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Topic: Undersampling

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Oversampling

Sampling frequency

Domain decomposition method

Dehydroalanine

	2MASS Facts - Data Characterstics - Undersampling
		The sum of the point source flux from the coadd image is 4 in units of image pixels, which is the same as 2 in units of camera pixels.
		The combination of undersampling and a dead pixel has caused 25% of the flux of the point source to be lost from the coadd image!
		The physical basis for this error is that due to undersampling, pixels with zero flux are averaged into the final PSF of the coadded image.
	spider.ipac.caltech.edu /staff/tchester/2mass/facts/undersampling_flux_underestimation.html (1223 words)

	In the article “Turning Nyquist upside down by undersampling”, are reported the following two formulae
		These are the fundamental formulae for undersampling (bandpass sampling, subsampling, downsampling, sub-Nyquist, super-Nyquist, harmonic sampling) even if I did not use any of these terms in my original report [3] because, at that time, I was not concerned about any specific terminology for this kind of operation.
		Moreover, when the frequency bands of the three antennas are separated in such a manner to not interfere each other and to satisfy, in the whole, the requirements for undersampling, the three received signals are mixed together [10] before sampling, reducing at one third the required sampling rate.
		After having undersampled the signal of each scan, we partition them in a number of segments and for each segment we apply the FFT to extract the spectrum shown in Fig.6.
	spazioscuola.altervista.org /UndersamplingAR/UndersamplingARnv.htm (2521 words)

	Detection of Shack-Hartmann Spots (1)
		The purpose of this technical report is to examine the dual impact of undersampling and background noise on the estimate of the x-y centroid of a Shack-Hartmann spot.
		Five levels of undersampling are used, with progressively higher degrees of quantization (29x29, 17x17, 12x12, 9x9, and 7x7 pixels).
		Each variant of undersampling is repeated at all five additive noise levels, for a total of twenty five simulations.
	research.opt.indiana.edu /Library/olm/dotsampling/dotSampler.html (171 words)

	Substepping and its Application to HST Imaging
		For the HST, undersampling means that the size of the pixel in a camera is larger than the critical value determined by the optics of the telescope, and aliasing takes place.
		Undersampling with WFPC2 occurs because of the large pixel size of the CCD chips.
		The undersampling problem with FOS arises from the large size of the diodes used for data acquisition.
	www.adass.org /adass/proceedings/adass97/wun.html (1099 words)

	7.6 Dithering with WFPC2 (Site not responding. Last check: 2007-10-16)
		One strategy that can be used to minimize the effects of undersampling and to reduce the effects of hot pixels and imperfect flat fields is to dither, that is, to offset the telescope by either integer-pixel or sub-pixel steps.
		Undersampling: Individual images taken with sub-pixel offsets can be combined to form an image with higher spatial resolution than that of the original images.
		It is particularly difficult to correct stellar images for cosmic rays, due to the undersampling of the WFPC2 (particularly in the WF images).
	www.stsci.edu:8083 /instruments/wfpc2/Wfpc2_hand5/ch7_strategy7.html (1460 words)

	In the article “Turning Nyquist upside down by undersampling”, are reported the following two formulae
		I was surprised by that because I have been using the undersampling technique since the beginning of the eighties and even wrote a report (Angelo Ricotta, “Some remarks on the sampling and processing of SODAR data”, Technical Report, IFA-CNR, July 1983) where I gave two simple and practical formulae to compute
		In the Ref.3 the undersampling (actually named “bandpass sampling theorem”) is listed among the problems left to the reader and the formula shown refers only to the lowest bound of the sampling frequency, but one of the terms may suggest, to an attentive reader, the way to compute
		Then I think of my small contribution to the undersampling as simplifying and clarifying the topic for the practical use, but it should not be underevaluated or ignored or, worse, usurped.
	spazioscuola.altervista.org /UndersamplingAR/UndersamplingAR.htm (994 words)

