Cleanup date June 2007 Modulation techniques Waveletmodulation , also known as fractal modulation , is a modulation technique that makes use of Waveletwavelet transformations to represent the data being transmitted. One of the objectives of this type of modulation is to send data at multiple rates over a channel communications channel that is unknown. ref name test http scholar.lib.vt.edu theses available etd 08072001 093853 unrestricted etdset.pdf&aclck http 3A 2F 2Fhomecatalogbiz.com 2Fsr4.php 3Fkeyword 3Dwavelet 2Bmodulation WaveletModulation in Gaussian and Rayleigh Fading Channels, Manish J. Manglani , Masters thesis ref If the channel is not clear for one specific bit rate , meaning that the signal will not be received, the signal can be sent at a different bit rate where the signal to noise ratio is higher. See Also Wavelet References reflist DEFAULTSORT WaveletModulation Category Quantized radio modulation modes Category Wavelets Telecomm stub de Wavelet Paket Transformation pt Modula o fractal ... more details
starting to be used for communication applications. Wavelet OFDM is the basic modulation scheme ...A wavelet is a wave like oscillation with an amplitude that starts out at zero, increases, and then decreases ... information from the unknown signal. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly a 32nd note . If this wavelet were to be convolved at periodic ..., the wavelet will resonate if the unknown signal contains information of similar frequency ... of resonance is at the core of many practical applications of wavelet theory. As a mathematical ... in wavelet based compression decompression algorithms where it is desirable to recover the original information with minimal loss. In formal terms, this representation is a wavelet series representation ... space of square integrable functions. Name The word wavelet has been used for decades in digital ... 1953 title WAVELET CONTRACTION, WAVELET EXPANSION, AND THE CONTROL OF SEISMIC RESOLUTION journal Geophysics .... Wavelet theory Wavelet theory is applicable to several subjects. All wavelet transforms may be considered ... to harmonic analysis . Almost all practically useful discrete wavelet transforms use discrete time filterbank s. These filter banks are called the wavelet and scaling coefficients in wavelets nomenclature ... IIR filters. The wavelets forming a continuous wavelet transform CWT are subject to the Fourier uncertainty ... bound. Thus, in the scaleogram of a continuous wavelet transform of this signal, such an event marks an entire region in the time scale plane, instead of just one point. Also, discrete wavelet bases may be considered in the context of other forms of the uncertainty principle. Wavelet transforms are broadly divided into three classes continuous, discrete and multiresolution based. Continuous wavelet transforms continuous shift and scale parameters In continuous wavelet transform s, a given signal ... 2 R math , the mother wavelet . For the example of the scale one frequency band math 1,2 math this function ... more details
DMT including adaptive modulation and bit loading. Waveletmodulation Trellis coded modulation TCM ...About musical change of key Modulation music other uses Modulation techniques In electronics and telecommunications , modulation is the process of varying one or more properties of a high frequency periodic ... , modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that can be physically transmitted. Modulation ... of the passband. A device that performs modulation is known as a modulator and a device that performs the inverse operation of modulation is known as a demodulator sometimes detector or demod . A device ... modulation is to transfer a digital bit stream over an analog bandpass Channel communications channel ... modulation is to transfer an analog signal analog baseband or lowpass signal, for example an audio ... modulation facilitate frequency division multiplexing FDM , where several low pass information signals ... several different carrier frequencies . The aim of digital baseband modulation methods, also ... filtered copper wire such as a serial bus or a wired local area network . The aim of pulse modulation ... synthesizers, modulation may be used to synthesise waveforms with an extensive overtone spectrum ... order or much lower than the modulating waveform. See for example frequency modulation synthesis or Ring modulation Use in music ring modulation synthesis . Analog modulation methods File Amfm3 en de.gif ... signal analog modulation, the modulation is applied continuously in response to the analog information signal. Common analog modulation techniques are ref cite book title Analog and Digital ... pages 163 184 url http books.google.com books?id JKfTrRRHT5QC&pg PA164 ref Amplitude modulation AM ... signal Double sideband modulation DSB Double sideband modulation with carrier DSB WC ... sideband reduced carrier transmission DSB RC Single sideband modulation SSB, or SSB AM SSB with carrier ... more details
