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Topic: Sinc function

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	Sinc function - Wikipedia, the free encyclopedia
		The above definition for the sinc function is preferred since it removes this singularity and yields a function which is analytic everywhere.
		An interesting property of the sinc function is that its local maxima correspond to its intersections with the cosine curve.
		Applications of the sinc function are found in digital signal processing, communication theory, control theory, and optics.
	en.wikipedia.org /wiki/Sinc_function (368 words)

	Talk:Sinc function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-09)
		The delta function article has a number of cases where it is assumed that the delta function is zero everywhere except at x=0, including the idea that the delta function is a probability distribution, and that its support is x=0.
		The delta function is not a "probability distribution", since they are functions which are monotonically non-decreasing (etc).
		Googling "dirac delta sinc limit" yields a number of possibilities, the best of which seems to be [1] which in turn references Bracewell (1986) on the subject a number of times.
	en.wikipedia.org /wiki/Talk:Sinc_function (2794 words)

	PlanetMath: sinc function
		The sinc function is relevant in several fields.
		The resulting function is in fact analytic on the entire complex plane.
		This is version 11 of sinc function, born on 2004-04-09, modified 2006-03-08.
	planetmath.org /encyclopedia/SincFunction.html (228 words)

	CS 248: Midterm Solutions (Site not responding. Last check: 2007-10-09)
		Convolving a function in the spatial domain with a sinc function is impractical because the sinc function has infinite extent.
		Thus, to perfectly low-pass filter the signal requires a convolution with a sinc function, and by the reasons described in 4A, this is impractical.
		The sinc function, however, is not 0 outside the Nyquist frequency, and so the copies of the spectra introduced by the sampling process are attenuated, but not removed.
	graphics.stanford.edu /courses/cs248-98-fall/Midterm/q4.html (578 words)

	Csound Magazine
		The frequency of the sinc function is set to match the sample rate so that all neighboring samples occur where the sinc function goes to zero, at integer values.
		The overall signal is the sum of all of the sinc functions of all of the samples.
		Sinc interpolation can be accomplished by adding together a number of sinc functions on both sides of the point being interpolated.
	www.csounds.com /ezine/summer2000/internals (1264 words)

	How Much Bandwidth Does Your Logic Analyzer Need?
		Since rise-time is defined as the time between these two solutions, the results are simply subtracted and yield a rule of thumb for the rise-time of an RC circuit.
		Since bandwidth is defined as the frequency at which the magnitude of the response is attenuated by 30%, then this expression can be solved to generate a rule of the thumb.
		The pulse is represented using the rectangle function and the periodicity of the data stream is represented with the Shaw function.
	www.techonline.com /community/ed_resource/37281?print (1766 words)

	Theory of Ideal Bandlimited Interpolation (Site not responding. Last check: 2007-10-09)
		The sinc function can be seen as a hyperbolically weighted sine function with its zero at the origin canceled out.
		A sinc function instance is translated to each signal sample and scaled by that sample, and the instances are all added together.
		linear combination of signal samples where the coefficient of each signal sample is given by the value of the sinc function at the location of each sample.
	ccrma-www.stanford.edu /~jos/cs/Theory_Ideal_Bandlimited_Interpolation.html (482 words)

	Windowed sinc function
		The Lanczos window, which is the central lobe of a sinc function scaled to a certain extend.
		The frequency responses of the sinc filter windowed with all these windows and the windows themselves are depicted in Appendix B.
		Windowed sinc functions are reported to perform quite well, based on a purely quantitative comparison to linear interpolation, with Welch, Lanzcos and Kaiser windows, the truncated sinc kernel is reported to be one of the worst performing kernels.
	www.cg.tuwien.ac.at /~theussl/DA/node34.html (769 words)

	Signal Processing (Site not responding. Last check: 2007-10-09)
		The sinc function is the Fourier transform of the rectangle function.
		The sombrero function somb(x) is the two-dimensional polar-coordinate analog of the sinc function.
		The Fourier transform of a translated function is the transform of the untranslated function multiplied by a linear phase factor.
	www.engr.udayton.edu /faculty/jloomis/ece561/notes/intro/signals.html (1078 words)

	[No title]
		The filters in this file are: a sinc function, a sinc squared function (sinc applied twice), a gaussian function, a circular sinc function (symmetric, but not seperable), and a simple low pass filter.
		Since these filters apply some function to the forier domain, they cause changes in the power spectra, thus reducing the total energy.
		In the sinc and circular sinc filters, you still see some of the aliasing of the original image (though not as much as was there originally).
	www.cs.utah.edu /~wyman/classes/imp/antialising/report/report.html (1206 words)

