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Decade (log Scale)
One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers. Example: Scientific notation When a real number like .007 is denoted alternatively by 7.0 × 10—3 then it is said that the number is represented in ''scientific notation''. More generally, to write a number in the form ''a'' × 10''b'', where 1 <= ''a'' < 10 and ''b'' is an , is to express it in scientific notation, and ''a'' is called the '' significand'' or the ''mantissa'', and ''b'' is its exponent. The numbers so expressible with an exponen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Decades
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the Caliphate in the 9th c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , then is the logarithm of to base , written , so . As a single-variable function, the logarithm to base is the inverse of exponentiation with base . The logarithm base is called the ''decimal'' or ''common'' logarithm and is commonly used in science and engineering. The ''natural'' logarithm has the number as its base; its use is widespread in mathematics and physics because of its very simple derivative. The ''binary'' logarithm uses base and is widely used in computer science, information theory, music theory, and photography. When the base is unambiguous from the context or irrelevant it is often omitted, and the logarithm is written . Logarithms were introduced by John Napier in 1614 as a means of simplifying calculation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Level
In science and engineering, a power level and a field level (also called a root-power level) are logarithmic magnitudes of certain quantities referenced to a standard reference value of the same type. * A ''power level'' is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel (dB). * A ''field level'' (or ''root-power level'') is a logarithmic quantity used to measure quantities of which the square is typically proportional to power (for instance, the square of voltage is proportional to power by the inverse of the conductor's resistance), etc., with commonly used units neper (Np) or decibel (dB). The type of level and choice of units indicate the scaling of the logarithm of the ratio between the quantity and its reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified by international standards. Power and field levels are u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-third Octave
A one-third octave is a logarithmic unit of frequency ratio equal to either one third of an octave (1200/3 = 400 cents: major third) or one tenth of a decade (3986.31/10 = 398.631 cents: M3 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade. Definitions Base 2 ISO 18405:2017 defines a "one-third octave" (or "one-third octave (base 2)") as one third of an octave, corresponding to a frequency ratio of 2^. A one-third octave (base 2) is precisely 400 cents. Base 10 IEC 61260-1:2014 and ANSI S1.6-2016 define a "one-third octave" as one tenth of a decade, corresponding to a frequency ratio of 10^. This unit is referred to by ISO 18405 as a "decidecade" or "one-third octave (base 10)".(This makes sense as, if we want one third of an octave, the ratio will be f2/f1=2^, and if we log10 both members of equation we have, log=log-> log(f2/f1)=log(2)*1/3, which is approximately 0,1. One decidecade is equal to 100 savarts (approximately 398.631 cents). See a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slide Rule
A slide rule is a hand-operated mechanical calculator consisting of slidable rulers for conducting mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry. It is one of the simplest analog computers. Slide rules exist in a diverse range of styles and generally appear in a linear, circular or cylindrical form. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in specialized calculations particular to those fields. The slide rule is closely related to nomograms used for application-specific computations. Though similar in name and appearance to a standard ruler, the slide rule is not meant to be used for measuring length or drawing straight lines. Maximum accuracy for standard linear slide rules is about three decimal significant digits, while scientific notation is used to keep track of the order of magnitude of results. English mathematician and clergy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whose level (logarithmic quantity), levels differ by one decibel have a power ratio of 101/10 (approximately ) or root-power ratio of 101/20 (approximately ). The strict original usage above only expresses a relative change. However, the word decibel has since also been used for expressing an Absolute scale, absolute value that is relative to some fixed reference value, in which case the dB symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is "#Voltage, V" (e.g., "20 dBV"). As it originated from a need to express power ratios, two principal types of scaling of the decibel are used to provide consistency depending on whether the scaling refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Butterworth Filter Bode Plot
Butterworth may refer to: Places * Butterworth, Greater Manchester, a former township and civil parish centred on Milnrow, England, formerly in Lancashire * Butterworth, Eastern Cape, now also known as Gcuwa, a town located in South Africa * Butterworth, Penang, the principal town of Seberang Perai in the state of Penang, Malaysia ** RMAF Butterworth, air base near Butterworth, Penang, Malaysia * Butterworth, Ohio, a ghost town, United States * Butterworth, Virginia, unincorporated community, United States People * Butterworth (surname), including a list of people with the name Other uses * Aston Butterworth, British racing car constructor * Butterworth filter, a type of electronic filter design, eponym of Stephen Butterworth * LexisNexis Butterworths, publisher * Mrs. Butterworth's, a brand of pre-packaged syrups and pancake mixes * ''Butterworth'' (1785 ship), originally a privateer, then a whaler ** Butterworth Squadron The ''Butterworth'' Squadron was a British commercia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Paper
Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available either as loose leaf paper or bound in notebooks or graph books. It is commonly found in mathematics and engineering education settings, exercise books, and in laboratory notebooks. The lines are often used as guides for mathematical notation, plotting graph of a function, graphs of functions or experimental data, and drawing curves. History The Metropolitan Museum of Art owns a pattern book dated to around 1596 in which each page bears a grid woodblock printing, printed with a woodblock. The owner has used these grids to create block pictures in black and white and in colour. The first commercially published "coordinate paper" is usually attributed to a Dr. Buxton of England, who patented paper printed with a rectangular coordinate grid, in 1794. A century later, E. H. Moore, a distinguished mathematician at the University of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bode Plot
In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments. Overview Among his several important contributions to circuit theory and control theory, engineer Hendrik Wade Bode, while working at Bell Labs in the 1930s, devised a simple but accurate method for graphing gain and phase-shift plots. These bear his name, ''Bode gain plot'' and ''Bode phase plot''. "Bode" is often pronounced in English as , whereas in Dutch it is usually , closer to English , which is preferred by his family, but less common among researchers.Van Valkenburg, M. E. University of Illinois at Urbana-Champaign, "In mem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear
In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x)=(ax,bx) that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables X, Y and Z is aX+bY+cZ+d. Linearity of a mapping is closely related to '' proportionality''. Examples in physics include the linear relationship of voltage and current in an electrical conductor ( Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are '' nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. Linearity of a polynomial means that its de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decade Vs Linear
A decade (from , , ) is a period of 10 years. Decades may describe any 10-year period, such as those of a person's life, or refer to specific groupings of calendar years. Usage Any period of ten years is a "decade". For example, the statement that "during his last decade, Mozart explored chromatic harmony to a degree rare at the time" refers to the last 10 years of Wolfgang Amadeus Mozart's life without regard to which calendar years are encompassed. Also, 'the first decade' of a person's life begins on the day of their birth and ends at the end of their 10th year of life when they have their 10th birthday; the second decade of life starts with their 11th year of life (during which one is typically still referred to as being "10") and ends at the end of their 20th year of life, on their 20th birthday; similarly, the third decade of life, when one is in one's twenties or 20s, starts with the 21st year of life, and so on, with subsequent decades of life similarly described by refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