Unreferenced date December 2009 In numerical analysis , continuous wavelet s are functions used by the continuous wavelet transform . These functions are defined as analytical expression s, as functions either of time or of frequency. Most of the continuous wavelets are used for both wavelet decomposition and composition transforms. That is they are the continuous counterpart of orthogonal wavelet s. The following continuous wavelets have been invented for various applications Morlet wavelet Modified Morlet wavelet Mexican hat wavelet Complex mexican hat wavelet Shannon wavelet Difference of Gaussians Hermitian wavelet Hermitian hat wavelet Beta wavelet Causal Waveletwavelet s Cauchy wavelet Addison wavelet See also Wavelet DEFAULTSORT Continuous Wavelet Category Continuous wavelets Category Numerical analysis Category Functional analysis ... more details
A biorthogonal wavelet is a wavelet where the associated Discrete wavelet transform wavelet transform is invertible but not necessarily Orthogonality orthogonal . Designing biorthogonal wavelets allows more degrees of freedom than orthogonal wavelet s. One additional degree of freedom is the possibility to construct symmetric wavelet functions. In the biorthogonal case, there are two scaling functions math phi, tilde phi math , which may generate different multiresolution analyses, and accordingly two different wavelet functions math psi, tilde psi math . So the numbers M and N of coefficients in the scaling sequences math a, tilde a math may differ. The scaling sequences must satisfy the following biorthogonality condition math sum n in Z a n tilde a n 2m 2 cdot delta m,0 math . Then the wavelet sequences can be determined as math b n 1 n tilde a M 1 n math , math n 0, dots,M 1 math and math tilde b n 1 n a M 1 n math , math n 0, dots,N 1 math . References St phane Mallat A Wavelet Tour of Signal Processing ISBN 0 12 466606 X Category Biorthogonal wavelets pl Falki biortogonalne ... more details
Wavelet noise is an alternative to Perlin noise which reduces the problems of aliasing and detail loss that are encountered when Perlin noise is Harmonic sum summed into a fractal . External links http graphics.pixar.com library WaveletNoise paper.pdf Wavelet Noise Paper at pixar.com. Category Computer graphics compu graphics stub ... more details
Context date October 2009 Shannon wavelet or sinc wavelet Two kinds of Shannon wavelets can be implemented br Real Shannon wavelet Complex Shannon wavelet br The signal analysis by ideal bandpass filter s define a decomposition known as Shannon wavelets or sinc wavelets . The Haar and sinc systems are Fourier duals of each other. Real Shannon wavelet File Wavelet Shan.svg thumb right Real Shannon wavelet The spectrum of the Shannon mother wavelet is given by math Psi operatorname Sha w prod left frac w 3 pi 2 pi right prod left frac w 3 pi 2 pi right . math where the normalised gate function is defined by math prod x begin cases 1, & mbox if x le 1 2 , 0 & mbox if mbox otherwise . end cases math The analytical expression of the real Shannon wavelet can be found by taking the inverse Fourier transform math psi operatorname Sha t operatorname sinc left frac t 2 right cdot cos left frac 3 pi t 2 right math or alternatively as math psi operatorname Sha t 2 cdot operatorname sinc 2t 1 operatorname sinc t , math where math operatorname sinc t frac sin pi t pi t math is the usual sinc function that appears in Shannon sampling theorem . This wavelet belongs to math C infty math class, but it decreases slowly at infinity and has no Support mathematics Compact support bounded support , since band limited signals cannot be time limited. The scaling function for the Shannon MRA or Sinc MRA is given by the sample function math phi Sha t frac sin pi t pi t operatorname sinc t . math Complex Shannon wavelet In the case of complex continuous wavelet, the Shannon wavelet is defined by math psi CSha t sinc t .e j2 pi t math , References S.G. Mallat, A Wavelet Tour of Signal Processing , Academic Press, 1999, ISBN 012466606X C. Sidney Burrus C.S. Burrus , R.A. Gopinath, H. Guo, Introduction to Wavelets and Wavelet Transforms A Primer , Prentice Hall, 1988, ISBN 0124896009. Category Continuous wavelets Category Functional analysis cs Shannonova vlnka ... more details
