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Grating Lobes
For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, a spatial aliasing effect allows plane waves incident to the array from visible angles other than the desired direction to be coherently added, causing grating lobes. Grating lobes are undesirable and identical to the main lobe. The perceived difference seen in the grating lobes is because of the radiation pattern of non-isotropic antenna elements, which effects main and grating lobes differently. For isotropic antenna elements, the main and grating lobes are identical. Definition In antenna or transducer arrays, a grating lobe is defined as "a lobe other than the main lobe, produced by an array antenna when the inter-element spacing is sufficiently large to permit the in-phase addition of radiated fields in more than one direction." Derivation To illustrate the concept of grating lobes, we will use a simple uniform linear array. The beam pattern (or array ...
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Typical Antenna Pattern With Grating Lobes
Typical may refer to: * ''Typical'' (album), Peter Hammill * "Typical" (song), song by MuteMath *"Typical", song by Frazier Chorus from ''Sue'', 1987 *''Typical'', story collection by Padgett Powell, 1991 See also *''Typical Rick ''Typical Rick'' is an American television series produced by Comedy Central, created by Nicholaus Goossen and Nick Swardson. Comedy Central declined to renew the series for a third season. Cast * Nick Swardson as Gary * Simon Rex as Rick * Mega ...
'', an American Comedy Central television series {{dab ...
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Phased Array
In antenna theory, a phased array usually means an electronically scanned array, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving the antennas. In a simple array antenna, the radio frequency current from the transmitter is fed to multiple individual antenna elements with the proper phase relationship so that the radio waves from the separate elements combine ( superpose) to form beams, to increase power radiated in desired directions and suppress radiation in undesired directions. In a phased array, the power from the transmitter is fed to the radiating elements through devices called ''phase shifters'', controlled by a computer system, which can alter the phase or signal delay electronically, thus steering the beam of radio waves to a different direction. Since the size of an antenna array must extend many wavelengths to achieve the high gain needed for narrow bea ...
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Aliasing
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when a signal reconstructed from samples is different from the original continuous signal. Aliasing can occur in signals sampled in time, for instance digital audio, or the stroboscopic effect, and is referred to as temporal aliasing. It can also occur in spatially sampled signals (e.g. moiré patterns in digital images); this type of aliasing is called spatial aliasing. Aliasing is generally avoided by applying low-pass filters or anti-aliasing filters (AAF) to the input signal before sampling and when converting a signal from a higher to a lower sampling rate. Suitable reconstruction filtering should then be used when restoring the sampled signal to the continuous domain or converting a signal from a lower to a higher sampling rate. For spa ...
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Phased Array Radiation Pattern
A phaser is an electronic sound processor used to filter a signal, and it has a series of troughs in its frequency-attenutation graph. The position (in Hz) of the peaks and troughs are typically modulated by an internal low-frequency oscillator so that they vary over time, creating a sweeping effect. Phasers are often used to give a "synthesized" or electronic effect to natural sounds, such as human speech. The voice of C-3PO from ''Star Wars'' was created by taking the actor's voice and treating it with a phaser. Process The electronic phasing effect is created by splitting an audio signal into two paths. One path treats the signal with an all-pass filter, which preserves the amplitude of the original signal and alters the phase. The amount of change in phase depends on the frequency. When signals from the two paths are mixed, the frequencies that are out of phase will cancel each other out, creating the phaser's characteristic notches. Changing the mix ratio changes the d ...
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Uniform Linear Array
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summer camp ...
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Beam Pattern
Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized group of electrically charged particles ***Cathode ray, or electron beam or e-beam, streams of electrons observed in discharge tubes ***X-ray beam, a penetrating form of high-energy electromagnetic radiation ** Molecular beam, a beam of particles moving at approximately equal velocities Arts, entertainment and media * Beam (music), a connection line in musical notation * Beam, to transport matter using the Transporter in the ''Star Trek'' fictional universe * Beam (rapper), American hip hop artist * BEAM.TV, an online digital delivery and content management platform * BEAM Channel 31, a Philippines television network * Beam (website), later Mixer, a former video game live streaming platform * BeamNG.drive, an open-world vehicle simulation ...
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Array Factor
An array is simply a group of objects, and the array factor is a measure of how much a specific characteristic changes because of the grouping. This phenomenon is observed when antennas are grouped together. The radiation (or reception) pattern of the antenna group is considerably different from that of a single antenna. This is due to the constructive and destructive interference properties of radio waves. A well designed antenna array, allows the broadcast power to be directed to where it is needed most. These antenna arrays are typically one dimensional, as seen on collinear dipole arrays, or two dimensional as on military phased arrays. In order to simplify the mathematics, a number of assumptions are typically made: 1. all radiators are equal in every respect 2. all radiators are uniformly spaced 3. the signal phase shift between radiators is constant. The array factor AF is the complex-valued far-field radiation pattern obtained for an array of N isotropic radiat ...
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Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In mo ...
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Steering Vector
Steering is a system of components, linkages, and other parts that allows a driver to control the direction of the vehicle. Introduction The most conventional steering arrangement allows a driver to turn the front wheels of a vehicle using a hand–operated steering wheel positioned in front of the driver. The steering wheel is attached to a steering column, which is linked to rods, pivots and gears that allow the driver to change the direction of the front wheels. Other arrangements are sometimes found on different types of vehicles; for example, a tiller or rear-wheel steering. Tracked vehicles such as bulldozers and tanks usually employ differential steering, where the tracks are made to move at different speeds or even in opposite directions, using clutches and brakes, to achieve a change of direction. Land vehicle steering Basic geometry Ackerman Steering Linkage.gif, Ackermann steering Bell-Crank Steering Linkage.gif, Bell-crank steering Rack-And-Pinion Steering Link ...
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Manifold Vector
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. ...
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L'Hôpital's Rule
In calculus, l'Hôpital's rule or l'Hospital's rule (, , ), also known as Bernoulli's rule, is a theorem which provides a technique to evaluate limits of indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be easily evaluated by substitution. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital. Although the rule is often attributed to l'Hôpital, the theorem was first introduced to him in 1694 by the Swiss mathematician Johann Bernoulli. L'Hôpital's rule states that for functions and which are differentiable on an open interval except possibly at a point contained in , if \lim_f(x)=\lim_g(x)=0 \text \pm\infty, and g'(x)\ne 0 for all in with , and \lim_\frac exists, then :\lim_\frac = \lim_\frac. The differentiation of the numerator and denominator often simplifies the quotient or converts it to a limit that can be evaluated directly. History Guillaume ...
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Visible Region
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye will respond to wavelengths from about 380 to about 750 nanometers. In terms of frequency, this corresponds to a band in the vicinity of 400–790  terahertz. These boundaries are not sharply defined and may vary per individual. Under optimal conditions these limits of human perception can extend to 310 nm (ultraviolet) and 1100 nm (near infrared). The optical spectrum is sometimes considered to be the same as the visible spectrum, but some authors define the term more broadly, to include the ultraviolet and infrared parts of the electromagnetic spectrum as well. The spectrum does not contain all the colors that the human visual system can distinguish. '' Unsaturated colors'' such as pink, or purple variations like magenta, for example, are ab ...
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