebuilding the original signal or an approximation thereof. Signal compressors Digital signal processors Differential equations Recurrence relation Transform theory Time-frequency analysis – for processing non-stationary signals Spectral estimation – for determining the spectral content of a
International Standard Serial Number
An International Standard Serial Number is an eight-digit serial number used to uniquely identify a serial publication, such as a magazine. The ISSN is helpful in distinguishing between serials with the same title. ISSN are used in ordering, interlibrary loans, other practices in connection with serial literature; the ISSN system was first drafted as an International Organization for Standardization international standard in 1971 and published as ISO 3297 in 1975. ISO subcommittee TC 46/SC 9 is responsible for maintaining the standard; when a serial with the same content is published in more than one media type, a different ISSN is assigned to each media type. For example, many serials are published both in electronic media; the ISSN system refers to these types as electronic ISSN, respectively. Conversely, as defined in ISO 3297:2007, every serial in the ISSN system is assigned a linking ISSN the same as the ISSN assigned to the serial in its first published medium, which links together all ISSNs assigned to the serial in every medium.
The format of the ISSN is an eight digit code, divided by a hyphen into two four-digit numbers. As an integer number, it can be represented by the first seven digits; the last code digit, which may be 0-9 or an X, is a check digit. Formally, the general form of the ISSN code can be expressed as follows: NNNN-NNNC where N is in the set, a digit character, C is in; the ISSN of the journal Hearing Research, for example, is 0378-5955, where the final 5 is the check digit, C=5. To calculate the check digit, the following algorithm may be used: Calculate the sum of the first seven digits of the ISSN multiplied by its position in the number, counting from the right—that is, 8, 7, 6, 5, 4, 3, 2, respectively: 0 ⋅ 8 + 3 ⋅ 7 + 7 ⋅ 6 + 8 ⋅ 5 + 5 ⋅ 4 + 9 ⋅ 3 + 5 ⋅ 2 = 0 + 21 + 42 + 40 + 20 + 27 + 10 = 160 The modulus 11 of this sum is calculated. For calculations, an upper case X in the check digit position indicates a check digit of 10. To confirm the check digit, calculate the sum of all eight digits of the ISSN multiplied by its position in the number, counting from the right.
The modulus 11 of the sum must be 0. There is an online ISSN checker. ISSN codes are assigned by a network of ISSN National Centres located at national libraries and coordinated by the ISSN International Centre based in Paris; the International Centre is an intergovernmental organization created in 1974 through an agreement between UNESCO and the French government. The International Centre maintains a database of all ISSNs assigned worldwide, the ISDS Register otherwise known as the ISSN Register. At the end of 2016, the ISSN Register contained records for 1,943,572 items. ISSN and ISBN codes are similar in concept. An ISBN might be assigned for particular issues of a serial, in addition to the ISSN code for the serial as a whole. An ISSN, unlike the ISBN code, is an anonymous identifier associated with a serial title, containing no information as to the publisher or its location. For this reason a new ISSN is assigned to a serial each time it undergoes a major title change. Since the ISSN applies to an entire serial a new identifier, the Serial Item and Contribution Identifier, was built on top of it to allow references to specific volumes, articles, or other identifiable components.
Separate ISSNs are needed for serials in different media. Thus, the print and electronic media versions of a serial need separate ISSNs. A CD-ROM version and a web version of a serial require different ISSNs since two different media are involved. However, the same ISSN can be used for different file formats of the same online serial; this "media-oriented identification" of serials made sense in the 1970s. In the 1990s and onward, with personal computers, better screens, the Web, it makes sense to consider only content, independent of media; this "content-oriented identification" of serials was a repressed demand during a decade, but no ISSN update or initiative occurred. A natural extension for ISSN, the unique-identification of the articles in the serials, was the main demand application. An alternative serials' contents model arrived with the indecs Content Model and its application, the digital object identifier, as ISSN-independent initiative, consolidated in the 2000s. Only in 2007, ISSN-L was defined in the
In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued. The simplest case arises in taking the square root of a positive real number. For example, 4 has two square roots: 2 and –2. Consider the complex logarithm function log z, it is defined as the complex number w such. This means. Iπ/2 is a solution, but is it the only solution? Of course, there are other solutions, evidenced by considering the position of i in the complex plane and in particular its argument arg i. We can rotate counterclockwise π/2 radians from 1 to reach i but if we rotate further another 2π we reach i again. So, we can conclude that i is a solution for log i, it becomes clear that we can add any multiple of 2πi to our initial solution to obtain all values for log i. But this has a consequence that may be surprising in comparison of real valued functions: log i does not have one definite value! For log z, we have log z = ln | z | + i = ln | z | + i for an integer k, where Arg z is the argument of z defined to lie in the interval values in the range ( − π, π ] To compute these values one can use functions: atan2 with principal value in the range ( − π, π ] atan with principal value in the range ( − π 2, π 2 ] Principal branch Branch point