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Sunday, November 7, 2010

mechanical engineering devlopment

Development

Applications of mechanical engineering are found in the records of many ancient and medieval societies throughout the globe. In ancient Greece, the works of Archimedes (287 BC–212 BC) deeply influenced mechanics in the Western tradition and Heron of Alexandria (c. 10–70 AD) created the first steam engine.[2] In China, Zhang Heng (78–139 AD) improved a water clock and invented a seismometer, and Ma Jun (200–265 AD) invented a chariot with differential gears. The medieval Chinese horologist and engineer Su Song (1020–1101 AD) incorporated an escapement mechanism into his astronomical clock tower two centuries before any escapement can be found in clocks of medieval Europe, as well as the world's first known endless power-transmitting chain drive.[3]
During the years from 7th to 15th century, the era called the Islamic Golden Age, there have been remarkable contributions from Muslim inventors in the field of mechanical technology. Al-Jazari, who was one of them, wrote his famous Book of Knowledge of Ingenious Mechanical Devices in 1206, and presented many mechanical designs. He is also considered to be the inventor of such mechanical devices which now form the very basic of mechanisms, such as the crankshaft and camshaft.[4]
Important breakthroughs in the foundations of mechanical engineering occurred in England during the 17th century when Sir Isaac Newton both formulated the three Newton's Laws of Motion and developed calculus. Newton was reluctant to publish his methods and laws for years, but he was finally persuaded to do so by his colleagues, such as Sir Edmund Halley, much to the benefit of all mankind.
During the early 19th century in England, Germany and Scotland, the development of machine tools led mechanical engineering to develop as a separate field within engineering, providing manufacturing machines and the engines to power them.[5] The first British professional society of mechanical engineers was formed in 1847, thirty years after civil engineers formed the first such professional society.[6] On the European continent, Johann Von Zimmermann (1820–1901) founded the first factory for grinding machines in Chemnitz (Germany) in 1848.
In the United States, the American Society of Mechanical Engineers (ASME) was formed in 1880, becoming the third such professional engineering society, after the American Society of Civil Engineers (1852) and the American Institute of Mining Engineers (1871).[7] The first schools in the United States to offer an engineering education were the United States Military Academy in 1817, an institution now known as Norwich University in 1819, and Rensselaer Polytechnic Institute in 1825. Education in mechanical engineering has historically been based on a strong foundation in mathematics and science.[8]

[edit] Education

Degrees in mechanical engineering are offered at universities worldwide. In Bangladesh, China, India, Nepal, North America, and Pakistan, mechanical engineering programs typically take four to five years of study and result in a Bachelor of Science (B.Sc), Bachelor of Technology (B.Tech), Bachelor of Engineering (B.Eng), or Bachelor of Applied Science (B.A.Sc) degree, in or with emphasis in mechanical engineering. In Spain, Portugal and most of South America, where neither BSc nor BTech programs have been adopted, the formal name for the degree is "Mechanical Engineer", and the course work is based on five or six years of training. In Italy the course work is based on five years of training; but in order to qualify as an Engineer you have to pass a state exam at the end of the course.
In the United States, most undergraduate mechanical engineering programs are accredited by the Accreditation Board for Engineering and Technology (ABET) to ensure similar course requirements and standards among universities. The ABET web site lists 276 accredited mechanical engineering programs as of June 19, 2006.[9] Mechanical engineering programs in Canada are accredited by the Canadian Engineering Accreditation Board (CEAB),[10] and most other countries offering engineering degrees have similar accreditation societies.
Some mechanical engineers go on to pursue a postgraduate degree such as a Master of Engineering, Master of Technology, Master of Science, Master of Engineering Management (MEng.Mgt or MEM), a Doctor of Philosophy in engineering (EngD, PhD) or an engineer's degree. The master's and engineer's degrees may or may not include research. The Doctor of Philosophy includes a significant research component and is often viewed as the entry point to academia.[11] The Engineer's degree exists at a few institutions at an intermediate level between the master's degree and the doctorate.

