Akula-class submarine
Project 971 Щука-Б is a nuclear-powered attack submarine first deployed by the Soviet Navy in 1986. The class is known under the name Bars. There are four sub-classes or flights of Shchuka, consisting of the original seven Akula Is, commissioned between 1984 and 1990; the Russians call all of the submarines Shchuka-B, regardless of modifications. Some potential for confusion may exist, as the name Akula was used by the Soviets for a different submarine, the Projekt 941, known in the West as the Typhoon class. By contrast, the Projekt 971 was named Shchuka-B by the Soviets but designated as the "Akula class" by the West after the name of the lead ship, K-284; the launch of the first submarine in 1985, according to defense analyst Norman Polmar, "shook everyone up", as Western intelligence agencies had not expected the Soviet Union to produce such a boat for another ten years. The Akula incorporates a double hull system composed of an inner pressure hull and an outer "light" hull; this allows more freedom in the design of the exterior hull shape, resulting in a submarine with more reserve buoyancy than its western analogs.
This design requires more power than single-hull submarines because of the greater wetted surface area, which increases drag. The distinctive "bulb" or "can" seen on top of the Akula's rudder houses its towed sonar array, when retracted. Most Akulas have the SOCKS hydrodynamic sensors, which detect changes in salinity, they are located on the leading edge of the sail, on the outer hull casing in front of the sail and on the bottom of the hull forward of the sail. All Akulas have two T-shaped doors on the aft bottom of the hull, on either side; these are where the OK-300 auxiliary propulsion devices are located, which can propel the submarine at up to 5 knots. Akulas are armed with four 533 mm torpedo tubes which can use Type 53 torpedoes or the SS-N-15 Starfish missile, four 650 mm torpedo tubes which can use Type 65 torpedoes or the SS-N-16 Stallion missile; these torpedo tubes are arranged in two rows of four tubes each. Improved Akulas, Akula IIs have an additional six 533 mm torpedo tubes mounted externally, capable of launching up to 6 decoys each.
The external tubes are mounted outside the pressure hull in one row, above the torpedo tubes, can only be reloaded in port or with the assistance of a submarine tender. The 650 mm tubes can be fitted with liners to use the 533 mm weaponry; the submarine is able to use its torpedo tubes to deploy mines. As with many Soviet/Russian craft, information on the status of the Akula-class submarines is sparse, at best. Information provided by sources varies widely. Of the seven original Akulas, only three are known to still be in service; these boats are equipped with MGK-500 Skat sonar system. The lead boat of the class, K-284 Akula was decommissioned in 2001 to help save money in the cash-strapped Russian Navy. K-322 Kashalot and K-480 Bars are in reserve. K-480 Bars was put into reserve in 1998, is being dismantled in February 2010. Pantera returned to service in January 2008 after a comprehensive overhaul. All were retrofitted with the SOCKS hydrodynamic sensors. All submarines before K-391 Bratsk have reactor coolant scoops that are similar to the ones of the Typhoon-class SSBNs, long and tubular.
Bratsk and subsequent submarines have reactor coolant scoops similar to the short ones on the Oscar IIs. The six Akulas of this class are all thought to be in service, they are quieter than the original Akulas. The MGK-500 sonar is upgraded to MGK-501 Skat-MS. Sources disagree as to whether construction of this class has been suspended, or if there are a further two units planned. Improved Akula-I Hulls: K-328 Leopard, K-461 Volk, K-154 Tigr, K-419 Kuzbass, K-295 Samara and K-152 Nerpa; these submarines are much quieter than early Akula class submarines and all have the SOCKS hydrodynamic sensors except Leopard. The Akula-I Improved submarines have six 533 mm decoy launching tubes, they have a different arrangement of limber holes on the outer hull than Akula Is. Nerpa and Iribis have a different rescue chamber in the sail, which can be distinguished by the large dome on the top surface. K-157 Vepr is the only completed Akula II; the Akula II is 3 metres longer and displaces about 700 tons more than the Akula I.
