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Steered-Response Power Phase Transform
Steered-Response Power Phase Transform (SRP-PHAT) is a popular algorithm for acoustic source localization, well known for its robust performance in adverse acoustic environments. The algorithm can be interpreted as a beamforming-based approach that searches for the candidate position that maximizes the output of a steered delay-and-sum beamformer. Algorithm Steered-Response Power Consider a system of M microphones, where each microphone is denoted by a subindex m \in \. The discrete-time output signal from a microphone is s_m (n). The (unweighted) steered-response power (SRP) at a spatial point \mathbf = , y, z can be expressed as P_0(\mathbf) \triangleq \sum_ \left\vert \sum_^ s_m(n-\tau_m(\mathbf)) \right\vert^, where \mathbb denotes the set of integer numbers and \tau_m(\mathbf) would be the time-lag due to the propagation from a source located at \mathbf to the m-th microphone. The (weighted) SRP can be rewritten as P(\mathbf) = \frac \sum_^\sum_^ \int_^ \Phi_(e^)S_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustic Source Localization
Acoustic location is the use of sound to determine the distance and direction of its source or reflector. Location can be done actively or passively, and can take place in gases (such as the atmosphere), liquids (such as water), and in solids (such as in the earth). * ''Active'' acoustic location involves the creation of sound in order to produce an echo, which is then analyzed to determine the location of the object in question. * ''Passive'' acoustic location involves the detection of sound or vibration created by the object being detected, which is then analyzed to determine the location of the object in question. Both of these techniques, when used in water, are known as sonar; passive sonar and active sonar are both widely used. Acoustic mirrors and dishes, when using microphones, are a means of passive acoustic localization, but when using speakers are a means of active localization. Typically, more than one device is used, and the location is then triangulated between t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beamforming
Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in an antenna array in such a way that signals at particular angles experience constructive interference while others experience destructive interference. Beamforming can be used at both the transmitting and receiving ends in order to achieve spatial selectivity. The improvement compared with omnidirectional reception/transmission is known as the directivity of the array. Beamforming can be used for radio or sound waves. It has found numerous applications in radar, sonar, seismology, wireless communications, radio astronomy, acoustics and biomedicine. Adaptive beamforming is used to detect and estimate the signal of interest at the output of a sensor array by means of optimal (e.g. least-squares) spatial filtering and interference rejection. Techniques To change the directionality of the array when transm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete-time Beamforming
Beamforming is a signal processing technique used to spatially select propagating waves (most notably acoustic and electromagnetic waves). In order to implement beamforming on digital hardware the received signals need to be discretized. This introduces quantization error, perturbing the array pattern. For this reason, the sample rate must be generally much greater than the Nyquist rate. Introduction Beamforming aims to solve the problem of filtering signals coming from a certain direction as opposed to an omni-directional approach. Discrete-time beamforming is primarily of interest in the fields of seismology, acoustics, sonar and low frequency wireless communications. Antennas regularly make use of beamforming but it is mostly contained within the analog domain. Beamforming begins with an array of sensors to detect a 4-D signal (3 physical dimensions and time). A 4-D signal s(\mathbf,t) exists in the spatial domain at position \mathbf and at time t. The 4-D Fourier transform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete-time Fourier Transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function. Under certain theoretical conditions, described by the sampling theorem, the original continuous function can be recovered perfectly from the DTFT and thus from the original discrete samples. The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see ), which is by far the most common method of modern Fourier analysis. Both transforms are invertible. The inverse DTFT is the origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multilateration
Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth (geopositioning). When more than three distances are involved, it may be called multilateration, for emphasis. The distances or ranges might be ordinary Euclidean distances (slant ranges) or spherical distances (scaled central angles), as in '' true-range multilateration''; or biased distances (pseudo-ranges), as in ''pseudo-range multilateration''. Trilateration or multilateration should not be confused with ''triangulation'', which uses angles for positioning; and ''direction finding'', which determines the line of sight direction to a target without determining the radial distance. Terminology Multiple, sometimes overlapping and conflicting terms are employed for similar concepts – e.g., ''multilateration'' without modification has been used for aviation systems employing both true-ranges and pseudo-ranges."Multilateration (MLAT) Conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as well as the medium through which a sound wave is propagating. At , the speed of sound in air is about . The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior. In colloquial speech, ''speed of sound'' refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases, faster in liquids, and fastest in solids. For example, while sound travels at in air, it travels at in water (almost 4.3 times as fast) and at in iron (almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the Euclidean norm, or 2-norm, which may also be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a ''seminormed vector space''. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality "\,\leq\," in the homogeneity axiom. It can also re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustic Source Localization
Acoustic location is the use of sound to determine the distance and direction of its source or reflector. Location can be done actively or passively, and can take place in gases (such as the atmosphere), liquids (such as water), and in solids (such as in the earth). * ''Active'' acoustic location involves the creation of sound in order to produce an echo, which is then analyzed to determine the location of the object in question. * ''Passive'' acoustic location involves the detection of sound or vibration created by the object being detected, which is then analyzed to determine the location of the object in question. Both of these techniques, when used in water, are known as sonar; passive sonar and active sonar are both widely used. Acoustic mirrors and dishes, when using microphones, are a means of passive acoustic localization, but when using speakers are a means of active localization. Typically, more than one device is used, and the location is then triangulated between t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Audio Signal Processing
Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals. Audio signals are electronic representations of sound waves—longitudinal waves which travel through air, consisting of compressions and rarefactions. The energy contained in audio signals is typically measured in decibels. As audio signals may be represented in either digital or analog format, processing may occur in either domain. Analog processors operate directly on the electrical signal, while digital processors operate mathematically on its digital representation. History The motivation for audio signal processing began at the beginning of the 20th century with inventions like the telephone, phonograph, and radio that allowed for the transmission and storage of audio signals. Audio processing was necessary for early radio broadcasting, as there were many problems with studio-to-transmitter links. The theory of signal processing and its appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History 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. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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