[edit] Coursework

Standards set by each country's accreditation society are intended to provide uniformity in fundamental subject material, promote competence among graduating engineers, and to maintain confidence in the engineering profession as a whole. Engineering programs in the U.S., for example, are required by ABET to show that their students can "work professionally in both thermal and mechanical systems areas."[12] The specific courses required to graduate, however, may differ from program to program. Universities and Institutes of technology will often combine multiple subjects into a single class or split a subject into multiple classes, depending on the faculty available and the university's major area(s) of research.
The fundamental subjects of mechanical engineering usually include:
Mechanical engineers are also expected to understand and be able to apply basic concepts from chemistry, physics, chemical engineering, civil engineering, and electrical engineering. Most mechanical engineering programs include multiple semesters of calculus, as well as advanced mathematical concepts including differential equations, partial differential equations, linear algebra, abstract algebra, and differential geometry, among others.
In addition to the core mechanical engineering curriculum, many mechanical engineering programs offer more specialized programs and classes, such as robotics, transport and logistics, cryogenics, fuel technology, automotive engineering, biomechanics, vibration, optics and others, if a separate department does not exist for these subjects.[15]
Most mechanical engineering programs also require varying amounts of research or community projects to gain practical problem-solving experience. In the United States it is common for mechanical engineering students to complete one or more internships while studying, though this is not typically mandated by the university. Cooperative education is another option.

[edit] License

Engineers may seek license by a state, provincial, or national government. The purpose of this process is to ensure that engineers possess the necessary technical knowledge, real-world experience, and knowledge of the local legal system to practice engineering at a professional level. Once certified, the engineer is given the title of Professional Engineer (in the United States, Canada, Japan, South Korea, Bangladesh and South Africa), Chartered Engineer (in the United Kingdom, Ireland, India and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (much of the European Union). Not all mechanical engineers choose to become licensed; those that do can be distinguished as Chartered or Professional Engineers by the post-nominal title P.E., P.Eng., or C.Eng., as in: Mike Thompson, P.Eng.
In the U.S., to become a licensed Professional Engineer, an engineer must pass the comprehensive FE (Fundamentals of Engineering) exam, work a given number of years as an Engineering Intern (EI) or Engineer-in-Training (EIT), and finally pass the "Principles and Practice" or PE (Practicing Engineer or Professional Engineer) exams.
In the United States, the requirements and steps of this process are set forth by the National Council of Examiners for Engineering and Surveying (NCEES), a national non-profit representing all states. In the UK, current graduates require a BEng plus an appropriate masters degree or an integrated MEng degree, a minimum of 4 years post graduate on the job competency development, and a peer reviewed project report in the candidates specialty area in order to become chartered through the Institution of Mechanical Engineers.
In most modern countries, certain engineering tasks, such as the design of bridges, electric power plants, and chemical plants, must be approved by a Professional Engineer or a Chartered Engineer. "Only a licensed engineer, for instance, may prepare, sign, seal and submit engineering plans and drawings to a public authority for approval, or to seal engineering work for public and private clients."[16] This requirement can be written into state and provincial legislation, such as in the Canadian provinces, for example the Ontario or Quebec's Engineer Act.[17]
In other countries, such as Australia, no such legislation exists; however, practically all certifying bodies maintain a code of ethics independent of legislation that they expect all members to abide by or risk expulsion.[18]

[edit] Salaries and workforce statistics

The total number of engineers employed in the U.S. in 2009 was roughly 1.6 million. Of these, 239,000 were mechanical engineers (14.9%), the second largest discipline by size behind civil (278,000). The total number of mechanical engineering jobs in 2009 was projected to grow 6% over the next decade, with average starting salaries being $58,800 with a bachelor's degree.[19] The median annual income of mechanical engineers in the U.S. workforce was roughly $74,900. This number was highest when working for the government ($86,250), and lowest in education ($63,050).[20]
In 2007, Canadian engineers made an average of CAD$29.83 per hour with 4% unemployed. The average for all occupations was $18.07 per hour with 7% unemployed. Twelve percent of these engineers were self-employed, and since 1997 the proportion of female engineers had risen to 6%.[21]

[edit] Modern tools

An oblique view of a four-cylinder inline crankshaft with pistons
Many mechanical engineering companies, especially those in industrialized nations, have begun to incorporate computer-aided engineering (CAE) programs into their existing design and analysis processes, including 2D and 3D solid modeling computer-aided design (CAD). This method has many benefits, including easier and more exhaustive visualization of products, the ability to create virtual assemblies of parts, and the ease of use in designing mating interfaces and tolerances.
Other CAE programs commonly used by mechanical engineers include product lifecycle management (PLM) tools and analysis tools used to perform complex simulations. Analysis tools may be used to predict product response to expected loads, including fatigue life and manufacturability. These tools include finite element analysis (FEA), computational fluid dynamics (CFD), and computer-aided manufacturing (CAM).
Using CAE programs, a mechanical design team can quickly and cheaply iterate the design process to develop a product that better meets cost, performance, and other constraints. No physical prototype need be created until the design nears completion, allowing hundreds or thousands of designs to be evaluated, instead of a relative few. In addition, CAE analysis programs can model complicated physical phenomena which cannot be solved by hand, such as viscoelasticity, complex contact between mating parts, or non-Newtonian flows
As mechanical engineering begins to merge with other disciplines, as seen in mechatronics, multidisciplinary design optimization (MDO) is being used with other CAE programs to automate and improve the iterative design process. MDO tools wrap around existing CAE processes, allowing product evaluation to continue even after the analyst goes home for the day. They also utilize sophisticated optimization algorithms to more intelligently explore possible designs, often finding better, innovative solutions to difficult multidisciplinary design problems.