The added space was used for additional quieting measures. The MGK-501 Skat sonar system on Akula-I is replaced to a new MGK-540 Skat-3 sonar system. K-157 Vepr became the first Soviet submarine, quieter than the latest U. S. attack submarines of that time, the improved Los Angeles class. Two of these submarines were used to build the Borei-class SSBNs; the K-335 Gepard is the 14th submarine of the class and the only completed Akula III built for the Russian Navy. It was the first submarine commissioned in the Russian Navy since the Kursk disaster, as a result, its commissioning ceremony was an important morale boost for the Russian Navy with President Vladimir Putin in attendance. There is no NATO classification for the Akula III, it is longer and has a larger displacement compared to the Akula II it has an enlarged sail and a different towed-array dispenser on the vertical fin. Again, more noise reduction methods were employed; the Gep
Multibeam echosounder
A multibeam echosounder is a type of sonar, used to map the seabed. Like other sonar systems, multibeam systems emit sound waves in a fan shape beneath a ship's hull; the amount of time it takes for the sound waves to bounce off the seabed and return to a receiver is used to determine water depth. Unlike other sonars, multibeam systems use beamforming to extract directional information from the returning soundwaves, producing a swath of depth readings from a single ping. Multibeam sonar sounding systems known as swathe or swath, originated for military applications; the Sonar Array Sounding System was developed in the early 1960s by the US Navy, in conjunction with General Instrument to map large swaths of the ocean floor to assist the underwater navigation of its submarine force. SASS was tested aboard the USS Compass Island; the final array system, composed of sixty-one one degree beams with a swath width of 1.15 times water depth, was installed on the USNS Bowditch, USNS Dutton and USNS Michelson.
Starting in the 1970s, companies such as General Instrument in the United States, Krupp Atlas and Elac Nautik in Germany, Simrad in Norway and RESON now Teledyne RESON A/S in Denmark developed systems that could be mounted to the hull of large ships, small boats. The first commercial multibeam is now known as the SeaBeam Classic and was put in service in May 1977 on the Australian survey vessel HMAS Cook; this system produced up to 16 beams across a 45-degree arc. The term "SeaBeam Classic" was coined after the manufacturer developed newer systems such as the SeaBeam 2000 and the SeaBeam 2112 in the late 1980s; the second SeaBeam Classic installation was on the French Research Vessel Jean Charcot. The SB Classic arrays on the Charcot were damaged in a grounding and the SeaBeam was replaced with an EM120 in 1991. Although it seems that the original SeaBeam Classic installation was not used much, the others were used, subsequent installations were made on many vessels. SeaBeam Classic systems were subsequently installed on the US academic research vessels USNS Thomas Washington, the USNS Robert D. Conrad and the RV Atlantis II.
As technology improved in the 1980s and 1990s, higher-frequency systems suitable for high-resolution mapping in shallow water were developed, such systems are used for shallow-water hydrographic surveying in support of navigational charting. Multibeam echosounders are commonly used for geological and oceanographic research, since the 1990s for offshore oil and gas exploration and seafloor cable routing. In 1989, Atlas Electronics installed a second-generation deep-sea multibeam called Hydrosweep DS on the German research vessel Meteor; the Hydrosweep DS produced up to 59 beams across a 90-degree swath, a vast improvement and was inherently ice-strengthened. Early HS-DS systems were installed on the RV Meteor, the RV Polarstern, the RV Maurice Ewing and the ORV Sagar Kanya in 1989 and 1990 and subsequently on a number of other vessels including the RV Thomas G. Thompson and RV Hakurei Maru; as the cost of components has decreased, the number of multibeam systems sold and in operation worldwide has increased significantly.
Smaller, portable systems can be operated on a small launch or tender vessel unlike the older systems that required considerable time and effort to attach to a ship's hull. Some multibeam echosounders such as the Teledyne Odom MB2 incorporate a motion sensor at the face of the acoustic transducer, allowing faster installation on small vessels. Multibeam echosounders like this are allowing many smaller hydrographic survey companies to move from traditional single beam echosounders to swath systems. Multibeam data includes bathymetry, acoustic backscatter, water column data. Gas plumes now identified in midwater multibeam data are termed flares. A multibeam echosounder is a device used by hydrographic surveyors to determine the depth of water and the nature of the seabed. Most modern systems work by transmitting a broad acoustic fan shaped pulse from a specially designed transducer across the full swath acrosstrack with a narrow alongtrack forming multiple receive beams that are much narrower in the acrosstrack.
