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Line Spectral Pairs
Line spectral pairs (LSP) or line spectral frequencies (LSF) are used to represent linear prediction coefficients (LPC) for transmission over a channel. LSPs have several properties (e.g. smaller sensitivity to quantization noise) that make them superior to direct quantization of LPCs. For this reason, LSPs are very useful in speech coding. LSP representation was developed by Fumitada Itakura, at Nippon Telegraph and Telephone (NTT) in 1975. From 1975 to 1981, he studied problems in speech analysis and synthesis based on the LSP method. In 1980, his team developed an LSP-based speech synthesizer chip. LSP is an important technology for speech synthesis and coding, and in the 1990s was adopted by almost all international speech coding standards as an essential component, contributing to the enhancement of digital speech communication over mobile channels and the internet worldwide. LSPs are used in the code-excited linear prediction (CELP) algorithm, developed by Bishnu S. Atal and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Predictive Coding
Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model. LPC is the most widely used method in speech coding and speech synthesis. It is a powerful speech analysis technique, and a useful method for encoding good quality speech at a low bit rate. Overview LPC starts with the assumption that a speech signal is produced by a buzzer at the end of a tube (for voiced sounds), with occasional added hissing and popping sounds (for voiceless sounds such as sibilants and plosives). Although apparently crude, this Source–filter model is actually a close approximation of the reality of speech production. The glottis (the space between the vocal folds) produces the buzz, which is characterized by its intensity (loudness) and frequency (pitch). The vocal tract (the throat and mouth) forms the tube, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Polynomial
In algebra, given a polynomial :p(x) = a_0 + a_1x + a_2x^2 + \cdots + a_nx^n, with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial,* denoted by or , is the polynomial :p^*(x) = a_n + a_x + \cdots + a_0x^n = x^n p(x^). That is, the coefficients of are the coefficients of in reverse order. They arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix. In the special case where the field is the complex numbers, when :p(z) = a_0 + a_1z + a_2z^2 + \cdots + a_nz^n, the conjugate reciprocal polynomial, denoted , is defined by, :p^(z) = \overline + \overlinez + \cdots + \overlinez^n = z^n\overline, where \overline denotes the complex conjugate of a_i, and is also called the reciprocal polynomial when no confusion can arise. A polynomial is called self-reciprocal or palindromic if . The coefficients of a self-reciprocal polynomial satisfy for all . Properties Reciprocal polynomials have several connec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jonathan Stein
Jonathan may refer to: *Jonathan (name), a masculine given name Media * ''Jonathan'' (1970 film), a German film directed by Hans W. Geißendörfer * ''Jonathan'' (2016 film), a German film directed by Piotr J. Lewandowski * ''Jonathan'' (2018 film), an American film directed by Bill Oliver * ''Jonathan'' (Buffy comic), a 2001 comic book based on the ''Buffy the Vampire Slayer'' television series * ''Jonathan'' (TV show), a Welsh-language television show hosted by ex-rugby player Jonathan Davies People and biblical figures Bible *Jonathan (1 Samuel), son of King Saul of Israel and friend of David, in the Books of Samuel *Jonathan (Judges), in the Book of Judges Judaism *Jonathan Apphus, fifth son of Mattathias and leader of the Hasmonean dynasty of Judea from 161 to 143 BCE *Rabbi Jonathan, 2nd century *Jonathan (High Priest), a High Priest of Israel in the 1st century Other *Jonathan (apple), a variety of apple * "Jonathan" (song), a 2015 song by French singer and songwrite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log Area Ratio
Log area ratios (LAR) can be used to represent reflection coefficients (another form for linear prediction coefficients) for transmission over a channel. While not as efficient as line spectral pairs (LSPs), log area ratios are much simpler to compute. Let r_k be the ''k''th reflection coefficient of a filter, the ''k''th LAR is: : A_k = \log Use of Log Area Ratios have now been mostly replaced by Line Spectral Pairs, but older codecs, such as GSM-FR use LARs. See also * Line spectral pairs Line spectral pairs (LSP) or line spectral frequencies (LSF) are used to represent linear prediction coefficients (LPC) for transmission over a channel. LSPs have several properties (e.g. smaller sensitivity to quantization noise) that make them s ... Lossy compression algorithms {{Compu-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Conjugate Root Theorem
In mathematics, the complex conjugate root theorem states that if ''P'' is a polynomial in one variable with real coefficients, and ''a'' + ''bi'' is a root of ''P'' with ''a'' and ''b'' real numbers, then its complex conjugate ''a'' − ''bi'' is also a root of ''P''. Preview available aGoogle books/ref> It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is odd, it must have at least one real root. That fact can also be proved by using the intermediate value theorem. Examples and consequences * The polynomial ''x''2 + 1 = 0 has roots ± ''i''. * Any real square matrix of odd degree has at least one real eigenvalue. For example, if the matrix is orthogonal, then 1 or −1 is an eigenvalue. * The polynomial ::x^3 - 7x^2 + 41x - 87 :has roots ::3,\, 2 + 5i,\, 2 - 5i, :and thus can be factored as ::(x - 3)(x - 2 - 5i)(x - 2 + 5i). :In computing the product of the last two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Circle