[edit] Subdisciplines

The field of mechanical engineering can be thought of as a collection of many mechanical disciplines. Several of these subdisciplines which are typically taught at the undergraduate level are listed below, with a brief explanation and the most common application of each. Some of these subdisciplines are unique to mechanical engineering, while others are a combination of mechanical engineering and one or more other disciplines. Most work that a mechanical engineer does uses skills and techniques from several of these subdisciplines, as well as specialized subdisciplines. Specialized subdisciplines, as used in this article, are more likely to be the subject of graduate studies or on-the-job training than undergraduate research. Several specialized subdisciplines are discussed in this section.

[edit] Mechanics

Mohr's circle, a common tool to study stresses in a mechanical element
Mechanics is, in the most general sense, the study of forces and their effect upon matter. Typically, engineering mechanics is used to analyze and predict the acceleration and deformation (both elastic and plastic) of objects under known forces (also called loads) or stresses. Subdisciplines of mechanics include
Mechanical engineers typically use mechanics in the design or analysis phases of engineering. If the engineering project were the design of a vehicle, statics might be employed to design the frame of the vehicle, in order to evaluate where the stresses will be most intense. Dynamics might be used when designing the car's engine, to evaluate the forces in the pistons and cams as the engine cycles. Mechanics of materials might be used to choose appropriate materials for the frame and engine. Fluid mechanics might be used to design a ventilation system for the vehicle (see HVAC), or to design the intake system for the engine.

[edit] Kinematics

Kinematics is the study of the motion of bodies (objects) and systems (groups of objects), while ignoring the forces that cause the motion. The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed four-bar linkage.
Mechanical engineers typically use kinematics in the design and analysis of mechanisms. Kinematics can be used to find the possible range of motion for a given mechanism, or, working in reverse, can be used to design a mechanism that has a desired range of motion.

[edit] Mechatronics and robotics

Training FMS with learning robot SCORBOT-ER 4u, workbench CNC Mill and CNC Lathe
Mechatronics is an interdisciplinary branch of mechanical engineering, electrical engineering and software engineering that is concerned with integrating electrical and mechanical engineering to create hybrid systems. In this way, machines can be automated through the use of electric motors, servo-mechanisms, and other electrical systems in conjunction with special software. A common example of a mechatronics system is a CD-ROM drive. Mechanical systems open and close the drive, spin the CD and move the laser, while an optical system reads the data on the CD and converts it to bits. Integrated software controls the process and communicates the contents of the CD to the computer.
Robotics is the application of mechatronics to create robots, which are often used in industry to perform tasks that are dangerous, unpleasant, or repetitive. These robots may be of any shape and size, but all are preprogrammed and interact physically with the world. To create a robot, an engineer typically employs kinematics (to determine the robot's range of motion) and mechanics (to determine the stresses within the robot).
Robots are used extensively in industrial engineering. They allow businesses to save money on labor, perform tasks that are either too dangerous or too precise for humans to perform them economically, and to insure better quality. Many companies employ assembly lines of robots, and some factories are so robotized that they can run by themselves. Outside the factory, robots have been employed in bomb disposal, space exploration, and many other fields. Robots are also sold for various residential applications.

[edit] Structural analysis

Structural analysis is the branch of mechanical engineering (and also civil engineering) devoted to examining why and how objects fail and to fix the objects and their performance. Structural failures occur in two general modes: static failure, and fatigue failure. Static structural failure occurs when, upon being loaded (having a force applied) the object being analyzed either breaks or is deformed plastically, depending on the criterion for failure. Fatigue failure occurs when an object fails after a number of repeated loading and unloading cycles. Fatigue failure occurs because of imperfections in the object: a microscopic crack on the surface of the object, for instance, will grow slightly with each cycle (propagation) until the crack is large enough to cause ultimate failure.
Failure is not simply defined as when a part breaks, however; it is defined as when a part does not operate as intended. Some systems, such as the perforated top sections of some plastic bags, are designed to break. If these systems do not break, failure analysis might be employed to determine the cause.
Structural analysis is often used by mechanical engineers after a failure has occurred, or when designing to prevent failure. Engineers often use online documents and books such as those published by ASM[23] to aid them in determining the type of failure and possible causes.
Structural analysis may be used in the office when designing parts, in the field to analyze failed parts, or in laboratories where parts might undergo controlled failure tests.

