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Küpfmüller's Uncertainty Principle
Küpfmüller's uncertainty principle by Karl Küpfmüller in the year 1924 states that the relation of the rise time of a bandlimited signal to its bandwidth is a constant. :\Delta f\Delta t \ge k with k either 1 or \frac Proof A bandlimited signal u(t) with fourier transform \hat(f) in frequency space is given by the multiplication of any signal \underline(f) with \hat(f) = with a rectangular function of width \Delta f :\hat(f) = \operatorname \left(\frac \right) =\chi_(f) := \begin1 & , f, \le\Delta f/2 \\ 0 & \text \end as (applying the convolution theorem) :\hat(f) \cdot \hat(f) = (g * u)(t) Since the fourier transform of a rectangular function is a sinc function and vice versa, follows : g(t) = \frac1 \int \limits_^ 1 \cdot e^ df = \frac1 \cdot \Delta f \cdot \operatorname \left( \frac \right) Now the first root of g(t) is at \pm \frac , which is the rise time \Delta t of the pulse g(t) , now follows : \Delta t = \frac Equality is given as long a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Küpfmüller
Karl Küpfmüller (6 October 1897 – 26 December 1977) was a German electrical engineer, who was prolific in the areas of communications technology, measurement and control engineering, acoustics, communication theory, and theoretical electro-technology. Biography Küpfmüller was born in Nuremberg, where he studied at the Ohm-Polytechnikum. After returning from military service in World War I, he worked at the telegraph research division of the German Post in Berlin as a co-worker of Karl Willy Wagner, and, from 1921, he was lead engineer at the central laboratory of Siemens & Halske AG in the same city. In 1928 he became full professor of general and theoretical electrical engineering at the ''Technische Hochschule'' in Danzig, and later held the same position in Berlin. Küpfmüller joined the National Socialist Motor Corps in 1933. In the following year he also joined the SA. In 1937 Küpfmüller joined the NSDAP and became a member of the SS, where he reached the rank of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangular Function
The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as \operatorname(t) = \Pi(t) = \left\{\begin{array}{rl} 0, & \text{if } , t, > \frac{1}{2} \\ \frac{1}{2}, & \text{if } , t, = \frac{1}{2} \\ 1, & \text{if } , t, \frac{1}{2} \\ \frac{1}{2} & \mbox{if } , t, = \frac{1}{2} \\ 1 & \mbox{if } , t, < \frac{1}{2}. \\ \end{cases} See also * * * * |
Convolution Theorem
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms. Functions of a continuous variable Consider two functions g(x) and h(x) with Fourier transforms G and H: \begin G(f) &\triangleq \mathcal\(f) = \int_^g(x) e^ \, dx, \quad f \in \mathbb\\ H(f) &\triangleq \mathcal\(f) = \int_^h(x) e^ \, dx, \quad f \in \mathbb \end where \mathcal denotes the Fourier transform operator. The transform may be normalized in other ways, in which case constant scaling factors (typically 2\pi or \sqrt) will appear in the convolution theorem below. The convolution of g and h is defined by: r(x) = \(x) \triangleq \int_^ g(\t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Function
In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatornamex = \frac. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(''x''). In digital signal processing and information theory, the normalized sinc function is commonly defined for by \operatornamex = \frac. In either case, the value at is defined to be the limiting value \operatorname0 := \lim_\frac = 1 for all real . The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of . The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse (signal Processing)
A pulse in signal processing is a rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. Pulse shapes Pulse shapes can arise out of a process called pulse-shaping. Optimum pulse shape depends on the application. Rectangular pulse These can be found in pulse waves, square waves, boxcar functions, and rectangular functions. In digital signals the up and down transitions between high and low levels are called the rising edge and the falling edge. In digital systems the detection of these sides or action taken in response is termed edge-triggered, rising or falling depending on which side of rectangular pulse. A digital timing diagram is an example of a well-ordered collection of rectangular pulses. Nyquist pulse A Nyquist pulse is one which meets the Nyquist ISI criterion and is important in data transmission. An example of a pulse which meets this condition is the sinc function. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisenberg's Uncertainty Principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, ''x'', and momentum, ''p'', can be predicted from initial conditions. Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Introduced first in 1927 by the German physicist Werner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technische Universität Hamburg-Harburg
The Hamburg University of Technology (in German Technische Universität Hamburg, abbreviated TUHH (HH as acronym of Hamburg state) or TU Hamburg) is a research university in Germany. The university was founded in 1978 and in 1982/83 lecturing followed. Around 100 senior lecturers/professors and 1,475 members of staff (639 scientists, including externally funded researchers) work at the TUHH. It is located in Harburg, a district in the south of Hamburg. Interdisciplinary Studies Instead of traditional faculties, the TUHH has separate administrations for teaching and for research: research is conducted in departments, teaching is divided into schools of study. Scientists from different subjects work together in the departments. Curricula are organized by academic speciality, depending on the course of study followed. In the year 2000, the TUHH defined the following strategic topics of research activities: # Information as economic value # Organization for enterprises # Product ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teubner Verlag
The Bibliotheca Teubneriana, or ''Bibliotheca Scriptorum Graecorum et Romanorum Teubneriana'', also known as Teubner editions of Greek and Latin texts, comprise one of the most thorough modern collection published of ancient (and some medieval) Greco-Roman literature. The series consists of critical editions by leading scholars. They now always come with a full critical apparatus on each page, although during the nineteenth century there were ''editiones minores'', published either without critical apparatuses or with abbreviated textual appendices, and ''editiones maiores'', published with a full apparatus. Teubneriana is an abbreviation used to denote mainly a single volume of the series (fully: ''editio Teubneriana''), rarely the whole collection; correspondingly, ''Oxoniensis'' is used with reference to the ''Scriptorum Classicorum Bibliotheca Oxoniensis'', mentioned above as ''Oxford Classical Texts''. The only comparable publishing ventures producing authoritative scholarl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Engineering
Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current flow. Previously electrical engineering only used passive devices such as mechanical switches, resistors, inductors and capacitors. It covers fields such as: analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. It is also involved in many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, robotics. The Institute of Electrical and Electronics Engineers (IEEE) is one of the most important professional bodies for electronics engineers in the US; the equivalent body in the UK is the Institution of Engineering and Technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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