Image Jpeg2000 2 level wavelet transform lichtenstein.png thumb 300px An example of the 2D discrete wavelet transform that is used in JPEG2000 . In mathematics , a wavelet series is a representation of a square ... by a certain orthonormal series mathematics series generated by a wavelet . This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform . Formal definition A function math psi in L 2 mathbb R math is called an orthonormal wavelet if it can ... mathematics Properties convergence in norm . Such a representation of a function f is known as a wavelet series . This implies that an orthonormal wavelet is dual wavelet self dual . Wavelet transform The integral wavelet transform is the integral transform defined as math left W psi f right a,b frac 1 sqrt a int infty infty overline psi left frac x b a right f x dx , math The wavelet coefficients ... position . Wavelet compression Wavelet compression is a form of data compression well suited for image ... data in as little space as possible in a Computer file file . Wavelet compression can be either lossless ... a 5 3 wavelet for lossless reversible transform and a 9 7 wavelet for lossy irreversible transform. ref Using a wavelet transform, the wavelet compression methods are adequate for representing Transient ... if some other transform, such as the more widespread discrete cosine transform , had been used. Wavelet compression is not good for all kinds of data transient signal characteristics mean good wavelet ... issues of current methods using wavelets for video compression. Method First a wavelet transform is applied ... encoded . A few 1D and 2D applications of wavelet compression use a technique called wavelet footprints ... 2005 V14 part6 p1 A New and Novel Image Compression Algorithm Using Wavelet Footprints ref ref Ho Tatt Wei and Jeoti, V. A wavelet footprints based compression scheme for ECG signals . cite doi 10.1109 TENCON.2004.1414412 ref Other practical applications The wavelet transform can provide us with the frequency ... more details
An orthogonal wavelet is a wavelet whose associated Discrete wavelet transform wavelet transform is Orthogonality orthogonal . That is, the inverse wavelet transform is the Adjoint of an operator adjoint of the wavelet transform. If this condition is weakened you may end up with biorthogonal wavelet s. Basics The scaling function is a refinable function . That is, it is a fractal functional equation, called the refinement equation twin scale relation or dilation equation math phi x sum k 0 N 1 a k phi 2x k math , where the sequence math a 0, dots, a N 1 math of real number s is called a scaling sequence or scaling mask. The wavelet proper is obtained by a similar linear combination, math psi x sum k 0 M 1 b k phi 2x k math , where the sequence math b 0, dots, b M 1 math of real numbers is called a wavelet sequence or wavelet mask. A necessary condition for the orthogonality of the wavelets is that the scaling sequence is orthogonal to any shifts of it by an even number of coefficients math sum n in Z a n a n 2m 2 delta m,0 math In this case there is the same number M N of coefficients in the scaling as in the wavelet sequence, the wavelet sequence can be determined as math b n 1 n a N 1 n math . In some cases the opposite sign is chosen. Vanishing moments, polynomial approximation and smoothness A necessary condition for the existence of a solution to the refinement equation is that some power 1 Z sup A sup , A 0 , divides the polynomial math a Z a 0 a 1Z dots a N 1 Z N 1 math see Z transform . The maximally possible power A is called polynomial approximation order or pol. app. power or number of vanishing moments . It describes the ability to represent polynomials up to degree A 1 with linear combinations of integer translates of the scaling function. In the biorthogonal case, an approximation order A of math phi math corresponds to A vanishing moments of the dual wavelet ... wavelet, see below. References Ingrid Daubechies Ten Lectures on Wavelets , SIAM 1992, Category ... more details