From this narrow beam, a two way travel time of the acoustic pulse is established utilizing a bottom detection algorithm. If the speed of sound in water is known for the full water column profile, the depth and position of the return signal can be determined from the receive angle and the two-way travel time. In order to determine the transmit and receive angle of each beam, a multibeam echosounder requires accurate measurement of the motion of the sonar relative to a cartesian coordinate system; the measured values are heave, roll and heading. To compensate for signal loss due to spreading and absorption a time-varied gain circuit is designed into the receiver. For deep water systems, a steerable transmit beam is required to compensate for pitch; this can be accomplished with beamforming. A Note on Fifty Years of Multi-beam Sounding Pole to Sea Beam MB-System open source software for processing multibeam data News and application articles of multibeam equipment on Hydro International
Short baseline acoustic positioning system
A short baseline acoustic positioning system is one of three broad classes of underwater acoustic positioning systems that are used to track underwater vehicles and divers. The other two classes are ultra short baseline systems and long baseline systems. Like USBL systems, SBL systems do not require any seafloor mounted transponders or equipment and are thus suitable for tracking underwater targets from boats or ships that are either anchored or under way. However, unlike USBL systems, which offer a fixed accuracy, SBL positioning accuracy improves with transducer spacing. Thus, where space permits, such as when operating from larger vessels or a dock, the SBL system can achieve a precision and position robustness, similar to that of sea floor mounted LBL systems, making the system suitable for high-accuracy survey work; when operating from a smaller vessel where transducer spacing is limited, the SBL system will exhibit reduced precision. Short baseline systems determine the position of a tracked target such as a ROV by measuring the target's distance from three or more transducers that are, for example, lowered over the side of the surface vessel from which tracking operations take place.
These range measurements, which are supplemented by depth data from a pressure sensor, are used to triangulate the position of the target. In figure 1, baseline transducer sends a signal, received by a transponder on the tracked target; the transponder replies, the reply is received by the three baseline transducers. Signal run time measurements now yield the distances B-A, B-C and B-D; the resulting target positions are always relative to the location of the baseline transducers. In cases where tracking is conducted from a moving boat but the target position must be known in earth coordinates such as latitude/longitude or UTM, the SBL positioning system is combined with a GPS receiver and an electronic compass, both mounted on the boat; these instruments determine the location and orientation of the boat, which are combined with the relative position data from the SBL system to establish the position of the tracked target in earth coordinates. Short baseline systems get their name from the fact that the spacing of the baseline transducers is much less than the distance to the target, such as a robotic vehicle or diver venturing far from the boat As with any acoustic positioning system, a larger baseline yields better positioning accuracy.
SBL systems use this concept to an advantage by adjusting transducer spacing for best results When operating from larger ships, from docks or from the sea ice where greater transducer spacing can be used, SBL systems can yield a positioning accuracy and robustness approaching that of sea-floor mounted LBL systems. SBL systems are found employed in a variety of specialized applications; the first implementation of any underwater acoustic positioning system was a SBL system installed on the U. S. Navy oceanographic vessel USNS Mizar. In 1963, this system guided the bathyscaphe Trieste 1 to the wreck site of the American nuclear submarine USS Thresher. However, performance was still so poor that out of ten search dives by Trieste 1, visual contact was only made once with the wreckage; the Woods Hole Oceanographic Institution is using a SHARPS SBL system to guide their JASON tethered deep ocean robotic vehicle relative to the MEDEA depressor weight and docking station associated with the vehicle.
Rather than tracking both vehicles with a positioning system from the surface which would result in degraded accuracy as the pair's deployment distance, the SBL baseline transducers are mounted on MEDEA. Yielding the position of JASON relative to MEDEA with good accuracy independent of the system's deployment depth; the reported accuracy is 0.09m An example of SBL technology is underway in Antarctica, where the Moss Landing Marine Laboratory is using a PILOT SBL system to guide the SCINI remotely operated vehicle. SCINI is a small, torpedo-shaped tethered vehicle designed for rapid and uncomplicated deployment and exploration of remote sites around Antarctica, including Heald Island, Cape Evans and Bay of Sails. SCINI system is designed to be compact and light-weight so as to facilitate rapid deployment by helicopter, tracked vehicle and man-hauled sleds. Once on site, its torpedo shaped body allows it to access the ocean through small holes drilled into the sea ice; the mission's science goals however demand high accuracy in navigation, to support tasks including running 10-m video transects, providing precise positions for still images to document the distribution and population density of benthic organisms and marking and re-visiting sites for further investigation.
