In audio signal processing and acoustics, echo is a reflection of sound that arrives at the listener with a delay after the direct sounds. The delay is directly proportional to the distance of the reflecting surface from the source and the listener. Typical examples are the echo produced by the bottom of a well, by a buildings, or by the wall of an enclosed room and an empty room. A true echo is a single reflection of the sound source; the word echo derives from the Greek ἠχώ, itself from ἦχος, "sound". Echo in the folk story of Greek is a mountain nymph whose ability to speak was cursed, only able to repeat the last words anyone spoke to her; some animals use echo for location navigation, such as cetaceans and bats. Acoustic waves are reflected by other hard surfaces, such as mountains and privacy fences; the reason of reflection may be explained as a discontinuity in the propagation medium. This can be heard when the reflection returns with sufficient magnitude and delay to be perceived distinctly.
When sound, or the echo itself, is reflected multiple times from multiple surfaces, the echo is characterized as a reverberation. The human ear cannot distinguish echo from the original direct sound if the delay is less than 1/10 of a second; the velocity of sound in dry air is 343 m/s at a temperature of 25 °C. Therefore, the reflecting object must be more than 15.7m from the sound source for echo to be perceived by a person located at the source. When a sound produces an echo in two seconds, the reflecting object is 343m away. In nature, canyon walls or rock cliffs facing water are the most common natural settings for hearing echoes; the strength of echo is measured in dB sound pressure level relative to the directly transmitted wave. Echoes may be undesirable. In music performance and recording, electric echo effects have been used since the 1950s; the Echoplex is a tape delay effect, first made in 1959 that recreates the sound of an acoustic echo. Designed by Mike Battle, the Echoplex set a standard for the effect in the 1960s and was used by most of the notable guitar players of the era.
While Echoplexes were used by guitar players, many recording studios used the Echoplex. Beginning in the 1970s, Market built the solid-state Echoplex for Maestro. In the 2000s, most echo effects units use electronic or digital circuitry to recreate the echo effect. Inchindown oil tanks, current record holder for longest echo. Hamilton Mausoleum, South Lanarkshire, Scotland: Its high stone means it takes 15 seconds for the sound of a slammed door to delay. Gol Gumbaz of Bijapur, India: Any whisper, clap or sound gets echoed repeatedly; the Golkonda Fort of Hyderabad, India The Echo Wall at the Temple of Heaven, China The Whispering Gallery of St Paul's Cathedral, England, UK Echo Point, the Three Sisters, Australia The Temple of Kukulcan El Castillo, Chichen Itza, Mexico The Baptistry of Pisa, Italy The echo near Milan visited by Mark Twain in The Innocents Abroad The echo in Chinon, France, used in a traditional local rhyme The gazebo of Napier Museum in Trivandrum, India Light echo More information on Chinon echo.
Listen to Duck echoes and an animated demonstration of how an echo is formed
An earthquake is the shaking of the surface of the Earth, resulting from the sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to toss people around and destroy whole cities; the seismicity, or seismic activity, of an area is the frequency and size of earthquakes experienced over a period of time. The word tremor is used for non-earthquake seismic rumbling. At the Earth's surface, earthquakes manifest themselves by shaking and displacing or disrupting the ground; when the epicenter of a large earthquake is located offshore, the seabed may be displaced sufficiently to cause a tsunami. Earthquakes can trigger landslides, volcanic activity. In its most general sense, the word earthquake is used to describe any seismic event—whether natural or caused by humans—that generates seismic waves. Earthquakes are caused by rupture of geological faults, but by other events such as volcanic activity, mine blasts, nuclear tests.
An earthquake's point of initial rupture is called its hypocenter. The epicenter is the point at ground level directly above the hypocenter. Tectonic earthquakes occur anywhere in the earth where there is sufficient stored elastic strain energy to drive fracture propagation along a fault plane; the sides of a fault move past each other smoothly and aseismically only if there are no irregularities or asperities along the fault surface that increase the frictional resistance. Most fault surfaces do have such asperities and this leads to a form of stick-slip behavior. Once the fault has locked, continued relative motion between the plates leads to increasing stress and therefore, stored strain energy in the volume around the fault surface; this continues until the stress has risen sufficiently to break through the asperity allowing sliding over the locked portion of the fault, releasing the stored energy. This energy is released as a combination of radiated elastic strain seismic waves, frictional heating of the fault surface, cracking of the rock, thus causing an earthquake.
This process of gradual build-up of strain and stress punctuated by occasional sudden earthquake failure is referred to as the elastic-rebound theory. It is estimated that only 10 percent or less of an earthquake's total energy is radiated as seismic energy. Most of the earthquake's energy is used to power the earthquake fracture growth or is converted into heat generated by friction. Therefore, earthquakes lower the Earth's available elastic potential energy and raise its temperature, though these changes are negligible compared to the conductive and convective flow of heat out from the Earth's deep interior. There are three main types of fault, all of which may cause an interplate earthquake: normal and strike-slip. Normal and reverse faulting are examples of dip-slip, where the displacement along the fault is in the direction of dip and movement on them involves a vertical component. Normal faults occur in areas where the crust is being extended such as a divergent boundary. Reverse faults occur in areas.