Context date October 2009 Image with unknown copyright status removed Image Haar Wavelet 20080121.png thumb right The Haar wavelet Deletable image caption 1 Sunday, 13 April 2008 date March 2012 In mathematics, the Haar wavelet is a sequence of rescaled square shaped functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function ... is now recognised as the first known wavelet basis and extensively used as a teaching example. The Haar ... of wavelets, and even the term wavelet , did not come until much later. As a special case of the Daubechies wavelet , the Haar wavelet is also known as D2 . The Haar wavelet is also the simplest possible wavelet. The technical disadvantage of the Haar wavelet is that it is not continuous function continuous .... ref cite journal first B. last Lee first2 Y. S. last2 Tarng title Application of the discrete wavelet ... 243 doi 10.1007 s001700050062 ref Image Haar wavelet.svg thumb right The Haar wavelet The Haar wavelet s mother wavelet function math psi t math can be described as math psi t begin cases 1 quad & 0 ... 1 leq p infty math . This basis is unconditional for p 1. Haar wavelet properties The Haar wavelet ... is math psi t math itself. 4. Wavelet scaling functions with different scale m have a functional relationship ... Image Haar Wavelet 20080121 1.png thumb center Haar matrix The 2 2 Haar matrix that is associated with the Haar wavelet is math H 2 begin bmatrix 1 & 1 1 & 1 end bmatrix . math Using the discrete wavelet ... math left left s 0,d 0 right , dots, left s n,d n right right math of one stage of the fast Haar wavelet ... wavelet transform. Compare with a Walsh matrix , which is a non localized 1 1 matrix. Haar transform The Haar transform is the simplest of the wavelet transform s. This transform cross multiplies a function against the Haar wavelet with various shifts and stretches, like the Fourier transform cross ... matrix Walsh transform Wavelet Notes Reflist References Haar A. Zur Theorie der orthogonalen Funktionensysteme ... more details
refimprove date October 2010 In mathematics , a dual wavelet is the dual space dual to a wavelet . In general, the wavelet series generated by a square integrable function mathematics function will have a dual series, in the sense of the Riesz representation theorem . However, the dual series is not in general representable by a square integral function itself. Definition Given a square integrable function math psi in L 2 mathbb R math , define the series math psi jk math by math psi jk x 2 j 2 psi 2 jx k math for integers math j,k in mathbb Z math . Such a function is called an R function if the linear span of math psi jk math is dense set dense in math L 2 mathbb R math , and if there exist positive constants A , B with math 0 A leq B infty math such that math A Vert c jk Vert 2 l 2 leq bigg Vert sum jk infty infty c jk psi jk bigg Vert 2 L 2 leq B Vert c jk Vert 2 l 2 , math for all bi infinite square summable series math c jk math . Here, math Vert cdot Vert l 2 math denotes the square sum norm math Vert c jk Vert 2 l 2 sum jk infty infty vert c jk vert 2 math and math Vert cdot Vert L 2 math denotes the usual norm on math L 2 mathbb R math math Vert f Vert 2 L 2 int infty infty vert f x vert 2 dx math By the Riesz representation theorem , there exists a unique dual basis math ... tilde psi math is called the dual wavelet or the wavelet dual to &psi . In general, for some given R function &psi , the dual will not exist. In the special case of math psi tilde psi math , the wavelet is said to be an orthogonal wavelet . An example of an R function without a dual is easy to construct. Let math phi math be an orthogonal wavelet. Then define math psi x phi x z phi 2x math for some complex number z . It is straightforward to show that this &psi does not have a wavelet dual. See also Multiresolution analysis References Charles K. Chui, An Introduction to Wavelets Wavelet ... Category Duality theories Wavelet ... more details
20 2 d waveletWavelet Fn X Scaling Fn Named after Ingrid Daubechies , the Daubechies wavelets are a family of orthogonal wavelet s defining a discrete wavelet transform and characterized by a maximal number of vanishing Moment mathematics moments for some given support. With each wavelet type of this class, there is a scaling function also called father wavelet which generates an orthogonal multiresolution ... extremal phase. The wavelet transform is also easy to put into practice using the fast wavelet transform ... in terms of the resulting scaling and wavelet functions in fact, they are not possible ... number of times. class wikitable scaling and wavelet functions Image Daubechies4 functions.svg ... Fourier transforms of the scaling blue and wavelet red functions. Daubechies orthogonal wavelets D2 .... Each wavelet has a number of zero moments or vanishing moments equal to half the number of coefficients. For example, D2 the Haar wavelet has one vanishing moment, D4 has two, etc. A vanishing moment limits the wavelet s ability to represent polynomial behaviour or information in a signal. For example ... invariant wavelet transform shift invariant discrete wavelet transform . Construction Both the scaling sequence Low Pass Filter and the wavelet