[edit] Thermodynamics and thermo-science

Thermodynamics is an applied science used in several branches of engineering, including mechanical and chemical engineering. At its simplest, thermodynamics is the study of energy, its use and transformation through a system. Typically, engineering thermodynamics is concerned with changing energy from one form to another. As an example, automotive engines convert chemical energy (enthalpy) from the fuel into heat, and then into mechanical work that eventually turns the wheels.
Thermodynamics principles are used by mechanical engineers in the fields of heat transfer, thermofluids, and energy conversion. Mechanical engineers use thermo-science to design engines and power plants, heating, ventilation, and air-conditioning (HVAC) systems, heat exchangers, heat sinks, radiators, refrigeration, insulation, and others.

[edit] Drafting

A CAD model of a mechanical double seal
Drafting or technical drawing is the means by which mechanical engineers create instructions for manufacturing parts. A technical drawing can be a computer model or hand-drawn schematic showing all the dimensions necessary to manufacture a part, as well as assembly notes, a list of required materials, and other pertinent information. A U.S. mechanical engineer or skilled worker who creates technical drawings may be referred to as a drafter or draftsman. Drafting has historically been a two-dimensional process, but computer-aided design (CAD) programs now allow the designer to create in three dimensions.
Instructions for manufacturing a part must be fed to the necessary machinery, either manually, through programmed instructions, or through the use of a computer-aided manufacturing (CAM) or combined CAD/CAM program. Optionally, an engineer may also manually manufacture a part using the technical drawings, but this is becoming an increasing rarity, with the advent of computer numerically controlled (CNC) manufacturing. Engineers primarily manually manufacture parts in the areas of applied spray coatings, finishes, and other processes that cannot economically or practically be done by a machine.
Drafting is used in nearly every subdiscipline of mechanical engineering, and by many other branches of engineering and architecture. Three-dimensional models created using CAD software are also commonly used in finite element analysis (FEA) and computational fluid dynamics (CFD).

[edit] Frontiers of research

Mechanical engineers are constantly pushing the boundaries of what is physically possible in order to produce safer, cheaper, and more efficient machines and mechanical systems. Some technologies at the cutting edge of mechanical engineering are listed below (see also exploratory engineering).

[edit] Micro electro-mechanical systems (MEMS)

Micron-scale mechanical components such as springs, gears, fluidic and heat transfer devices are fabricated from a variety of substrate materials such as silicon, glass and polymers like SU8. Examples of MEMS components will be the accelerometers that are used as car airbag sensors, gyroscopes for precise positioning and microfluidic devices used in biomedical applications.

[edit] Friction stir welding (FSW)

Friction stir welding, a new type of welding, was discovered in 1991 by The Welding Institute (TWI). This innovative steady state (non-fusion) welding technique joins materials previously un-weldable, including several aluminum alloys. It may play an important role in the future construction of airplanes, potentially replacing rivets. Current uses of this technology to date include welding the seams of the aluminum main Space Shuttle external tank, Orion Crew Vehicle test article, Boeing Delta II and Delta IV Expendable Launch Vehicles and the SpaceX Falcon 1 rocket, armor plating for amphibious assault ships, and welding the wings and fuselage panels of the new Eclipse 500 aircraft from Eclipse Aviation among an increasingly growing pool of uses.[24][25][26][27][dead link]

[edit] Composites

Composite cloth consisting of woven carbon fiber.
Composites or composite materials are a combination of materials which provide different physical characteristics than either material separately. Composite material research within mechanical engineering typically focuses on designing (and, subsequently, finding applications for) stronger or more rigid materials while attempting to reduce weight, susceptibility to corrosion, and other undesirable factors. Carbon fiber reinforced composites, for instance, have been used in such diverse applications as spacecraft and fishing rods.

[edit] Mechatronics

Mechatronics is the synergistic combination of mechanical engineering, Electronic Engineering, and software engineering. The purpose of this interdisciplinary engineering field is the study of automata from an engineering perspective and serves the purposes of controlling advanced hybrid systems.

[edit] Nanotechnology

At the smallest scales, mechanical engineering becomes nanotechnology —one speculative goal of which is to create a molecular assembler to build molecules and materials via mechanosynthesis. For now that goal remains within exploratory engineering.