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as because it is a one-dimensional unit -sphere. If is a point on the unit circle's circumference, then and are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, and satisfy the equation x^2 + y^2 = 1. Since for all , and since the reflection of any point on the unit circle about the - or -axis is also on the unit circle, the above equation holds for all points on the unit circle, not only those in the first quadrant. The interior of the unit circle is called the open unit disk, while the interior of the unit circle combined with the unit circle itself is called the closed unit disk. One may also use other notions of "dista ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero Of A Function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) ''vanishes'' at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. A "zero" of a function is thus an input value that produces an output of 0. A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by f(x)=x^2-5x+6 has the two roots (or zeros) that are 2 and 3. f(2)=2^2-5\times 2+6= 0\textf(3)=3^2-5\times 3+6=0. If the function maps real numbers to real numbers, then it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glottis
The glottis is the opening between the vocal folds (the rima glottidis). The glottis is crucial in producing vowels and voiced consonants. Etymology From Ancient Greek ''γλωττίς'' (glōttís), derived from ''γλῶττα'' (glôtta), variant of ''γλῶσσα'' (glôssa, "tongue"). Function Phonation As the vocal folds vibrate, the resulting vibration produces a "buzzing" quality to the speech, called voice or voicing or pronunciation. Sound production that involves moving the vocal folds close together is called ''glottal''. English has a voiceless glottal transition spelled "h". This sound is produced by keeping the vocal folds spread somewhat, resulting in non-turbulent airflow through the glottis. In many accents of English the glottal stop (made by pressing the folds together) is used as a variant allophone of the phoneme (and in some dialects, occasionally of and ); in some languages, this sound is a phoneme of its own. Skilled players of the Australian di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry. Etymology The word ''polynomial'' join ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speech Coding
Speech coding is an application of data compression of digital audio signals containing speech. Speech coding uses speech-specific parameter estimation using audio signal processing techniques to model the speech signal, combined with generic data compression algorithms to represent the resulting modeled parameters in a compact bitstream. Some applications of speech coding are mobile telephony and voice over IP (VoIP). The most widely used speech coding technique in mobile telephony is linear predictive coding (LPC), while the most widely used in VoIP applications are the LPC and modified discrete cosine transform (MDCT) techniques. The techniques employed in speech coding are similar to those used in audio data compression and audio coding where knowledge in psychoacoustics is used to transmit only data that is relevant to the human auditory system. For example, in voiceband speech coding, only information in the frequency band 400 to 3500 Hz is transmitted but the reconst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manfred R
''Manfred: A dramatic poem'' is a closet drama written in 1816–1817 by Lord Byron. It contains supernatural elements, in keeping with the popularity of the ghost story in England at the time. It is a typical example of a Gothic fiction. Byron commenced this work in late 1816, a few months after the famous ghost-story sessions with Percy Bysshe Shelley and Mary Shelley that provided the initial impetus for '' Frankenstein; or, The Modern Prometheus ''. The supernatural references are made clear throughout the poem. ''Manfred'' was adapted musically by Robert Schumann in 1852, in a composition entitled '' Manfred: Dramatic Poem with Music in Three Parts'', and in 1885 by Pyotr Ilyich Tchaikovsky in his ''Manfred Symphony''. Friedrich Nietzsche was inspired by the poem's depiction of a super-human being to compose a piano score in 1872 based on it, "Manfred Meditation". Background Byron wrote this "metaphysical drama", as he called it, after his marriage to Annabella Millbanke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bishnu S
Vishnu ( ; , ), also known as Narayana and Hari, is one of the Hindu deities, principal deities of Hinduism. He is the supreme being within Vaishnavism, one of the major traditions within contemporary Hinduism. Vishnu is known as "The Preserver" within the Trimurti, the triple deity of Para Brahman, supreme divinity that includes Brahma and Shiva.Gavin Flood, An Introduction to Hinduism' (1996), p. 17. In Vaishnavism, Vishnu is the Para Brahman, supreme being who creates, protects, and transforms the Hindu cosmology, universe. In the Shaktism tradition, the Goddess, or Adi Shakti, is described as the supreme para brahman, Para Brahman, yet Vishnu is revered along with Shiva and Brahma. Tridevi is stated to be the energy and creative power (Shakti) of each, with Lakshmi being the equal complementary partner of Vishnu. He is one of the five equivalent deities in Panchayatana puja of the Smarta tradition of Hinduism. According to Vaishnavism, the highest form of Ishvara is wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