Strike-slip faults are steep structures where the two sides of the fault slip horizontally past each other. Many earthquakes are caused by movement on faults that have components of both dip-slip and strike-slip. Reverse faults those along convergent plate boundaries are associated with the most powerful earthquakes, megathrust earthquakes, including all of those of magnitude 8 or more. Strike-slip faults continental transforms, can produce major earthquakes up to about magnitude 8. Earthquakes associated with normal faults are less than magnitude 7. For every unit increase in magnitude, there is a thirtyfold increase in the energy released. For instance, an earthquake of magnitude 6.0 releases 30 times more energy than a 5.0 magnitude earthquake and a 7.0 magnitude earthquake releases 900 times more energy than a 5.0 magnitude of earthquake. An 8.6 magnitude earthquake releases the same amount of energy as 10,000 atomic bombs like those used in World War II. This is so because the energy released in an earthquake, thus its magnitude, is proportional to the area of the fault that ruptures and the stress drop.
Therefore, the longer the length and the wider the width of the faulted area, the larger the resulting magnitude. The topmost, brittle part of the Earth's crust, the cool slabs of the tectonic plates that are descending down into the hot mantle, are the only parts of our planet which can store elastic energy and release it in fault ruptures. Rocks hotter than about 300 °C flow in response to stress; the maximum observed lengths of ruptures and mapped faults are 1,000 km. Examples are the earthquakes in Chile, 1960; the longest earthquake ruptures on strike-slip faults, like the San Andreas Fault, the North Anatolian Fault in Turkey and the Denali Fault in Alaska, are about half to one third as long as the lengths along subducting plate margins, those along normal faults are shorter. The most important parameter controlling the maximum earthquake magnitude on a fault is however not the maximum available length, but the available width because the latter varies by a factor of 20. Along converging plate margins, the dip angle of the rupture plane is shallow about 10 de
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
A bomb is an explosive weapon that uses the exothermic reaction of an explosive material to provide an sudden and violent release of energy. Detonations inflict damage principally through ground- and atmosphere-transmitted mechanical stress, the impact and penetration of pressure-driven projectiles, pressure damage, explosion-generated effects. Bombs have been utilized since the 11th century starting in East Asia; the term bomb is not applied to explosive devices used for civilian purposes such as construction or mining, although the people using the devices may sometimes refer to them as a "bomb". The military use of the term "bomb", or more aerial bomb action refers to airdropped, unpowered explosive weapons most used by air forces and naval aviation. Other military explosive weapons not classified as "bombs" include shells, depth charges, or land mines. In unconventional warfare, other names can refer to a range of offensive weaponry. For instance, in recent Middle Eastern conflicts, homemade bombs called "improvised explosive devices" have been employed by insurgent fighters to great effectiveness.
The word comes from the Latin bombus, which in turn comes from the Greek βόμβος, an onomatopoetic term meaning "booming", "buzzing". Explosive bombs were used by a Jurchen Jin army against a Chinese Song city. Bombs built using bamboo tubes appear in the 11th century. Bombs made of cast iron shells packed with explosive gunpowder date to 13th century China; the term was coined for this bomb during a Jin dynasty naval battle of 1231 against the Mongols. The History of Jin 《金史》 states that in 1232, as the Mongol general Subutai descended on the Jin stronghold of Kaifeng, the defenders had a "thunder-crash bomb" which "consisted of gunpowder put into an iron container... when the fuse was lit there was a great explosion the noise whereof was like thunder, audible for more than thirty miles, the vegetation was scorched and blasted by the heat over an area of more than half a mou. When hit iron armour was quite pierced through." The Song Dynasty official Li Zengbo wrote in 1257 that arsenals should have several hundred thousand iron bomb shells available and that when he was in Jingzhou, about one to two thousand were produced each month for dispatch of ten to twenty thousand at a time to Xiangyang and Yingzhou.
The Ming Dynasty text Huolongjing describes the use of poisonous gunpowder bombs, including the "wind-and-dust" bomb. During the Mongol invasions of Japan, the Mongols used the explosive "thunder-crash bombs" against the Japanese. Archaeological evidence of the "thunder-crash bombs" has been discovered in an underwater shipwreck off the shore of Japan by the Kyushu Okinawa Society for Underwater Archaeology. X-rays by Japanese scientists of the excavated shells confirmed. Explosive shock waves can cause situations such as body displacement, internal bleeding and ruptured eardrums. Shock waves produced by explosive events have two distinct components, the positive and negative wave; the positive wave shoves outward from the point of detonation, followed by the trailing vacuum space "sucking back" towards the point of origin as the shock bubble collapses. The greatest defense against shock injuries is distance from the source of shock; as a point of reference, the overpressure at the Oklahoma City bombing was estimated in the range of 28 MPa.
