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Topic: Rectangular function

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Sinc function

Continuous Fourier transform

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	Rectangular function - Wikipedia, the free encyclopedia
		The rectangular function (also known as the rectangle function, rect function, unit pulse, or the normalized boxcar function) is defined as,
		The unitary Fourier transforms of the rectangular function are,
		Viewing the rectangular function as a probability distribution function, its characteristic function is,
	en.wikipedia.org /wiki/Rectangular_function (111 words)

	GDI Functions
		This function retrieves red, green, and blue color values from a range of entries in the color table of the DIB that is currently selected into a specified device context.
		This function increases or decreases the width and height of the specified rectangle.
		This function sets the pixels in the specified rectangle on the device that is associated with the destination device context using color data from a DIB.
	msdn.microsoft.com /library/en-us/mobilesdk5/html/mob5lrfGDIFunctions.asp?frame=true (2009 words)

	Design of Extended Depth of Field Systems
		Through the use of the ambiguity function and the method of stationary phase, phase masks for an extended depth of field incoherent optical system are readily found.
		The ambiguity function related to this general mask can be used as a polar display of the OTF for all values of misfocus [10].
		Calculation of the magnitude of the ambiguity function of this one-dimensional rectangular function leads to the image shown in figure 1.
	www.colorado.edu /isl/papers/edf/node2.html (580 words)

	MASS ACTION IN THE NERVOUS SYSTEM-Chapter 2 (Site not responding. Last check: 2007-10-05)
		A function is defined as the relation between a set of ordered pairs of real numbers in which no two numbers in the range correspond to the same number in the domain.
		The input functions and output functions constituting input–output pairs are represented by symbols, such as v for potential, i for current, p for pulse, and f for any of these and are called functions of time, such as v(t), i(t), p(t), and f(t).
		The outstanding virtue of the rectangular basis function or digitizing interval is that it permits measurement to any desired degree of precision without the restriction as to the nature of the wave form being measured, and without inference regarding the underlying dynamics.
	sulcus.berkeley.edu /MANSWWW/MANSHTML/MANSChapt2.html (5327 words)

	Methode der Physik (Site not responding. Last check: 2007-10-05)
		Figure 2: A rectangular pulse function is represented by the sum of a finite trigonometric polynomial.
		Function h(x) is an approximation of h(x) and describes a periodic function of period T
		The Fourier transform of a periodic function consists of N values, if the N scanning values of the original function h(x) are regarded as a period of a periodic function.
	genome.gbf.de /wavepaper (1594 words)

	Rectangular
		The wireframe representation rectangular for rectangular surfaces, are not.
		The wireframe representation for surfaces, are not subdivided at intersections of surfaces are not precise.
		The facets are not subdivided rectangular at intersections of surfaces.
	rectangular.thebomaster.com (1081 words)

	Project B2 (Site not responding. Last check: 2007-10-05)
		In the graph the dependence of the peak intensity of the (0,0)-spot is shown as a function of the pump-pulse traveltime.
		The blue curve is the result of the convolution of the temperature dependence from the heat-diffusion-model with a rectangular function of width 80 ps.
		The resulting temporal profile of the surface temperature was convoluted with a rectangular function of width 80 ps to account for the velocity mismatch and is shown in fig.
	www.physik.uni-essen.de /sfb616/B2.htm (1274 words)

	[No title]
		The ambiguity function related to this general mask can be used as a polar display of the OTF for all values of misfocus \cite{kn:ambiguity}.
		Notice that the majority of power in the ambiguity function of the rectangular aperture is concentrated along the $v=0$ axis, which corresponds to the infocus OTF.
		By careful selection of the non-linear function $\theta(x)$ of the general mask given in (\ref{eq:form}), a phase function that produces an ambiguity function with the desired extended depth of field characteristics can be found.
	www.cdm-optics.com /wave/pubs/papers/edf/6905_paper (3557 words)

	Advanced DSP - FFT windows: window kernels
		The contribution from any real frequency component to a given FFT bin is weighted by the amplitude of the window function's frequency spectrum centred at the FFT bin.
		For example, in the special case of a rectangular window (that is, no window at all except for the inevitable truncation) the frequency spectrum of the window function is the 'sinc' function shown below.
		Confusingly, the Fourier Transform of a window function is often also called the window function (instead of the kernel) - we have to judge from the context whether we are talking about the frequency spectrum or the time domain function.
	www.bores.com /courses/advanced/windows/10_kern.htm (194 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-05)
		It wasn't until a decade later that he found a "fix." He defined the concept of equal "almost everywhere." The idea is that the "energy," defined in a certain way, of both the sinusoid version and the original square wave is the same.
		The energy of both functions at the discontinuities is zero, so they don't matter.
		So, if we had a periodic function, like a square wave, we would notice that certain frequencies would show up more (multiples of the frequency of the square wave itself) and others would not (non- multiples).
	mathforum.org /library/drmath/view/62097.html (889 words)

