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Lehmer Mean
In mathematics, the Lehmer mean of a tuple x of positive real numbers, named after Derrick Henry Lehmer, is defined as: :L_p(\mathbf) = \frac. The weighted Lehmer mean with respect to a tuple w of positive weights is defined as: :L_(\mathbf) = \frac. The Lehmer mean is an alternative to power means for interpolating between minimum and maximum via arithmetic mean and harmonic mean. Properties The derivative of p \mapsto L_p(\mathbf) is non-negative : \frac L_p(\mathbf) = \frac , thus this function is monotonic and the inequality :p \le q \Longrightarrow L_p(\mathbf) \le L_q(\mathbf) holds. The derivative of the weighted Lehmer mean is: : \frac = \frac Special cases *\lim_ L_p(\mathbf) is the minimum of the elements of \mathbf. *L_0(\mathbf) is the harmonic mean. *L_\frac\left((x_1, x_2)\right) is the geometric mean of the two values x_1 and x_2. *L_1(\mathbf) is the arithmetic mean. *L_2(\mathbf) is the contraharmonic mean. *\lim_ L_p(\mathbf) is the max ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defined inductively using the construction of an ordered pair. Mathematicians usually write tuples by listing the elements within parentheses "" and separated by a comma and a space; for example, denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "nbsp; or angle brackets "⟨ ⟩". Braces "" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term ''tuple'' can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lowpass
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. In optics, high-pass and low-pass may have different meanings, depending on whether referring to frequency or wavelength of light, since these variables are inversely related. High-pass frequency filters would act as low-pass wavelength filters, and vice versa. For this reason it is a good practice to refer to wavelength filters as ''short-pass'' and ''long-pass'' to avoid confusion, which would correspond to ''high-pass'' and ''low-pass'' frequencies. Low-pass filters exist in many different forms, including electronic circuits such as a hiss filter used in audio, anti-aliasing fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Mean
Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may also refer to: Mathematics, science and technology Computing * IBM POWER (software), an IBM operating system enhancement package * IBM POWER architecture, a RISC instruction set architecture * Power ISA, a RISC instruction set architecture derived from PowerPC * IBM Power microprocessors, made by IBM, which implement those RISC architectures * Power.org, a predecessor to the OpenPOWER Foundation * SGI POWER Challenge, a line of SGI supercomputers Mathematics * Exponentiation, "''x'' to the power of ''y''" * Power function * Power of a point * Statistical power Physics * Magnification, the factor by which an optical system enlarges an image * Optical power, the degree to which a lens converges or diverges light Social sciences and politi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithmetic mean'', also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the ''sample mean'' (\bar) to distinguish it from the mean, or expected value, of the underlying distribution, the ''population mean'' (denoted \mu or \mu_x).Underhill, L.G.; Bradfield d. (1998) ''Introstat'', Juta and Company Ltd.p. 181/ref> Outside probability and statistics, a wide range of other notions of mean are o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salt-and-pepper Noise
Salt-and-pepper noise, also known as impulse noise, is a form of noise sometimes seen on digital images. This noise can be caused by sharp and sudden disturbances in the image signal. It presents itself as sparsely occurring white and black pixels. An effective noise reduction Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an und ... method for this type of noise is a median filter or a morphological filter. For reducing either salt noise or pepper noise, but not both, a contraharmonic mean filter can be effective. See also * Defective pixel References Noise (graphics) Digital photography Image noise reduction techniques {{Photo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filter (signal Processing)
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics. There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be: *non-linear or linear *time-variant or t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass Spectrum
A mass spectrum is a histogram plot of intensity vs. ''mass-to-charge ratio'' (''m/z'') in a chemical sample, usually acquired using an instrument called a ''mass spectrometer''. Not all mass spectra of a given substance are the same; for example, some mass spectrometers break the analyte molecules into '' fragments''; others observe the intact molecular masses with little fragmentation. A mass spectrum can represent many different types of information based on the type of mass spectrometer and the specific experiment applied. Common fragmentation processes for organic molecules are the ''McLafferty rearrangement'' and ''alpha cleavage''. Straight chain alkanes and alkyl groups produce a typical series of peaks: 29 (CH3CH2+), 43 (CH3CH2CH2+), 57 (CH3CH2CH2CH2+), 71 (CH3CH2CH2CH2CH2+) etc. X-axis: ''m/z'' (mass-to-charge ratio) The x-axis of a mass spectrum represents a relationship between the mass of a given ion and the number of elementary charges that it carries. This is writte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baseline (spectrometry)
A baseline is a line that is a base for measurement or for construction. The word baseline may refer to: * Baseline (configuration management), the process of managing change * Baseline (sea), the starting point for delimiting a coastal state's maritime zones ** Baselines of the Chinese territorial sea ** Baselines of Indonesia ** Baselines of the Philippines * Baseline, in underwater diving, a value used to convert cylinder pressure of a tank to free gas volume * Baseline (surveying), a line between two points of the earth's surface and the direction and distance between them * Baseline (typography), the line upon which most letters "sit" and below which descenders extend * Baseline (budgeting), an estimate of budget expected during a fiscal year * Baseline (medicine), information found at the beginning of a study * Baseline (pharmacology), a person's state of mind or being, in the absence of drugs * The isoelectric line of an electrocardiogram * Baseline (interferometry), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectifier
A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation (converting DC to AC) is performed by an Power inverter, inverter. The process is known as ''rectification'', since it "straightens" the direction of current. Physically, rectifiers take a number of forms, including Vacuum tube#Diodes, vacuum tube diodes, wet chemical cells, mercury-arc valves, stacks of copper and selenium rectifier, selenium oxide plates, Diode#Semiconductor diodes, semiconductor diodes, silicon-controlled rectifiers and other silicon-based semiconductor switches. Historically, even synchronous electromechanical switches and motor-generator sets have been used. Early radio receivers, called crystal radios, used a "Cat's-whisker detector, cat's whisker" of fine wire pressing on a crystal of galena (lead sulfide) to serve as a point-contact rectifier or "crystal detec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envelope Detector
An envelope detector (sometimes called a peak detector) is an electronic circuit that takes a (relatively) high-frequency amplitude modulated signal as input and provides an output, which is the demodulated ''envelope'' of the original signal. Circuit operation The capacitor in the circuit above stores charge on the rising edge and releases it slowly through the resistor when the input signal amplitude falls. The diode in series rectifies the incoming signal, allowing current flow only when the positive input terminal is at a higher potential than the negative input terminal. General considerations Most practical envelope detectors use either half-wave or full-wave rectification of the signal to convert the AC audio input into a pulsed DC signal. Filtering is then used to smooth the final result. This filtering is rarely perfect and some "ripple" is likely to remain on the envelope follower output, particularly for low frequency inputs such as notes from a bass instrum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moving Average
In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, cumulative, or weighted forms (described below). Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next value in the subset. A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly. It is also used in economics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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