A thermal wave is created by the sudden release of heat caused by an explosion. Military bomb tests have documented temperatures of up to 2,480 °C. While capable of inflicting severe to catastrophic burns and causing secondary fires, thermal wave effects are considered limited in range compared to shock and fragmentation; this rule has been challenged, however, by military development of thermobaric weapons, which employ a combination of negative shock wave effects and extreme temperature to incinerate objects within the blast radius. This would be fatal to humans. Fragmentation is produced by the acceleration of shattered pieces of bomb casing and adjacent physical objects; the use of fragmentation in bombs dates to the 14th century, appears in the Ming Dynasty text Huolongjing. The fragmentation bombs were filled with iron pieces of broken porcelain. Once the bomb explodes, the resulting shrapnel is capable of piercing the skin and blinding enemy soldiers. While conventionally viewed as small metal shards moving at super-supersonic and hypersonic speeds, fragmentation can occur in epic proportions and travel for extensive distances.
When the SS Grandcamp exploded in the Texas City Disaster on April 16, 1947, one fragment of that blast was a two-ton anchor, hurled nearly two miles inland to embed itself in the parking lot of the Pan American refinery. Fragmentation should not be confused with shrapnel, which relies on the momentum of a shell to cause damage. To people who are close to a blast incident, such as bomb disposal technicians, soldiers wearing body armor, deminers, or individuals wearing little to no protection, there are four types of blast effects on the human body: overpressure, fragmentation and heat. Overpressure refers to the sudden and drastic rise in ambient pressure that can damage the internal organs leading to permanent damage or death. Fragmentation includes the shrapnel described above but can include sand and vegetation from the area surrounding the blast source; this is common in anti-personnel mine blasts. The projection of materials poses a lethal threat caused by cuts in soft tiss
Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques are applied, followed by mapping back to the original domain. This concept was developed in the 1960s by Thomas Stockham, Alan V. Oppenheim, Ronald W. Schafer at MIT and independently by Bogert and Tukey in their study of time series. Homomorphic filter is sometimes used for image enhancement, it normalizes the brightness across an image and increases contrast. Here homomorphic filtering is used to remove multiplicative noise. Illumination and reflectance are not separable, but their approximate locations in the frequency domain may be located. Since illumination and reflectance combine multiplicatively, the components are made additive by taking the logarithm of the image intensity, so that these multiplicative components of the image can be separated linearly in the frequency domain. Illumination variations can be thought of as a multiplicative noise, can be reduced by filtering in the log domain.
To make the illumination of an image more the high-frequency components are increased and low-frequency components are decreased, because the high-frequency components are assumed to represent the reflectance in the scene, whereas the low-frequency components are assumed to represent the illumination in the scene. That is, high-pass filtering is used to suppress low frequencies and amplify high frequencies, in the log-intensity domain. Homomorphic Filtering can be used for improving the appearance of a grayscale image by simultaneous intensity range compression and contrast enhancement. M = i ∙ r Where, m = image, i = illumination, r = reflectance We have to transform the equation into frequency domain in order to apply high pass filter. However, it's difficult to do calculation after applying Fourier transformation to this equation because it's not a product equation anymore. Therefore, we use'log' to help solving this problem. Ln = ln + ln Then, applying Fourier transformation ϝ = ϝ + ϝ Or M = I + R Next, applying high-pass filter to the image.
To make the illumination of an image more the high-frequency components are increased and low-frequency components are decrease. N = H ∙ M Where H = any high-pass filter N = filtered image in frequency domain Afterward, returning frequency domain back to the spatial domain by using inverse Fourier transform. N = i n v F Finally, using exponential function to eliminate the log we used at the beginning to get the enhanced image n e w I m a g e = e x p The following figures show the results by applying homomorphic filter, high-pass filter, both homomorphic and high-pass filter. All figures are produced by using Matlab. According to the figures one to four, we can see that how homomorphic filtering is used for correcting non-uniform illumination in image, the image become clearer than the original image. On the other hand, if we apply high pass filter to homomorphic filtered image, the edges of the images become sharper and the other areas become dimmer; this result is as similar as just doing high pass filter only to the original image.
