Hexagonal Sampling
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Hexagonal Sampling
A multidimensional signal is a function of M independent variables where M \ge 2. Real world signals, which are generally continuous time signals, have to be discretized (sampled) in order to ensure that digital systems can be used to process the signals. It is during this process of discretization where sampling comes into picture. Although there are many ways of obtaining a discrete representation of a continuous time signal, periodic sampling is by far the simplest scheme. Theoretically, sampling can be performed with respect to any set of points. But practically, sampling is carried out with respect to a set of points that have a certain algebraic structure. Such structures are called lattices.Ton Kalker,"On Multidimensional Sampling", Philip Research Laboratories, Eindhoven, chapter 4, section 4.2 Mathematically, the process of sampling an N-dimensional signal can be written as: :w(\hat) = w(V.\hat) where \hat is continuous domain M-dimensional vector (M-D) that is being ...
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Digital Systems
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals. Digital electronic circuits are usually made from large assemblies of logic gates, often packaged in integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. History The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it was the brain-child of George Boole in the mid 19th century. In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits.Peirce, C. S., "Letter, Peirce to A. Marquand", dated 1886, '' Writings of Charles S. Peirce'', v. 5, 1993, pp. 541–3. GooglPreview See Burks, Arthur ...
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Retina
The retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye of most vertebrates and some molluscs. The optics of the eye create a focused two-dimensional image of the visual world on the retina, which then processes that image within the retina and sends nerve impulses along the optic nerve to the visual cortex to create visual perception. The retina serves a function which is in many ways analogous to that of the film or image sensor in a camera. The neural retina consists of several layers of neurons interconnected by synapses and is supported by an outer layer of pigmented epithelial cells. The primary light-sensing cells in the retina are the photoreceptor cells, which are of two types: rods and cones. Rods function mainly in dim light and provide monochromatic vision. Cones function in well-lit conditions and are responsible for the perception of colour through the use of a range of opsins, as well as high-acuity vision used for task ...
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Sensor
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends the information to other electronics, frequently a computer processor. Sensors are always used with other electronics. Sensors are used in everyday objects such as touch-sensitive elevator buttons (tactile sensor) and lamps which dim or brighten by touching the base, and in innumerable applications of which most people are never aware. With advances in micromachinery and easy-to-use microcontroller platforms, the uses of sensors have expanded beyond the traditional fields of temperature, pressure and flow measurement, for example into Attitude and heading reference system, MARG sensors. Analog sensors such as potentiometers and force-sensing resistors are still widely used. Their applications include manufacturing and machinery, airplane ...
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Sensor Resolution
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends the information to other electronics, frequently a computer processor. Sensors are always used with other electronics. Sensors are used in everyday objects such as touch-sensitive elevator buttons (tactile sensor) and lamps which dim or brighten by touching the base, and in innumerable applications of which most people are never aware. With advances in micromachinery and easy-to-use microcontroller platforms, the uses of sensors have expanded beyond the traditional fields of temperature, pressure and flow measurement, for example into MARG sensors. Analog sensors such as potentiometers and force-sensing resistors are still widely used. Their applications include manufacturing and machinery, airplanes and aerospace, cars, medicine, robot ...
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Quantization (signal Processing)
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Example For example, rounding a real number x to the nearest integer value forms a very basic type of quantizer – a ''uniform'' one. A typical (''mid-tread'') uni ...
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Quantization Error
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Example For example, rounding a real number x to the nearest integer value forms a very basic type of quantizer – a ''uniform'' one. A typical (''mid-tread'') uni ...
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Hexagonal Sampling Grid
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A ''regular hexagon'' has Schläfli symbol and can also be constructed as a truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries (''rotational symmetry of order six'') and six reflection symmetries (''six lines of symmetry''), making up the dihedral group D6. The longest diagonal ...
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Discrete Fourier Transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle. The DFT is the most important discret ...
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Satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope thermoelectric generators (RTGs). Most satellites also have a method of communication to ground stations, called Transponder (satellite communications), transponders. Many satellites use a Satellite bus, standardized bus to save cost and work, the most popular of which is small CubeSats. Similar satellites can work together as a group, forming Satellite constellation, constellations. Because of the high launch cost to space, satellites are designed to be as lightweight and robust as possible. Most communication satellites are radio Broadcast relay station, relay stations in orbit and carry dozens of transponders, each with a bandwidth of tens of megahertz. Satellites are placed from the surface to orbit by launch vehicles, high enough to ...
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SPOT (satellite)
SPOT (french: Satellite Pour l’Observation de la Terre, lit. "Satellite for observation of Earth") is a commercial high-resolution optical Earth imaging satellite system operating from space. It is run by Spot Image, based in Toulouse, France. It was initiated by the CNES (''Centre national d'études spatiales'' – the French space agency) in the 1970s and was developed in association with the SSTC (Belgian scientific, technical and cultural services) and the Swedish National Space Board (SNSB). It has been designed to improve the knowledge and management of the Earth by exploring the Earth's resources, detecting and forecasting phenomena involving climatology and oceanography, and monitoring human activities and natural phenomena. The SPOT system includes a series of satellites and ground control resources for satellite control and programming, image production, and distribution. Earlier satellites were launched using the European Space Agency's Ariane 2, 3, and 4 rocket ...
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Microlens
A microlens is a small lens, generally with a diameter less than a millimetre (mm) and often as small as 10 micrometres (µm). The small sizes of the lenses means that a simple design can give good optical quality but sometimes unwanted effects arise due to optical diffraction at the small features. A typical microlens may be a single element with one plane surface and one spherical convex surface to refract the light. Because micro-lenses are so small, the substrate that supports them is usually thicker than the lens and this has to be taken into account in the design. More sophisticated lenses may use aspherical surfaces and others may use several layers of optical material to achieve their design performance. A different type of microlens has two flat and parallel surfaces and the focusing action is obtained by a variation of refractive index across the lens. These are known as gradient-index (GRIN) lenses. Some micro-lenses achieve their focusing action by both a variation ...
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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 the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR, bandwidth, and channel capacity of a communication channel are connected by the Shannon–Hartley theorem. Definition Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input): : \mathrm = \frac, where is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. Depending on whether the signal is a constant () or a random variable (), the signal-to-noise ratio for random noise becomes: : \mathrm = \frac where E refers to the expected value, i.e. in this case ...
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