	Math 112
		This course is part II of a pre-calculus sequence that provides exploration and application of rational and trigonometric functions and their inverses modeled algebraically, numerically, and graphically; trigonometric identities and equations; and vectors.
		Determine any trigonometric function value given the measure of the angle in degrees or radians, or given the coordinates of a point through which the terminal side of the angle passes.
		Sketch the graph of any trigonometric function or its inverse using the aid of a graphing calculator, scaling the horizontal axes with radian measurement of the angle.
	www.mhcc.edu /pages/2069.asp (2086 words)

	Quiz 8 (Site not responding. Last check: 2007-10-05)
		Recall that in rectangular coordinates we could visualize a function f(x) by setting y=f(x) and looking at the set of points (x,y) that satisfied the relation y=f(x).
		Given a function f(t) there's a distinct difference in the graph y=f(x) and r=f(theta).(Can you articulate this difference using the terminology of the previous worksheet?) If we have a function r=f(theta) a natural question would be to ask what it looks like as a rectangular coordinate function y=g(x).
		Worksheet 43: Deriving an Area Formula for Polar Coordinate Functions Given a rectangular coordinate function y=f(x), the integral from a to b of f(x) with respect to x defines the signed area bound between the curve y=f(x) and the line y=0(the x-axis).
	www.math.uiuc.edu /~mjames2/fa05math230/quiz8.html (523 words)

	Rectangular function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-05)
		The rectangular function (also known as the rectangle function or the normalized boxcar function) is defined as
		The Fourier transform of the rectangular function is
		Viewing the rectangular function as a probability distribution function, its characteristic function is therefore written
	www.godseye.com /stat/en/r/e/c/Rectangular_function.html (90 words)

	Mathlets: Rectangular Coordinates (3-D Graphing) (Site not responding. Last check: 2007-10-05)
		Graphs functions of the form f (x,y) using 3-dimensional rectangular coordinates.
		The text input fields can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates.
		The "wireframe" representation for surfaces, in which the surface is transparent, only draws one surface at a time.
	cs.jsu.edu /mcis/faculty/leathrum/Mathlets/grapher3d.html (194 words)

	Sinc function - Wikipedia, the free encyclopedia
		In both cases, the value of the function at the removable singularity at zero is sometimes specified explicitly as 1.
		(integers); that is, it is an interpolating function.
		correspond to its intersections with the cosine function.
	en.wikipedia.org /wiki/Sinc_function (345 words)

	Rectangular Hyperbola -- from Wolfram MathWorld
		The inverse curve of a rectangular hyperbola with inversion center at the center of the hyperbola is a lemniscate (Wells 1991).
		Equivalently, if four points form an orthocentric system, then there is a family of rectangular hyperbolas through the points.
		If four points do not form an orthocentric system, then there is a unique rectangular hyperbola passing through them, and its center is given by the intersection of the nine-point circles of the points taken three at a time (Wells 1991).
	mathworld.wolfram.com /RectangularHyperbola.html (287 words)

	The Universe of Discourse : Excellent numbers (Site not responding. Last check: 2007-10-05)
		All we need is some way to determine whether a given number q is rectangular, and that is not very hard to do.
		One way is simply to precompute a table of all rectangular numbers up to a certain size, and look up q in the table.
		This function returns false if its argument is not rectangular; and it returns the rectangular root otherwise.
	newbabe.pobox.com /~mjd/blog/math/excellent.html (1242 words)

	PHP: imagecopyresampled - Manual
		This function requires GD 2.0.1 or later (2.0.28 or later is recommended).
		I also tried using that bicubic image resizing function in some earlier post here, but it was only faster when the thumbnails were smaller than 120x90 and the quality was not very good.
		Here's a function i made that will force a given set of constraints on an image (usrfull if you want to make thumbnails that are all the same size) while keeping aspect ratio.
	de3.php.net /manual/en/function.imagecopyresampled.php (2122 words)

	Trigonometry and Basic Functions - Numericana
		Polynomial functions: The value y is obtained from the variable x using only a finite number of additions and/or multiplications involving given constants.
		Alternately, such functions may be construed as univalued (ordinary) functions of a variable whose domain is a so-called Riemann surface for which several points may have the same projection on the complex plane.
		The so-called sine cardinal, or sampling function, is sinc(x) = sin(x)/x (it often arises to express the Fourier transtorm of a rectangular function).
	home.att.net /~numericana/answer/functions.htm (3889 words)

	Internal Programming ofthe 9100A Calculator
		1, seemingly a trivial function, is as complex as most of the mathematical functions.
		The circular routines (sin, cos, tan), the inverse circular routines (arcsin, arccos, arctan) and the polar to rectangular and rectangular to polar conversions are all accomplished by iterating through a transformation which rotates the axes.
		In performing the rectangular to polar function, the signs of both the X and Y vectors are retained to place the resulting angle in the right quadrant.
	www.hpmuseum.org /journals/9100iprg.htm (1294 words)