[edit] Finite element analysis

This field is not new, as the basis of Finite Element Analysis (FEA) or Finite Element Method (FEM) dates back to 1941. But evolution of computers has made FEM a viable option for analysis of structural problems. Many commercial codes such as ANSYS, Nastran and ABAQUS are widely used in industry for research and design of components.
Other techniques such as finite difference method (FDM) and finite-volume method (FVM) are employed to solve problems relating heat and mass transfer, fluid flows, fluid surface interaction etc.

[edit] Related fields

Manufacturing engineering and Aerospace Engineering are sometimes grouped with mechanical engineering. A bachelor's degree in these areas will typically have a difference of a few specialized classes.

[edit] See also

[edit] Associations

[edit] Wikibooks

[edit] Notes and references

  1. ^ engineering "mechanical engineering. (n.d.)". The American Heritage Dictionary of the English Language, Fourth Edition. Retrieved: May 08, 2010.
  2. ^ "Heron of Alexandria". Encyclopædia Britannica 2010 - Encyclopædia Britannica Online. Accessed: 09 May 2010.
  3. ^ Needham, Joseph (1986). Science and Civilization in China: Volume 4. Taipei: Caves Books, Ltd.
  4. ^ Al-Jazarí. The Book of Knowledge of Ingenious Mechanical Devices: Kitáb fí ma'rifat al-hiyal al-handasiyya. Springer, 1973. ISBN 9027703299.
  5. ^ Engineering - Encyclopedia Brittanica, accessed 06 May 2008
  6. ^ R. A. Buchanan. The Economic History Review, New Series, Vol. 38, No. 1 (Feb., 1985), pp. 42–60.
  7. ^ ASME history, accessed 06 May 2008.
  8. ^ The Columbia Encyclopedia, Sixth Edition. 2001-07, engineering, accessed 06 May 2008
  9. ^ ABET searchable database of accredited engineering programs, Accessed June 19, 2006.
  10. ^ Accredited engineering programs in Canada by the Canadian Council of Professional Engineers, Accessed April 18, 2007.
  11. ^ Types of post-graduate degrees offered at MIT - Accessed 19 June 2006.
  12. ^ 2008-2009 ABET Criteria, p. 15.
  13. ^ University of Tulsa Required ME Courses - http://www.me.utulsa.edu/Undergraduate.html - Accessed 19 June 2006
  14. ^ Harvard Mechanical Engineering Page - Accessed 19 June 2006
  15. ^ Mechanical Engineering courses, MIT. Accessed 14 June 2008.
  16. ^ "Why Get Licensed?". National Society of Professional Engineers. http://www.nspe.org/Licensure/WhyGetLicensed/index.html. Retrieved May 6, 2008. 
  17. ^ "Engineers Act". Quebec Statutes and Regulations (CanLII). http://www.canlii.org/qc/laws/sta/i-9/20050616/whole.html. Retrieved July 24, 2005. 
  18. ^ "Codes of Ethics and Conduct". Online Ethics Center. Archived from the original on June 19, 2005. http://web.archive.org/web/20050619081942/http://onlineethics.org/codes/. Retrieved July 24, 2005. 
  19. ^ 2010-11 Edition, Engineers - Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, Accessed: 9 May 2010.
  20. ^ Document National Sector NAICS Industry-Specific estimates (xls) Accessed: 9 May 2010.
  21. ^ Mechanical Engineers - Jobfutures.ca, Accessed: June 30, 2007.
  22. ^ Note: fluid mechanics can be further split into fluid statics and fluid dynamics, and is itself a subdiscipline of continuum mechanics. The application of fluid mechanics in engineering is called hydraulics and pneumatics.
  23. ^ ASM International's site containing more than 20,000 searchable documents, including articles from the ASM Handbook series and Advanced Materials & Processes
  24. ^ Advances in Friction Stir Welding for Aerospace Applications
  25. ^ PROPOSAL NUMBER: 08-1 A1.02-9322 - NASA 2008 SBIR
  26. ^ Nova-Tech LLC
  27. ^ http://www.comsol.com/industry/htmlpaper/colegrove_stir_welding

[edit] Further reading

  • Burstall, Aubrey F. (1965). A History of Mechanical Engineering. The MIT Press. ISBN 0-262-52001-X. 

[edit] External links

mechanical engineering

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools.[1] It is one of the oldest and broadest engineering disciplines.
The engineering field requires a solid understanding of core concepts including mechanics, kinematics, thermodynamics, materials science, and structural analysis. Mechanical engineers use these core principles along with tools like computer-aided engineering and product lifecycle management to design and analyze manufacturing plants, industrial equipment and machinery, heating and cooling systems, motorized vehicles, aircraft, watercraft, robotics, medical devices and more.