The SBL navigation system consists of three small, 5 cm diameter sonar baseline transducers that are linked by cable to a control box. A small, cylinder shaped transponder is mounted on the SCINI vehicle. Accuracy is optimized by making use of the flat sea ice to place the baseline transducers well apart. 35m for most SCINI deployments. Figure 4 reviews SCINI operations guided by the SBL system. Figure 4A is an improvised ROV control room, in this case in a cabin hauled on top of an ice hole at Cape Armitage. From left, the displays are the ROV controls screen, the main camera view, the navigation screen and the science display; the ROV pilot will watch the main camera view. He will glance at the navigation screen, which shows the current ROV position and track overlaid on a chart, for orientation and to guide the ROV to the location instructed by the scientist; the scientist, shown here seat
Hydroacoustics
Hydroacoustics is the study and application of sound in water. Hydroacoustics, using sonar technology, is most used for monitoring of underwater physical and biological characteristics. Hydroacoustics can be used to detect the depth of a water body, as well as the presence or absence, distribution and behavior of underwater plants and animals. Hydroacoustic sensing involves "passive acoustics" or active acoustics making a sound and listening for the echo, hence the common name for the device, echo sounder or echosounder. There are a number of different causes of noise from shipping; these can be subdivided into those caused by the propeller, those caused by machinery, those caused by the movement of the hull through the water. The relative importance of these three different categories will depend, amongst other things, on the ship type One of the main causes of hydro acoustic noise from submerged lifting surfaces is the unsteady separated turbulent flow near the surface's trailing edge that produces pressure fluctuations on the surface and unsteady oscillatory flow in the near wake.
The relative motion between the surface and the ocean creates a turbulent boundary layer that surrounds the surface. The noise is generated by the fluctuating velocity and pressure fields within this TBL. Surveillance Towed Array Sensor System Fisheries acoustics Acoustic Doppler current profiler for water speed measurement Acoustic camera Passive acoustic monitoring Quality assurance of hydroacoustic surveys: the repeatability of fish-abundance and biomass estimates in lakes within and between hydroacoustic systems Hydroacoustics as a tool for assessing fish biomass and size distribution associated with discrete shallow water estuarine habitats in Louisiana Acoustic assessment of squid stocks Summary of the use of hydroacoustics for quantifying the escapement of adult salmonids in rivers. Ransom, B. H. S. V. Johnston, T. W. Steig. 1998. Presented at International Symposium and Workshop on Management and Ecology of River Fisheries, University of Hull, England, 30 March-3 April 1998 Multi-frequency acoustic assessment of fisheries and plankton resources.
Torkelson,T. C. T. C. Austin, P. H. Weibe. 1998. Presented at the 135th Meeting of the Acoustical Society of America and the 16th Meeting of the International Congress of Acoustics, Washington. Acoustics Unpacked A great reference for freshwater hydroacoustics for resource assessment Inter-Calibration of Scientific Echosounders in the Great Lakes Hydroacoustic Evaluation of Spawning Red Hind Aggregations Along the Coast of Puerto Rico in 2002 and 2003 Feasibility Assessment of Split-Beam Hydroacoustic Techniques for Monitoring Adult Shortnose Sturgeon in the Delaware River Categorising Salmon Migration Behaviour Using Characteristics of Split-beam Acoustic Data Evaluation of Methods to Estimate Lake Herring Spawner Abundance in Lake Superior Estimating Sockeye Salmon Smolt Flux and Abundance with Side-Looking Sonar Herring Research: Using Acoustics to Count Fish. Hydroacoustic Applications in Lake and Marine environments for study of plankton, vegetation, substrate or seabed classification, bathymetry.
Hydroacoustics: Rivers Hydroacoustics: Lakes and Reservoirs PAMGUARD: An Open-Source Software Community Developing Marine Mammal Acoustic Detection and Localisation Software to Benefit the Marine Environment.
Acoustic Doppler current profiler
An acoustic Doppler current profiler is a hydroacoustic current meter similar to a sonar, used to measure water current velocities over a depth range using the Doppler effect of sound waves scattered back from particles within the water column. The term ADCP is a generic term for all acoustic current profilers, although the abbreviation originates from an instrument series introduced by RD Instruments in the 1980s; the working frequencies range of ADCPs range from 38 kHz to several Megahertz. The device used in the air for wind speed profiling using sound is known as SODAR and works with the same underlying principles. ADCPs contain piezoelectric transducers to receive sound signals; the traveling time of sound waves gives an estimate of the distance. The frequency shift of the echo is proportional to the water velocity along the acoustic path. To measure 3D velocities, at least three beams are required. In rivers, only the 2D velocity is relevant and ADCPs have two beams. In recent years, more functionality has been added to ADCPs and systems can be found with 2,3,4,5 or 9 beams.