sequence Band Pass Filter see orthogonal wavelet for details ... representation for a scaling sequence of an orthogonal discrete wavelet transform with approximation ... approximation order Below are the coefficients for the scaling functions for D2 20. The wavelet ... the sign of every second one, i.e., D4 wavelet 0.1830127, 0.3169873, 1.1830127, 0.6830127 . Mathematically ... of the wavelet sequence and a a coefficient of the scaling sequence. N is the wavelet index ... to have sum 2 D2 Haar wavelet Haar D4 D6 D8 D10 D12 D14 D16 D18 D20 1 0.6830127 0.47046721 0.32580343 ... Cohen Daubechies Feauveau wavelet s CDFs . Implementation While software such as Mathematica supports ... Daubechies Wavelet in Mathematica ref a basic implementation is simple in MATLAB in this case, Daubechies ... more details
File MorletWaveletMathematica.svg thumb 250px Morlet wavelet Morlet In mathematics , the Morlet wavelet , named after Jean Morlet , was originally formulated by Goupillaud, Grossmann and Morlet in 1984 as a constant math kappa sigma math subtracted from a plane wave and then localised by a Gaussian Window function Gauss windows window math Psi sigma t c sigma pi frac 1 4 e frac 1 2 t 2 e i sigma t kappa sigma math where math kappa sigma e frac 1 2 sigma 2 math is defined by the admissibility criterion and the normalisation constant math c sigma math is math c sigma left 1 e sigma 2 2e frac 3 4 sigma 2 right frac 1 2 math The Fourier transform of the Morlet wavelet is math hat Psi sigma omega c sigma pi frac 1 4 left e frac 1 2 sigma omega 2 kappa sigma e frac 1 2 omega 2 right math The central frequency math omega Psi math is the position of the global maximum of math hat Psi sigma omega math which, in this case, is given by the solution of the equation math omega Psi sigma 2 1 omega Psi 2 1 e sigma omega Psi math The parameter math sigma math in the Morlet wavelet allows trade between time and frequency resolutions. Conventionally, the restriction math sigma 5 math is used to avoid problems with the Morlet wavelet at low math sigma math high temporal resolution . For signals containing only slowly varying frequency and amplitude modulations audio, for example it is not necessary to use small values of math sigma math . In this case, math kappa sigma math becomes very small e.g. math sigma 5 quad Rightarrow quad kappa sigma 10 5 , math and is, therefore, often neglected. Under the restriction math sigma 5 math , the frequency of the Morlet wavelet is conventionally taken to be math omega Psi simeq sigma math . References P. Goupillaud, A. Grossman, and J. Morlet. Cycle Octave ..., B. Escudi , P. Guillemain, R. Kronland Martinet, P. Tchamitchian, and B. Torr sani. Asymptotic wavelet ... See also Gabor atom Gabor transform Category Continuous wavelets cs Morletova vlnka sv Morlet wavelet ... more details
Unreferenced date December 2009 Hermitian wavelets are a family of continuous wavelets, used in the continuous wavelet transform . The math n textrm th math Hermitian wavelet is defined as the math n textrm th math derivative of a Gaussian math Psi n t 2n frac n 2 c n H n left frac t sqrt n right e frac 1 2n t 2 math where math H n left x right math denotes the math n textrm th math Hermite polynomial . The normalisation coefficient math c n math is given by math c n left n frac 1 2 n Gamma n frac 1 2 right frac 1 2 left n frac 1 2 n sqrt pi 2 n 2n 1 right frac 1 2 quad n in mathbb Z . math The prefactor math C Psi math in the resolution of the identity of the continuous wavelet transform for this wavelet is given by math C Psi frac 4 pi n 2n 1 math i.e. Hermitian wavelets are admissible for all positive math n math . In computer vision and image processing , Gaussian derivative operators of different orders are frequently used as a basis for expressing various types of visual operations see scale space and N jet . Examples of Hermitian wavelets Starting from a Gaussian function with math mu 0, sigma 1 math math f t pi 1 4 e t 2 2 math the first 3 derivatives read math begin align f t & pi 1 4 te t 2 2 f t & pi 1 4 t 2 1 e t 2 2 f 3 t & pi 1 4 3t t 3 e t 2 2 end align math and their math L 2 math norms math f sqrt 2 2, f sqrt 3 2, f 3 sqrt 30 4 math So the wavelets which are the negative normalized derivatives are math begin align Psi 1 t & sqrt 2 pi 1 4 te t 2 2 Psi 2 t & frac 2 3 sqrt 3 pi 1 4 1 t 2 e t 2 2 Psi 3 t & frac 2 15 sqrt 30 pi 1 4 t 3 3t e t 2 2 end align math DEFAULTSORT Hermitian Wavelet Category Continuous wavelets ... more details