Homomorphic filtering is used in the log-spectral domain to separate filter effects from excitation effects, for example in the computation of the cepstrum as a sound representation. Homomorphic filtering was used to removes the effect of the stochastic impulse trains, which originates the sEMG signal, from the power spectrum of sEMG signal itself. In this way, only information on motor unit action potentialn shape and amplitude were maintained, used to est
Manfred R. Schroeder
Manfred Robert Schroeder was a German physicist, most known for his contributions to acoustics and computer graphics. He published over 150 articles in his field. Born in Ahlen, he studied at the University of Göttingen, earning a vordiplom in mathematics and Dr. rer. nat. in physics. His thesis showed, he joined the technical staff at Bell Labs in New Jersey researching speech and graphics, securing forty-five patents. With Bishnu Atal he was a promoter of linear predictive coding. Still affiliated with Bell, he rejoined University of Göttingen as Universitätsprofessor Physik becoming professor emeritus, he was a visiting professor at University of Tokyo. With B. S. Atal he developed code excited linear prediction. With Ning Xiang he was a promoter of a synchronous dual channel measurement method using reciprocal maximum-length sequences, he led a famed study of 22 concert halls worldwide, leading to a comparison method requiring no travel. Number Theory in Science and Communication: With Applications in Cryptography, Biology, Digital Information, Computing.
Fractals, Power Laws: Minutes from an Infinite Paradise Computer speech recognition, synthesis. With H. Quast and H. W. Strube Hundert Jahre Friedrich Hund: Ein Rückblick auf das Wirken eines bedeutenden Physikers 1969 First Prize at the International Computer Art Competition for his application of concepts from mathematics and physics to the creation of artistic works. Fellow of the Acoustical Society of America IEEE Fellow. Audio Engineering Society fellow and Gold medalist Member of the United States National Academy of Engineering, for "founding the statistical theory of wave propagation in multi-mode media and contributions to speech coding and acoustics". Fellow of the American Academy of Arts and Sciences. Helmholtz Medal of the German Acoustical Society 1975 Max Planck Society appointed foreign scientific member New York Academy of Sciences member 1978 Rayleigh Medal 1984 and 1987 Gold Medal from the Acoustical Society of America, for "theoretical and practical contributions to human communication through innovative application of mathematics to speech and concert hall acoustics".
ISCA Medal for Scientific Achievement from the International Speech Communication Association. Technology Award from the German Eduard Rhein Foundation
In mathematics convolution is a mathematical operation on two functions to produce a third function that expresses how the shape of one is modified by the other. The term convolution refers to the process of computing it; some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, it differs from cross-correlation only in that either f or g is reflected about the y-axis. For continuous functions, the cross-correlation operator is the adjoint of the convolution operator. Convolution has applications that include probability, computer vision, natural language processing and signal processing and differential equations; the convolution can be defined for functions on Euclidean space, other groups. For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. A discrete convolution can be defined for functions on the set of integers. Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, in the design and implementation of finite impulse response filters in signal processing.
Computing the inverse of the convolution operation is known as deconvolution. The convolution of f and g is written f ∗ g, using an star, it is defined as the integral of the product of the two functions after one is shifted. As such, it is a particular kind of integral transform: An equivalent definition is: ≜ ∫ − ∞ ∞ f g d τ. While the symbol t is used above, it need not represent the time domain, but in that context, the convolution formula can be described as a weighted average of the function f at the moment t where the weighting is given by g shifted by amount t. As t changes, the weighting function emphasizes different parts of the input function. For functions f, g supported on only [0, ∞), the integration limits can be truncated, resulting in: = ∫ 0 t f g d τ for f, g: [ 0, ∞ ) → R. For the multi-dimensional formulation of convolution, see domain of definition. A common engineering convention is: f ∗ g ≜ ∫ − ∞ ∞ f g d τ ⏟, which has to be interpreted to avoid confusion. For instance, f ∗ g is equivalent to.
Convolution describes the output of an important class of operations known as linear time-invariant. See LTI system theory for a derivation of convolution as the result of LTI constraints. In terms of the Fourier transforms of the input and output of an LTI operation, no new frequency components are created; the existing ones are only modified. In other words, the output transform is the pointwise product of the input transform with a third transform. See Convolution theorem for a derivation of that property of convolution. Conversely, convolution can be derived as the inverse Fourier transform of the pointwise product of two Fourier transforms. One of the earliest uses of the convolution integral appeared in D'Alembert's derivation of Taylor's theorem in Recherches sur différents points importants du système du monde, published in 1754. An expression of the type: ∫ f ⋅ g d u is used by Sylvestre François Lacroix on page 505 of his book entitled Treatise on differences and series, the last of 3 volumes of the encyclopedic series: Traité du calcul différentiel et du calcul intégral, Chez Courcier, Paris, 1797–1800.
Soon thereafter, convolution operations appear in the works of Pierre Simon Laplace, Jean-Baptiste Joseph Fourier, Siméon Denis Poisson, others. The term itself did not come into wide use until the 60s. Prior to that it was sometimes known as Faltung, composition product, superposition integral, Carson's integral, yet it appears as early as 1903. The o