Further components of an ADCP are an electronic amplifier, a receiver, a clock to measure the traveling time, a temperature sensor, a compass to know the heading, a pitch/roll sensor to know the orientation. An analog-to-digital converter and a digital signal processor are required to sample the returning signal in order to determine the Doppler shift. A temperature sensor is used to estimate the sound velocity at the instrument position using the seawater equation of state, uses this to estimate scale the frequency shift to water velocities; this procedure assumes. The results are saved to internal memory or output online to an external display software. Three common methods are used to calculate the Doppler shift and thus the water velocity along the acoustic beams; the first method uses a monochromatic transmit pulse and is referred to as "incoherent" or "narrowband". The method is robust and provides good quality mean current profiles but has limited space-time resolution; when the transmit pulse consists of coded elements that are repeated, the method is referred to as "repeat sequence coding" or "broadband".
This method improves the space-time resolution by a factor of 5. Commercially, this method was protected by US patent 5615173 until 2011; the pulse-to-pulse coherent method relies on a sequence of transmit pulses where the echo from subsequent pulses are assumed not to interfere with each other. This method is only applicable for short profiling ranges but the corresponding improvement in space time resolution is of order 1000. Depending on the mounting, one can distinguish between side-looking, downward- and upward-looking ADCPs. A bottom-mounted ADCP can measure the speed and direction of currents at equal intervals all the way to the surface. Mounted sideways on a wall or bridge piling in rivers or canals, it can measure the current profile from bank to bank. In deep water they can be lowered on cables from the surface; the primary usage is for oceanography. The instruments can be used in rivers and canals to continuously measure the discharge. Mounted on moorings within the water column or directly at the seabed, water current and wave studies may be performed.
They can stay underwater for years at a time, the limiting factor is the lifetime of the battery pack. Depending on the nature of the deployment the instrument has the ability to be powered from shore, using the same umbilical cable for data communication. Deployment duration can be extended by a factor of three by substituting lithium battery packs for the standard alkaline packs. By adjusting the window where the Doppler shift is calculated, it is possible to measure the relative velocity between the instrument and the bottom; this feature is referred to as bottom-track. The process has two parts; when an ADCP is mounted on a moving ship, the bottom track velocity may be subtracted from the measured water velocity. The result is the net current profile. Bottom track provides the foundation for surveys of the water currents in coastal areas. In deep water where the acoustic signals cannot reach the bottom, the ship velocity is estimated from a more complex combination of velocity and heading information from GPS, etc.
In rivers, the ADCP is used to measure the total water transport. The method requires a vessel with an ADCP mounted over the side to cross from one bank to another while measuring continuously. Using the bottom track feature, the track of the boat as well as the cross sectional area is estimated after adjustment for left and right bank areas; the discharge can be calculated as the dot product between the vector track and the current velocity. The method is in use by hydrographic survey organisations across the world and forms an important component in the stage-discharge curves used in many places to continuously monitor river discharge. For underwater vehicles, the bottom tracking feature can be used as an important component in the navigation systems. In this case the velocity of the vehicle is combined with an initial position fix, compass or gyro heading, data from the acceleration sensor; the sensor suite is combined to estimate the position of the vehicle. This may help to navigate submarines and remotely operated underwater vehicles.
Some ADCPs can be configured to measure direction. The wave height is estimated with a vertical beam that measures the distance to the surface using the echo fro
Acoustical oceanography
Acoustical oceanography is the use of underwater sound to study the sea, its boundaries and its contents. Interest in developing echo ranging systems began in earnest following the sinking of the RMS Titanic in 1912. By sending a sound wave ahead of a ship, the theory went, a return echo bouncing off the submerged portion of an iceberg should give early warning of collisions. By directing the same type of beam downwards, the depth to the bottom of the ocean could be calculated; the first practical deep-ocean echo sounder was invented by Harvey C. Hayes, a U. S. Navy physicist. For the first time, it was possible to create a quasi-continuous profile of the ocean floor along the course of a ship; the first such profile was made by Hayes on board the U. S. S. Stewart, a Navy destroyer that sailed from Newport to Gibraltar between June 22 and 29, 1922. During that week, 900 deep-ocean soundings were made. Using a refined echo sounder, the German survey ship Meteor made several passes across the South Atlantic from the equator to Antarctica between 1925 and 1927, taking soundings every 5 to 20 miles.