Compactly supported wavelet s derived from Legendre polynomials are termed spherical harmonic or Legendre wavelets. ref Lira et al ref Legendre functions have widespread applications in which spherical coordinate system are appropriate. ref name Gradsh Gradshetyn and Ryzhik ref ref name Colomer Colomer and Colomer ref ref Ramm and Zaslavsky ref As with many wavelets there is no nice analytical formula for describing these harmonic spherical wavelets. The low pass filter associated to Legendre multiresolution ... with linear phase filters . These wavelets have been implemented on MATLAB wavelet toolbox . Although being compactly supported wavelet, legdN are not orthogonal but for N 1 . ref Herley and Vetterli ... for math nu math 1,3,5 N is the wavelet order. border 1 cellspacing 0 cellpadding 5 align center ... Legendre wavelets can be easily loaded into the MATLAB wavelet toolbox The m files to allow the computation of Legendre wavelet transform, details and filter are freeware available. The finite support ... . The wavelet has compact support and finite impulse response AMR filters FIR are used table 1 . The first wavelet of the Legendre s family is exactly the well known Haar wavelet . Figure 2 shows an emerging pattern that progressively looks like the wavelet s shape. br Image Figura legd2.jpg thumb .... The Legendre wavelet shape can be visualised using the wavemenu command of MATLAB. Figure 3 shows legd8 wavelet displayed using MATLAB sup TM sup . Legendre Polynomials are also associated with windows families. ref Jaskula ref Image Figura legd3.jpg thumb none 300px Figure 3 legd8 wavelet display over MATLAB sup TM sup using the wavemenu command. Legendre wavelet packets Wavelet packets WP ... functions derived from legd2. Image Figura legd5.jpg thumb none 350px Figure 5 Legendre legd2 Wavelet ... 546, 1994. C. Herley, M. Vetterli, Orthogonalization of Compactly Supported Wavelet Bases, IEEE ... Signal Decomposition The Wavelet Representation, IEEE Trans. Pattern Analysis and Machine ... more details
function of the detail filter of a Mathieu wavelet is math G nu omega e j nu 2 frac omega pi 2 . frac ... wavelet is math H nu omega e j nu frac omega 2 . frac ce nu frac omega 2 ,q ce nu 0,q . math The characteristic ..., i.e. math G nu 0 0 math and math G nu pi 1 math , which are compatible with wavelet filter requirements ... algorithm . Infinite Impulse Response filters IIR filter should be use since Mathieu wavelet has no compact support . Figure 3 shows emerging pattern that progressively looks like the wavelet ... retained coefficients per filter in both cases. a Mathieu Wavelet with &nu 5 and q 5 and b Mathieu wavelet with &nu 1 and q 5. References 1 M.M.S. Lira, H.M. de Oiveira, R.J.S. ..., Theory and Application of Mathieu Functions, New York Dover, 1964. DEFAULTSORT Mathieu Wavelet ... more details
1 m . math Beta wavelets Since math P cdot alpha , beta math is unimodal, the wavelet generated by math ... as the ratio between the lengths of the causal and non causal piece of the wavelet. The instant ... and wavelet for different parameters a math alpha 4 math , math beta 3 math b math alpha 3 math , math beta 7 math c math alpha 5 math , math beta 17 math . Beta wavelet spectrum The beta wavelet spectrum ... leftrightarrow Psi BETA omega alpha , beta math denote the Fourier transform pair associated with the wavelet ... , beta dt N . math This is henceforth referred to as an math N math order beta wavelet. They exist ... beta wavelet math alpha beta 3 math , math alpha beta 4 math , math alpha beta 5 math Image ..., math Psi BETA omega alpha , beta math math times omega math for Asymmetric beta wavelet math alpha ... more details
The modulation index or modulation depth of a modulation scheme describes by how much the modulated variable of the carrier signal varies around its unmodulated level. It is defined differently in each modulation scheme. See amplitude modulationModulation index Amplitude modulation index frequency modulationModulation index Frequency modulation index phase modulationModulation index Phase modulation index Disambig ... more details
Angle modulation is a class of analog signal analog modulation . These techniques are based on altering the angle or phase waves phase of a sinusoidal carrier wave to Transmission telecommunications transmit data, as opposed to varying the amplitude , such as in Amplitude modulation AM transmission. Angle Modulation is modulation in which the angle of a sine wave carrier is varied by a modulating wave. Frequency Modulation FM and Phase Modulation PM are two types of angle modulation. In frequency modulation the modulating signal causes the carrier frequency to vary. These variations are controlled by both the frequency and the amplitude of the modulating wave. In phase modulation the phase of the carrier is controlled by the modulating waveform. The two main types of angle modulation are Frequency modulation FM , with its digital correspondence frequency shift keying FSK . Phase modulation PM , with its digital correspondence phase shift keying PSK . See also Modulation Polar modulation External links http www.vk1od.net FM FM.htm Discussion of practical implementation of FM PM systems telecom stub Category Radio modulation modes de Winkelmodulation ru su Modulasi sudut ... more details
