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Similarity (signal Processing)
Similarity between two different signals is important in the field of signal processing. Below are some common methods for calculating similarity. For instance, let's consider two signals represented as x, n/math> and y, n/math>, where m = 0, 1, 2, ..., M-1 and n = 0, 1, 2, ..., N-1. Maximum error (ME) Measuring the maximum magnitude of the difference between two signals. Maximum error is useful for assessing the worst-case scenario of prediction accuracy ME= \max(\left, y ,nx ,n\) Mean squared error (MSE) Measuring the average squared difference between two signals. Unlike the maximum error, mean squared error takes into account the overall magnitude and spread of errors, offering a comprehensive assessment of the difference between the two signals. MSE= \frac \sum_^ \sum_^ \left, y ,nx ,n\^2 Normalized mean square error (NMSE) NMSE is an extension of MSE. It is calculated by normalizing the MSE with the signal power, enabling fair comparisons across differen ... [...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, Scalar potential, potential fields, Seismic tomography, seismic signals, Altimeter, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to 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 publis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Squared Error
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the true value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the ''empirical'' risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the erro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root-mean-square Deviation
The root mean square deviation (RMSD) or root mean square error (RMSE) is either one of two closely related and frequently used measures of the differences between true or predicted values on the one hand and observed values or an estimator on the other. The deviation is typically simply a differences of scalars; it can also be generalized to the vector lengths of a displacement, as in the bioinformatics concept of root mean square deviation of atomic positions. RMSD of a sample The RMSD of a sample is the quadratic mean of the differences between the observed values and predicted ones. These deviations are called '' residuals'' when the calculations are performed over the data sample that was used for estimation (and are therefore always in reference to an estimate) and are called ''errors'' (or prediction errors) when computed out-of-sample (aka on the full set, referencing a true value rather than an estimate). The RMSD serves to aggregate the magnitudes of the errors in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal-to-noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR is an important parameter that affects the performance and quality of systems that process or transmit signals, such as communication systems, audio systems, radar systems, imaging systems, and data acquisition systems. A high SNR means that the signal is clear and easy to detect or interpret, while a low SNR means that the signal is corrupted or obscured by noise and may be difficult to distinguish or recover. SNR can be improved by various methods, such as increasing the signal strength, reducing the noise level, filtering out unwanted noise, or using error correction techniques. SNR also determines the maximum possible amount of data that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peak Signal-to-noise Ratio
Peak signal-to-noise ratio (PSNR) is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed as a logarithmic quantity using the decibel scale. PSNR is commonly used to quantify reconstruction quality for images and video subject to lossy compression. Definition PSNR is most easily defined via the mean squared error (''MSE''). Given a noise-free ''m''×''n'' monochrome image ''I'' and its noisy approximation ''K'', ''MSE'' is defined as : \mathit = \frac\sum_^\sum_^ (i,j) - K(i,j)2. The PSNR (in dB) is defined as : \begin \mathit &= 10 \cdot \log_ \left( \frac \right) \\ &= 20 \cdot \log_ \left( \frac \right) \\ &= 20 \cdot \log_(\mathit_I) - 10 \cdot \log_ (\mathit). \end Here, ''MAXI'' is the maximum possible pixel value of the image. When the pixels are represented using 8 bits pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manhattan Distance
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two point (geometry), points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or Metric (mathematics), metric) called the ''taxicab distance'', ''Manhattan distance'', or ''city block distance''. The name refers to the island of Manhattan, or generically any planned city with a rectangular grid of streets, in which a taxicab can only travel along grid directions. In taxicab geometry, the distance between any two points equals the length of their shortest grid path. This different definition of distance also leads to a different definition of the length of a curve, for which a line segment between any two points has the same length as a grid path between those points rather than its Euclidean length. The taxicab distance is also sometimes known as ''rectilinear distance'' or distanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's ''Elements'', distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. The connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Similarity
The structural similarity index measure (SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. It is also used for measuring the similarity between two images. The SSIM index is a full reference metric; in other words, the measurement or prediction of image quality is based on an initial uncompressed or distortion-free image as reference. SSIM is a perception-based model that considers image degradation as perceived change in structural information, while also incorporating important perceptual phenomena, including both luminance masking and contrast masking terms. This distinguishes from other techniques such as mean squared error (MSE) or peak signal-to-noise ratio (PSNR) that instead estimate absolute errors. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. The sign of the covariance, therefore, shows the tendency in the linear relationship between the variables. If greater values of one variable mainly correspond with greater values of the other variable, and the same holds for lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when greater values of one variable mainly correspond to lesser values of the other (that is, the variables tend to show opposite behavior), the covariance is negative. The magnitude of the covariance is the geometric mean of the variances that are in common for the two random variables. The Pearson product-moment correlation coefficient, correlation coefficient normalizes the covariance by dividing by the geometric mean of the total variances for the two random variables. A distinction must be made between (1) the covariance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Range
Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' " power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics), the study of forces and their effect on motion Brands and enterprises * Dynamic (record label), an Italian record label in Genoa Mathematics * Dynamical system, a concept describing a point's time dependency ** Topological dynamics, the study of dynamical systems from the viewpoint of general topology * Symbolic dynamics, a method to model dynamical systems Social science * Group dynamics, the study of social group processes especially * Population dynamics, in life sciences, the changes in the composition of a population * Psychodynamics, the study of psychological forces driving human behavior * Social dynamics, the ability of a society to react to changes * Spiral Dynamics, a social development theory Other uses * Dynamics (music), the softness or loudness of a sound or note * DTA Dynami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