	SINC function (Site not responding. Last check: 2007-10-09)
		The so called "sinc" function turns up in many application areas, perhaps most often in signal processing and Fourier analysis as it is the form of the Fourier transform of a rectangular pulse.
		Generating the function in software is straightforward noting the special case near the origin.
		Since sin(x) is very close to linear as x -> 0, there are no numerical problems using a low order polynomial expansion for sin(x) in this region.
	astronomy.swin.edu.au /~pbourke/other/sinc (82 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The SINC modulated RF pulse trains in conjunction with a constant gradient illustrated in Figures 2A, 2B, 3A, 3B, and 4A, 4B, were implemented for both a phantom and an in vivo animal study.
		The method of claim 8, wherein the SINC modulating function is defined at least in part by the bandwidth of a main lobe, and wherein altering the bandwidth of the main lobe alters the width of the resulting tag lines.
		The computer readable media of claim 18, wherein the SINC modulating function is defined at least in part by the bandwidth of a main lobe, and wherein altering the bandwidth of the main lobe alters the width of the resulting tag lines.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=03/93871.031113&ELEMENT_SET=DECL (3766 words)

	Signal Sampling and Reconstruction
		Consider the case of a rectangular pulse signal and its transform, the sinc: as the pulse becomes taller and narrower, the sinc grows wider, until the limiting case where the pulse becomes an infinite-height impulse and the sinc becomes an infinite-extent constant signal.
		As a result, the "sinc" signal displayed by SampleMania is actually a sinc that has been multiplied by a rectangular window in the time domain, zeroing out the small ripples that extend to infinity in the original signal.
		Because the sinc function never drops off to zero, the magnitude spectrum of our windowed function is never identically zero, resulting in non-zero "ripples" of distortion that extend to infinity.
	www.jhu.edu /~signals/sampling/deepsamp.html (753 words)

	ipedia.com: List of mathematical functions Article (Site not responding. Last check: 2007-10-09)
		A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.
		Ackermann function: in the theory of computation, a recursive function that is not primitive recursive.
		Not a function but a distribution, but sometimes informally referred to as a function, particularly by physicists and engineers.
	www.ipedia.com /list_of_mathematical_functions.html (487 words)

	Ideal reconstruction
		3.6, sampling can be seen as multiplying a function with a comb function which means that the frequency response of the function gets convolved with the frequency response of the comb function, which is another comb function but with reciprocal spacing.
		Then the frequency response of the original function can be perfectly reconstructed by multiplying the frequency response of the sampled function with a box function which half-width is equal to the bandwidth of the original function.
		Then it happens that the replicas overlap with the original spectrum of our function and when we multiply in frequency domain with the box function we get an aliased, i.e., modified, spectrum, that is a spectrum which has aliases of higher frequencies (therefore this phenomenon is called aliasing).
	www.cg.tuwien.ac.at /~theussl/DA/node29.html (526 words)

	Preconditioning and periodic sinc functions
		The name ``periodic sinc'', or psinc, has been chosen to reflect the connection that this function has with the familiar ``cardinal sine'' or sinc function.
		The sinc function is a continuous integral of plane waves with unit coefficients up to a maximum cut-off frequency.
		The psinc function differs only in that this continous integral is replaced by a finite sum over the reciprocal lattice vectors of the simulation cell, as in Eq.
	www.tcm.phy.cam.ac.uk /~aam24/PAPERS/paper4/node6.html (289 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The 'Fourier Transform' of the sinusoid is a delta function.
		The transform of a windowed sine is the convolution of the a sinc function with two delta functions at + and - iw.
		This is not a sinc function, rather, it is two sinc functions, shifted by +/- w and multiplied by i.
	shoko.calarts.edu /pipermail/music-dsp/1999-August/002118.html (339 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Figure 5 (a) depicts the L-error and Figure 5 (b) the signature of the DAF smoothing to the periodically extended noisy sine function as a function of o/A. The M is fixed to be 12.
		By examining its behavior as a function of the DAF parameters, it is possible to obtain the overall frequency distribution of the original noisy signal.
		We force the noisy function to be periodic by padding the values of the function on these last 36 points, using only the known, noisy 220 values to periodically surround the gap.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=99/46731.990916&ELEMENT_SET=DECL (7619 words)

	Documentation for vtkWindowedSincPolyDataFilter (Site not responding. Last check: 2007-10-09)
		For each vertex v, the coordinates of v are modified using a windowed sinc function interpolation kernel.
		The transfer functions of the low-pass filters are approximated by Chebyshev polynomials.
		The NumberOfIterations corresponds to the degree of the polynomial that is used to approximate the windowed sinc function.
	scv.bu.edu /LIVE/localdocs/vtk/manhtml/vtkWindowedSincPolyDataFilter.html (1000 words)