Modulation is the process of varying one or more properties of a high frequency periodic waveform. Modulation may also refer to Modulation European Union , an authorized reduction in direct aid to producers In science Immunomodulation therapy Neuromodulation In music Modulation music , a change of key Modulations , a multimedia project about the history of electronic music Modulate album Modulate , a rock electronica album by Bob Mould Modulator EP Modulator , an electronica EP by Information Society Modulate band , UK electronic band disambig bg de Modulation et Modulatsioon es Modulaci n fr Modulation he nl Modulatie no Modulasjon andre betydninger ru fi Modulaatio ... more details
Unreferenced stub auto yes date December 2009 The modulation order of a digital communication scheme is determined by the number of the different symbols that can be transmitted using it. Modulation order can only be defined for digital modulation s. The simplest forms of digital modulation are of second order because they can transmit only two symbols usually denoted as 0 and 1 or as 1 and 1 . They are called binary shift keying BSK . Modulations which have an order of 4 and above usually are termed as higher order modulation s. Examples of these are quadrature phase shift keying QPSK and its generalisation as m ary quadrature amplitude modulation m QAM . Because existing computers and automation systems are based on binary logic most of the modulations have an order which is a power of two 2, 4, 8, 16, etc. In principle, however, the order of a modulation can be any integer greater than one. When the order of a digital modulation approaches infinity its properties approach those of the respective analog modulation. Thus the analogue modulations can be viewed as extreme cases of higher order digital modulations for which the order is equal to infinity. Category Telecommunication theory DEFAULTSORT Modulation Order Tech stub ... more details
Merge to instrument landing system date May 2012 discuss Talk instrument landing system Multiple merges Modulation techniques Space modulation is a radio Amplitude Modulation technique used in Instrument Landing System s that incorporates the use of multiple antennas fed with various radio frequency powers and phases to create different Difference in the Depth of Modulation depths of modulation within various volumes of three dimensional space three dimensional airspace. This modulation method differs from internal modulation methods inside most other radio transmitters in that the phases and powers of the two individual signals mix within airspace, rather than in a modulator. An aircraft with an on board ILS receiver within the capture area of an ILS, glideslope and localiser range , will detect varying depths of modulation according to the aircraft s position within that airspace, providing accurate positional information about the progress to the threshold. Method used to determine aircraft position The ILS uses two radio frequencies, one for each ground station about 110 MHz for LLZ and 330 MHz for the GP , to transmit two Amplitude modulation Amplitude Modulated signals 90 Hz and 150 Hz , along the glidepath GP and the localiser LLZ trajectories into airspace . It is this signal that is projected up from the runway which an aircraft using an instrument approach, uses to land. The modulation depth of each 90 Hz and 150 Hz signal changes according to the deviation of the aircraft from the correct position for the aircraft to touchdown on the threshold. The difference between the two signal modulation depths is zero when the aircraft is on the correct glideslope on approach to the runway i.e. No difference zero Difference in the depth of modulation DDM , produces no deviation from the middle indication of the instrument s needle within the cockpit of the aircraft. See also Difference in the Depth of Modulation Instrument Landing Syste ... more details