Mechanical engineering emerged as a field during the industrial revolution in Europe in the 19th century; however, its development can be traced back several thousand years around the world. The field has continually evolved to incorporate advancements in technology, and mechanical engineers today are pursuing developments in such fields as composites, mechatronics, and nanotechnology. Mechanical engineering overlaps with aerospace engineering, civil engineering, electrical engineering, and petroleum engineering to varying amount

Typical design requirements&The frequency function,The impulse response&Computational complexity

Typical design requirements

Typical requirements which are considered in the design process are:
  • The filter should have a specific frequency response
  • The filter should have a specific impulse response
  • The filter should be causal
  • The filter should be stable
  • The filter should be localized
  • The computational complexity of the filter should be low
  • The filter should be implemented in particular hardware or software

[edit] The frequency function

Typical examples of frequency function are:
  • A low-pass filter is used to cut unwanted high-frequency signals.
  • A high-pass filter passes high frequencies fairly well; it is helpful as a filter to cut any unwanted low frequency components.
  • A band-pass filter passes a limited range of frequencies.
  • A band-stop filter passes frequencies above and below a certain range. A very narrow band-stop filter is known as a notch filter.
  • A low-shelf filter passes all frequencies, but increases or reduces frequencies below the shelf frequency by specified amount.
  • A high-shelf filter passes all frequencies, but increases or reduces frequencies above the shelf frequency by specified amount.
  • A peak EQ filter makes a peak or a dip in the frequency response, commonly used in graphic equalizers.
  • An all-pass filter passes through all frequencies unchanged, but changes the phase of the signal. This is a filter commonly used in phaser effects.
An important parameter is the required frequency response. In particular, the steepness and complexity of the response curve is a deciding factor for the filter order and feasibility.
A first order recursive filter will only have a single frequency-dependent component. This means that the slope of the frequency response is limited to 6 dB per octave. For many purposes, this is not sufficient. To achieve steeper slopes, higher order filters are required.
In relation to the desired frequency function, there may also be an accompanying weighting function which describes, for each frequency, how important it is that the resulting frequency function approximates the desired one. The larger weight, the more important is a close approximation.

[edit] The impulse response

There is a direct correspondence between the filter's frequency function and its impulse response, the former is the Fourier transform of the latter. This means that any requirement on the frequency function is a requirement on the impulse response, and vice versa.
However, in certain applications it may be the filter's impulse response which is explicit and the design process then aims at producing as close an approximation as possible to the requested impulse response given all other requirements.
In some cases it may even be relevant to consider a frequency function and impulse response of the filter which are chosen independently from each other. For example, we may both want a specific frequency function of the filter and that the resulting filter have a small effective width in the signal domain as possible. The latter condition can be realized by considering a very narrow function as the wanted impulse response of the filter even though this function has no relation to the desired frequency function. The goal of the design process is then to realize a filter which tries to meet both these contradicting design goals as much as possible.

[edit] Causality

In order to be implementable, any time-dependent filter must be causal: the filter response only depends on the current and past inputs. A standard approach is to leave this requirement until the final step. If the resulting filter is not causal, it can be made causal by introducing an appropriate time-shift (or delay). If the filter is a part of a larger system (which it normally is) these types of delays have to be introduced with care since they affect the operation of the entire system.

[edit] Stability

A stable filter assures that every limited input signal produces a limited filter response. A filter which does not meet this requirement may in some situations prove useless or even harmful. Certain design approaches can guarantee stability, for example by using only feed-forward circuits such as an FIR filter. On the other hand, filter based on feedback circuits have other advantages and may therefore be preferred, even if this class of filters include unstable filters. In this case, the filters must be carefully designed in order to avoid instability.

[edit] Locality

In certain applications we have to deal with signals which contain components which can be described as local phenomena, for example pulses or steps, which have certain time duration. A consequence of applying a filter to a signal is, in intuitive terms, that the duration of the local phenomena is extended by the width of the filter. This implies that it is sometimes important to keep the width of the filter's impulse response function as short as possible.
According to the uncertainty relation of the Fourier transform, the product of the width of the filter's impulse response function and the width of its frequency function must exceed a certain constant. This means that any requirement on the filter's locality also implies a bound on its frequency function's width. Consequently, it may not be possible to simultaneously meet requirements on the locality of the filter's impulse response function as well as on its frequency function. This is a typical example of contradicting requirements.