	Theory of Ideal Bandlimited Interpolation
		These sinc functions would be used to reconstruct the bandlimited interpolation of the discrete-time signal
		The deviation from unity between samples can be thought of as ``overshoot'' or ``ringing'' of the lowpass filter which cuts off at half the sampling rate, or it can be considered a ``Gibbs phenomenon'' associated with bandlimiting.
		in the signal is translated under the peak of the sinc function, then create the output as a linear combination of signal samples where the coefficient of each signal sample is given by the value of the sinc function at the location of each sample.
	www.technick.net /public/code/cp_dpage.php?altmenu=1&aiocp_dp=guide_dar_006 (500 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		% % The sawtooth function generates a sawtooth wave with peaks at ±1 and a % period of 2*pi.
		The sinc function is the continuous inverse Fourier % transform of the rectangular pulse of width 2*pi and height 1.
		Below are several examples of % using the chirp function to generate linear or quadratic, convex and % concave quadratic chirps.
	www.clemson.edu /cle4_share/CWE/COES0915_CLUG/REFERENCE/matlabr14/toolbox/signal/sigdemos/waveformdemo.m (489 words)

	Sampling Theory and Spline Interpolation (Site not responding. Last check: 2007-10-09)
		In the spline method, the signal is reconstructed using sample-weighted cardinal splines as opposed to sample-weighted sinc functions.
		There are several desirable properties of the sinc function that make this strategy effective.
		First of all, the sinc function vanishes at all integers except at the origin.
	cnx.org /content/m11126/latest (464 words)

	Project 5
		This is a sinc function in two dimensions, sampled regularly at the middle of each pixel and not filtered in any way.
		The images of the sinc function I generated for this assignment came from a new material and object I created specifically for this task.
		When the image ray strikes a Function object before any other object in the scene, the function material accomplishes its shading simply by calling the Function object's eval method, then interpolating between two colors (specified at construction time) based on how far the function value is between two extreme values (also specified at construction time).
	www.sci.utah.edu /~roni/raytracing/project5 (642 words)

	Reconstruction from Samples--Pictorial Version
		The sinc functions are drawn with dashed lines, and they sum to produce the solid curve.
		Notice that each sinc function passes through zero at every sample instant but the one it is centered on, where it passes through 1.
		The sinc function has zeros at all the integers except 0, where it is 1.
	ccrma-www.stanford.edu /~jos/sines/Reconstruction_Samples_Pictorial_Version.html (200 words)

	sinc (Site not responding. Last check: 2007-10-09)
		This function is the continuous inverse Fourier transform of the rectangular pulse of width 2
		The space of functions bandlimited in the frequency band
		is spanned by the infinite (yet countable) set of sinc functions shifted by integers.
	grove.ufl.edu /matlab_help/toolbox/signal/sinc.html (151 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The intensity patterns due to Fraunhofer diffraction from a slit result in a sinc squared pattern.
		The function f(x) = sin(x)/x for z = 0 has a singularity at z = 0.
		The "sinc" function is particularly important n signal processing and is the Fourier transform of a rectangular pulse.
	www-users.york.ac.uk /~ncw2/optics/sinc.html (95 words)

	[No title]
		The Fourier transform of a comb function is another comb function, thus the Fourier transform of the sampled function is the Fourier transform of the original function, "replicated" infinitely often by the comb, see Figure 6.
		When reconstructing a function from its sampled version using linear interpolation, the scaled comb function representing the sample set is convolved with the triangle function of the same distance parameter.
		Truncating a function means multiplying it with a box filter, and this is equivalent to convolving the spectrum of the function with a sinc function.
	graphics.cs.ucdavis.edu /~okreylos/PhDStudies/Winter2000/SamplingTheory.html (3840 words)

	Evaluating Feynman Diagrams with the Sinc Function Representation (Site not responding. Last check: 2007-10-09)
		The Sinc function representation is a novel approach to the numerical evalutation of Feynman integrals.
		The Sinc Function Representation and Three-Loop Master Diagrams we used it to evalaute the master diagrams, whose analytic properties are described by
		This is the header for the Sinc function calculations.
	www.het.brown.edu /people/easther/feynman (498 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		A plot of the sinc function [IMAGE: $]to the left and right of the origin [IMAGE: $t=0$] is shown in Fig. 1.Note that peak is at amplitude [IMAGE: $1$], and zero-crossings occur at allnonzero integers.
		A sinc function instance istranslated to each signal sample and scaled by that sample, and theinstances are all added together.
		Since thenonzero samples of the digital signal are all [IMAGE: $1$], we might expect theinterpolated signal to be very close to [IMAGE: $1$] over the nonzero interval;however, this is far from being the case.
	www.technick.net /public/code/cp_html2txt.php?page=http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=guide_dar_006 (641 words)

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