unreferenced date September 2011 A modulation transformer is an Transformer audio frequency transformer that forms a major part of most Amplitude modulation AM transmitters. The primary winding of a modulation transformer is fed by an audio amplifier that has about 1 2 of the rated input power of the transmitter s final amplifier stage. The secondary winding is in series with the power supply of that final radio frequency amplifier stage, thereby lowering and raising the operating voltage of the power amplifier PA tube or transistor. Considering that the PA device is operated as a Electronic amplifier Class C class C amplifier, i.e. as a switch, the modulation transformer is responsible for the amplitude modulation AM of the transmitter. Category Transformers electrical ... more details
Unreferenced date December 2009 Modulation techniques Phase modulation PM is a form of modulation that represents information as variations in the instantaneous phase waves phase of a carrier wave . Unlike its more popular counterpart, frequency modulation FM , PM is not very widely used for radio transmissions. This is because it tends to require more complex receiving hardware and there can be ambiguity problems in determining whether, for example, the signal has changed phase by 180 or 180 . PM is used, however, in digital music synthesizers such as the Yamaha DX7 , even though these instruments are usually referred to as FM synthesizers both modulation types sound very similar, but PM is usually ... of phase modulation. The top diagram shows the modulating signal superimposed on the carrier ... modulation can thus be considered a special case of FM in which the carrier frequency modulation is given by the time derivative of the phase modulation. The mathematics of the spectral density spectral ..., PM is similar to amplitude modulation AM and exhibits its unfortunate doubling of baseband bandwidth ... M omega mathrm m 2 pi math and math h math is the modulation index defined below. This is also known as Carson bandwidth rule Carson s Rule for PM. Modulation index As with other modulation index modulation indices , this quantity indicates by how much the modulated variable varies around its unmodulated ... , math , where math Delta theta math is the peak phase deviation. Compare to the modulation index for frequency modulationModulation index frequency modulation . See also Angle modulation Automatic frequency control Modulation for a list of other modulation techniques Phase shift keying PSK , the digital version of PM Polar modulation Electro optic modulator for Pockel s Effect phase modulation for applying sidebands to a monochromatic wave DEFAULTSORT Phase Modulation Category Radio modulation ... Modulaci n de fase fr Modulation de phase ko it Modulazione di fase kk lv F zes ... more details
Multiple issues unreferenced October 2008 context October 2009 Quadrature modulation is the general technique of modulating two carriers. Examples include Quadrature amplitude modulation , Phase shift keying , and Minimum shift keying . Constellation diagram s are used to examine the modulation in the 2 D signal space. Explanation Sending a signal by amplitude modulation consists of sending the function math y t I t cdot cos omega c t math where math I t math is the signal to encode and math cos omega c t math is the carrier wave, math omega c math is the carrier frequency one is changing the amplitude of a carrier wave to encode the signal, hence amplitude modulation. In general one could also change the phase of the carrier wave, as in phase modulation there is a dimension of phase that is not being used. In fact, one can encode another signal that is 90 out of phase by using a sine wave, as in math z t I t cdot cos omega c t Q t cdot sin omega c t math this 90 the angle of a rectangle, or a 1 4 turn is why it is called quadrature modulation, and the symbols math I t math and math Q t math indicate the in phase signal and quadrature signal. In terms of Euler s formula , math e it cos t i sin t, math amplitude modulation encodes a 1 dimensional real signal, while quadrature modulation ... modulation exploits. Clocking The added channel capacity is not costless, however. An amplitude modulated ... uses quadrature amplitude modulation , this is conveyed by the color burst , a synchronization signal. By contrast, in polar modulation, clock drift simply degrades the phase modulated signal. Polar modulation Main Polar modulation Quadrature modulates two signals by changing the in phase and quadrature ... modulation is called polar modulation , and was developed earlier, in the 1874 quadruplex telegraph by Thomas Edison . See also Matrix decoder Polar modulation DEFAULTSORT Quadrature Modulation Category Radio modulation modes telecomm stub ... more details
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