[edit] Computational complexity

A general desire in any design is that the number of operations (additions and multiplications) needed to compute the filter response is as low as possible. In certain applications, this desire is a strict requirement, for example due to limited computational resources, limited power resources, or limited time. The last limitation is typical in real-time applications.
There are several ways in which a filter can have different computational complexity. For example, the order of a filter is more or less proportional to the number of operations. This means that by choosing a low order filter, the computation time can be reduced.
For discrete filters the computational complexity is more or less proportional to the number of filter coefficients. If the filter has many coefficients, for example in the case of multidimensional signals such as tomography data, it may be relevant to reduce the number of coefficients by removing those which are sufficiently close to zero.
Another issue related to computational complexity is separability, that is, if and how a filter can be written as a convolution of two or more simpler filters. In particular, this issue is of importance for multidimensional filters, e.g., 2D filter which are used in image processing. In this case, a significant reduction in computational complexity can be obtained if the filter can be separated as the convolution of one 1D filter in the horizontal direction and one 1D filter in the vertical direction. A result of the filter design process may, e.g., be to approximate some desired filter as a separable filter or as a sum of separable filters.

[edit] Other considerations

It must also be decided how the filter is going to be implemented:

[edit] Analog filters

The design of linear analog filters is for the most part covered in the linear filter section.

[edit] Digital filters

Digital filters are classified into one of two basic forms, according to how they respond to an unit impulse:
  • Finite impulse response, or FIR, filters express each output sample as a weighted sum of the last N inputs, where N is the order of the filter. Since they do not use feedback, they are inherently stable. If the coefficients are symmetrical (the usual case), then such a filter is linear phase, so it delays signals of all frequencies equally. This is important in many applications. It is also straightforward to avoid overflow in an FIR filter. The main disadvantage is that they may require significantly more processing and memory resources than cleverly designed IIR variants. FIR filters are generally easier to design than IIR filters - the Remez exchange algorithm is one suitable method for designing quite good filters semi-automatically. (See Methodology.)
  • Infinite impulse response, or IIR, filters are the digital counterpart to analog filters. Such a filter contains internal state, and the output and the next internal state are determined by a linear combination of the previous inputs and outputs (in other words, they use feedback, which FIR filters normally do not). In theory, the impulse response of such a filter never dies out completely, hence the name IIR, though in practice, this is not true given the finite resolution of computer arithmetic. IIR filters normally require less computing resources than an FIR filter of similar performance. However, due to the feedback, high order IIR filters may have problems with instability, arithmetic overflow, and limit cycles, and require careful design to avoid such pitfalls. Additionally, since the phase shift is inherently a non-linear function of frequency, the time delay through such a filter is frequency-dependent, which can be a problem in many situations. 2nd order IIR filters are often called 'biquads' and a common implementation of higher order filters is to cascade biquads. A useful reference for computing biquad coefficients is the RBJ Audio EQ Cookbook.

[edit] Sample rate

Unless the sample rate is fixed by some outside constraint, selecting a suitable sample rate is an important design decision. A high rate will require more in terms of computational resources, but less in terms of anti-aliasing filters. Interference[disambiguation needed] and beating with other signals in the system may also be an issue.

[edit] Anti-aliasing

For any digital filter design, it is crucial to analyze and avoid aliasing effects. Often, this is done by adding analog anti-aliasing filters at the input and output, thus avoiding any frequency component above the Nyquist frequency. The complexity (i.e., steepness) of such filters depends on the required signal to noise ratio and the ratio between the sampling rate and the highest frequency of the signal.

[edit] Theoretical basis

Parts of the design problem relate to the fact that certain requirements are described in the frequency domain while others are expressed in the signal domain and that these may contradict. For example, it is not possible to obtain a filter which has both an arbitrary impulse response and arbitrary frequency function. Other effects which refer to relations between the signal and frequency domain are
  • The uncertainty principle between the signal and frequency domains
  • The variance extension theorem
  • The asymptotic behaviour of one domain versus discontinuities in the other

[edit] The uncertainty principle

As stated in the uncertainty principle, the product of the width of the frequency function and the width of the impulse response cannot be smaller than a specific constant. This implies that if a specific frequency function is requested, corresponding to a specific frequency width, the minimum width of the filter in the signal domain is set. Vice versa, if the maximum width of the response is given, this determines the smallest possible width in the frequency. This is a typical example of contradicting requirements where the filter design process may try to find a useful compromise.