Their work created the first detailed map of the Mid-Atlantic Ridge. It showed that the Ridge was a rugged mountain range, not the smooth plateau that some scientists had envisioned. Since that time, both naval and research vessels have operated echo sounders continuously while at sea. Important contributions to acoustical oceanography have been made by: Leonid Brekhovskikh Walter Munk Herman Medwin John L. Spiesberger C. C. Leroy David E. Weston D. Van Holliday Charles Greenlaw The earliest and most widespread use of sound and sonar technology to study the properties of the sea is the use of a rainbow echo sounder to measure water depth. Sounders were the devices used that mapped the many miles of the Santa Barbara Harbor ocean floor until 1993. Fathometers measure the depth of the waters, it works by electronically sending sounds from ships, therefore receiving the sound waves that bounces back from the bottom of the ocean. A paper chart is calibrated to record the depth; as technology advances, the development of high resolution sonars in the second half of the 20th century made it possible to not just detect underwater objects but to classify them and image them.
Electronic sensors are now attached to ROVs since nowadays, ships or robot submarines have Remotely Operated Vehicles. There are cameras attached to these devices giving out accurate images; the oceanographers are able to get a precise quality of pictures. The'pictures' can be sent from sonars by having sound reflected off ocean surroundings. Oftentimes sound waves reflect off animals, giving information which can be documented into deeper animal behaviour studies. See Clay and Medwin. See Clay and Medwin. Applications of acoustical oceanography include: fish population surveys classification of fish species and other biota rain rate measurement wind speed measurement water depth measurement seabed classification ocean acoustic tomography global thermometry monitoring of ocean-atmospheric gas exchange The study of marine life, from microplankton to the blue whale, uses bioacoustics. Ocean exploration Cambridge Interferometer
Fourier analysis
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions simplifies the study of heat transfer. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term Fourier analysis refers to the study of both operations.
The decomposition process. Its output, the Fourier transform, is given a more specific name, which depends on the domain and other properties of the function being transformed. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, the general field is known as harmonic analysis; each transform used for analysis has a corresponding inverse transform that can be used for synthesis. Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, signal processing, digital image processing, probability theory, forensics, option pricing, numerical analysis, oceanography, optics, geometry, protein structure analysis, other areas; this wide applicability stems from many useful properties of the transforms: The transforms are linear operators and, with proper normalization, are unitary as well. The transforms are invertible; the exponential functions are eigenfunctions of differentiation, which means that this representation transforms linear differential equations with constant coefficients into ordinary algebraic ones.
Therefore, the behavior of a linear time-invariant system can be analyzed at each frequency independently. By the convolution theorem, Fourier transforms turn the complicated convolution operation into simple multiplication, which means that they provide an efficient way to compute convolution-based operations such as polynomial multiplication and multiplying large numbers; the discrete version of the Fourier transform can be evaluated on computers using Fast Fourier Transform algorithms. In forensics, laboratory infrared spectrophotometers use Fourier transform analysis for measuring the wavelengths of light at which a material will absorb in the infrared spectrum; the FT method is used to record the wavelength data. And by using a computer, these Fourier calculations are carried out, so that in a matter of seconds, a computer-operated FT-IR instrument can produce an infrared absorption pattern comparable to that of a prism instrument. Fourier transformation is useful as a compact representation of a signal.
For example, JPEG compression uses a variant of the Fourier transformation of small square pieces of a digital image. The Fourier components of each square are rounded to lower arithmetic precision, weak components are eliminated so that the remaining components can be stored compactly. In image reconstruction, each image square is reassembled from the preserved approximate Fourier-transformed components, which are inverse-transformed to produce an approximation of the original image; when processing signals, such as audio, radio waves, light waves, seismic waves, images, Fourier analysis can isolate narrowband components of a compound waveform, concentrating them for easier detection or removal. A large family of signal processing techniques consist of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, reversing the transformation; some examples include: Equalization of audio recordings with a series of bandpass filters. Most the unqualified term Fourier transform refers to the transform of functions of a continuous real argument, it produces a continuous function of frequency, known as a frequency distribution.
One function is transformed into another, the operation is reversible. When the domain of the input function is time, the domain of the output function is ordinary frequency, the transform of function s at frequen