	MATLAB Central - Loren on the Art of MATLAB » Blog Archive » Two-Dimensional Integration over a General ...
		Note that the inner integrand has integration 14 % limits that are a function of the semi-major and semi-minor ellipse 15 % axes, a and b.
		This is an area of performance (functions, nested functions, anonymous functions, and related) that we continue to work on.
		For some functions, we strive to eke out the maximum performance, but if we do so at the expense of significantly reduced clarity, we must think hard.
	blogs.mathworks.com /loren/?p=31 (1826 words)

	[No title]
		Clamping of the R texture coordinate for rectangular textures uses the standard [0,1] interval rather than the [0,w_s] or [0,h_s] intervals as in the case of S and T. This is because R represents a depth value in the [0,1] range whether using a 2D or rectangular texture.
		In the case of a rectangular texture, ws and hs equal the specified width and height respectively of the rectangular texture image while ds is 1." If EXT_paletted_texture is supported, add this paragraph too: "Rectangular textures do not support paletted formats.
		If the rectangular and either of the two- or one-dimensional textures is enabled, the rectangular texture is used.
	oss.sgi.com /projects/ogl-sample/registry/ARB/texture_rectangle.txt (3834 words)

	Rectangular Weir Discharge Calculator and Equations
		The rectangular weir is the most commonly used thin plate weir.
		The U.S. Bureau of Reclamation has conducted many weir tests over several decades using weirs with particular dimensions - usually b's in 1 ft. increments up to about 10 ft. Therefore, any weir outside their tested dimensions is non-standard, and their equations should not be used.
		To provide a single reliable, accurate method to model all rectangular weirs (suppressed, partially contracted, and fully contracted), the Kindsvater-Carter equation (Kindsvater and Carter, 1959) was developed.
	www.lmnoeng.com /Weirs/RectangularWeir.htm (871 words)

	Theory - Calculating Runoff - Rectangular Response Function
		Figure 7-18 illustrates a convolution process in which the response function is assumed to be rectangular with a dynamically varying time base equal to the time of concentration as defined by equation [7.41].
		The ordinate of the response function is given by umax = A/tc so that the evaluation of a discretized form of the convolution integral is relatively straightforward.
		If the effective rainfall is also a simple rectangular function the method reduces to the rational method.
	www.miduss.com /theory-Calculating-Runoff-Rectangular-Response-Function.htm (302 words)

	Graphs of functions - Topics in precalculus
		They are also called Cartesian coördinates, after the 17th century philosopher and mathematician René Descartes, for he was one of the first to exploit the geometrical possibilities of coördinates.
		Finally, the rectangular coördinates of a point are an ordered pair, (x, y).
		In which graph are the values of y a function of the values of x?
	www.themathpage.com /aPreCalc/graphs-of-functions.htm (445 words)

	FIR Digital Filter Design Applet: Notes
		Multiplying the sequence of filter coefficients by a rectangular window corresponds to truncating (chopping off) the sequence after a certain number of terms.
		The drawback of truncating the filter coefficients to produce a "cut-down" finite-order version of the filter is that it no longer has the ideal frequency response originally used as the basis for designing the filter.
		As indicated earlier, the choice of window function determines the minimum amount of attenuation provided in the stopband; the rectangular window, for example, has rather poor stopband performance, while the Blackman window gives much better stopband attenuation.
	www.dsptutor.freeuk.com /FIRFilterDesign/firfdes.htm (1581 words)

	Visual Basic Trigonometric Math
		Function returns an angle in radians that is between -Pi/2 and Pi/2.
		"Inverse Sine" or "Arcsine" Angle whose sine is X. Inverse of the Sine function.
		"Inverse Cotangent" or "Arccotangent" Angle whose cotangent is X. Inverse of the Cotangent function.
	www.entisoft.com /estools/MathTrigComplex.HTML (483 words)

	[No title]
		(1.81) Given the function y = 3cos(7x) + 5cos(13x) on the interval 0 to 10, plot: The function in rectangular coordinates; The function in polar coordinates.
		An example of the usage of the function is >> pfun('funct(x)') where funct is a MATLAB function such as sin.
		Using that function, write a program that plots the ration of area and perimeter versus the ratio of base to height.
	www.csupomona.edu /~tknguyen/egr599/Homework/Set1.doc (552 words)

	EE448 DSP - LAB 2
		(6), we truncated the infinite series in the transfer function equation by applying a rectangular window function with an amplitude of 1 between -Q and +Q, and ignoring the coefficients outside that window.
		The rectangular window function is the simplest window function used in FIR filter design.
		Use CONV function of Matlab to process the signal using the coefficients from the filter you designed.
	liu.ece.uic.edu /~dliu/DSP/fir.html (1764 words)

	C:\BELLBOOK\P001-100\HTMFILES\CSP0814.HTM (Site not responding. Last check: 2007-10-05)
		15, seemingly a trivial function, is as complex as most of the mathematical functions.
		Mathematical functions are similarly programmed defining a step-by-step procedure or algorithm for solving the desired mathematical problem.
		For instance, the "Polar to Rectangular" function uses the sin routine which uses multiply which uses add, etc.
	research.microsoft.com /~gbell/Computer_Structures_Principles_and_Examples/csp0814.htm (254 words)

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