[edit] The variance extension theorem

Let \sigma^{2}_{s} be the variance of the input signal and let \sigma^{2}_{f} be the variance of the filter. The variance of the filter response, \sigma^{2}_{r}, is then given by
\sigma^{2}_{r} = \sigma^{2}_{s} + \sigma^{2}_{f}
This means that σr > σf and implies that the localization of various features such as pulses or steps in the filter response is limited by the filter width in the signal domain. If a precise localization is requested, we need a filter of small width in the signal domain and, via the uncertainty principle, its width in the frequency domain cannot be arbitrary small.

[edit] Discontinuities versus asymptotic behaviour

Let f(t) be a function and let F(ω) be its Fourier transform. There is a theorem which states that if the first derivative of F which is discontinuous has order n \geq 0, then f has an asymptotic decay like t n − 1.
A consequence of this theorem is that the frequency function of a filter should be as smooth as possible to allow its impulse response to have a fast decay, and thereby a short width.

[edit] Methodology

One common method for designing FIR filters is the Remez exchange algorithm. Here the user specifies a desired frequency response, a weighting function for errors from this response, and a filter order N. The algorithm then finds the set of N coefficients that minimize the maximum deviation from the ideal. Intuitively, this finds the filter that is as close as you can get to the desired response given that you can use only N coefficients. This method is particularly easy in practice and at least one text[1] includes a program that takes the desired filter and N and returns the optimum coefficients. One possible drawback to filters designed this way is that they contain many small ripples in the passband(s), since such a filter minimizes the peak error.
Another method to finding a discrete FIR filter is filter optimization described in Knutsson et al., which minimizes the integral of the square of the error, instead of its maximum value. In its basic form this approach requires that an ideal frequency function of the filter FI(ω) is specified together with a frequency weighting function W(ω) and set of coordinates xk in the signal domain where the filter coefficients are located.
An error function \varepsilon is defined as
\varepsilon = \| W \cdot (F_{I} - \mathcal{F} \{ f \}) \|^{2}
where f(x) is the discrete filter and \mathcal{F} is the discrete-time Fourier transform defined on the specified set of coordinates. The norm used here is, formally, the usual norm on L2 spaces. This means that \varepsilon measures the deviation between the requested frequency function of the filter, FI, and the actual frequency function of the realized filter, \mathcal{F} \{ f \}. However, the deviation is also subject to the weighting function W before the error function is computed.
Once the error function is established, the optimal filter is given by the coefficients f(x) which minimize \varepsilon. This can be done by solving the corresponding least squares problem. In practice, the L2 norm has to be approximated by means of a suitable sum over discrete points in the frequency domain. In general, however, these points should be significantly more than the number of coefficients in the signal domain to obtain a useful approximation.

[edit] Simultaneous optimization in both domains

The previous method can be extended to include an additional error term related to a desired filter impulse response in the signal domain, with a corresponding weighting function. The ideal impulse response can be chosen independently of the ideal frequency function and is in practice used to limit the effective width and to remove ringing effects of the resulting filter in the signal domain. This is done by choosing a narrow ideal filter impulse response function, e.g., an impulse, and a weighting function which grows fast with the distance from the origin, e.g., the distance squared. The optimal filter can still be calculated by solving a simple least squares problem and the resulting filter is then a "compromise" which has a total optimal fit to the ideal functions in both domains. An important parameter is the relative strength of the two weighting functions which determines in which domain it is more important to have a good fit relative to the ideal function. b

[edit] See also

[edit] References

  1. ^ Rabiner, Lawrence R., and Gold, Bernard, 1975: Theory and Application of Digital Signal Processing (Englewood Cliffs, New Jersey: Prentice-Hall, Inc.) ISBN 0139141014
  • A. Antoniou (1993). Digital Filters: Analysis, Design, and Applications. McGraw-Hill, New York, NY. ISBN 0070021171. 
  • S.W.A. Bergen and A. Antoniou (2005). "Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function". EURASIP Journal on Applied Signal Processing 2005 (12): 1910. doi:10.1155/ASP.2005.1910. 
  • J.K. Kaiser (1974). "Nonrecursive Digital Filter Design Using the Io-sinh Window Function". Proc. 1974 IEEE Int. Symp. Circuit Theory. pp. 20–23. 
  • H. Knutsson, M. Andersson and J. Wiklund (June 1999). "Advanced Filter Design". Proc. Scandinavian Symposium on Image Analysis, Kangerlussuaq, Greenland. 
  • S.K. Mitra (1998). Digital Signal Processing: A Computer-Based Approach. McGraw-Hill, New York, NY. ISBN 0072865466. 
  • A.V. Oppenheim and R.W. Schafer and J.R. Buck (1999). Discrete-Time Signal Processing. Prentice-Hall, Upper Saddle River, NJ. ISBN 0137549202. 

[edit] External links