	Frequency Undersampling in Coulomb-Counting: Measuring Current Flow in Battery Applications - Maxim/Dallas
		While not meeting the strict definition of the intentional undersampling technique used for frequency down- conversion and waveform reconstruction, uncorrelated undersampling near the signal frequency accurately captures the average value (DC content) of a repetitive signal.
		While timebase errors are important for undersampling techniques applied to both waveform reconstruction and coulomb counting, waveform recovery using intentional undersampling is sensitive to distortion due to sample-to-sample jitter.
		The concept of uncorrelated undersampling near the signal frequency was shown qualitatively as an accurate method to capture DC content of a repetitive signal.
	www.maxim-ic.com /appnotes.cfm/appnote_number/1798 (2432 words)

	STIS Instrument Handbook for Cycle 13 (Site not responding. Last check: 2007-10-16)
		Undersampling of images: Individual images taken with subpixel offsets can be combined to form an image with higher spatial resolution than that of the original images.
		Undersampling of spectral images: The spatial undersampling of compact sources in spectral images becomes apparent after the images are rectified.
		In case the region of interest is at or near a sharp peak in the surface brightness distribution, one should consider dithering by a non-integer number of pixels to deal with the undulation issue due to undersampling (cf.
	www.stsci.edu:8082 /hst/stis/documents/handbooks/currentIHB/c11_datataking4.html (2121 words)

	Subtracting models from unsaturated WFPC2 PSFs
		The undersampling of the WPFC2 cameras results in the observed PSF being highly dependent on positioning at the subpixel level.
		A subsampled model should be generated, shifted to match the proper positioning of the observed PSF, and then rebinned to detector sampling.
		Because of undersampling, interpolating an observed PSF to match the position of another doesn't work well.
	www.stsci.edu /software/tinytim/subpsf.html (413 words)

	Undersampling in Comp.DSP
		I was planning to use undersampling (Fs=192kHz) to fold this signal to 48kHz in...
		If you undersample, then in fact you do need an analog hold circuit that is fast enough for the total carrier frequency (2G) - but your ADC need only be fast enough for the band you are in...
		Hi, I am new to the whole DSP thing (very new) and have a question regarding the use of undersampling and quadrature mixing to demodulate a signal in a given range.
	www.dsprelated.com /comp.dsp/keyword/Undersampling.php (955 words)

	Nyquist Sampling in Digital Microscopy
		The loss of image detail is proportional to the undersampling, and as such the quality of the subsequent image analysis.
		The Nyquist sampling theorem states that, when converting from an analog signal (sound or a microscope image) to digital, the sampling frequency must be greater than twice the highest frequency of the input signal in order to be able to reconstruct the original perfectly from the sampled version.
		Undersampling (magnification too low) will result in loss of detail in the digital image and will have a negative influence on the quality of the image analysis.
	ourworld.compuserve.com /homepages/pvosta/pcrnyq.htm (391 words)

	Motion Blur
		Our undersampling scheme applies 1, 3, 6, 15, 45, 153, etc. shading samples to each triangle, based on how many 4x subdivisions we wish to apply.
		The undersampling technique we've described was used with great success on the Cats and Dogs job.
		The image quality with undersampling is not compromised at all, and the speedup is substantial.
	www.rhythm.com /~ivan/mb.html (726 words)

	The alias theorems: practical undersampling for expert engineers - 6/21/2001 - EDN (Site not responding. Last check: 2007-10-16)
		This ability is an example of correlated undersampling, because a trigger exists, and the sample point moves deterministically through the waveform.
		Positive undersampling of a time-domain signal occurs when the repetition rate of the signal is slightly higher than the nearest integer multiple of the decimated (effective) sample rate.
		Alias theorem B is, therefore, a generalization of Alias theorem A. Alias theorem 1: For an ideal repetitive time-domain alias, time-related features on the alias, such as rise time, scale by the ratio of the repetition frequency of the alias to the repetition frequency of the original waveform.
	www.edn.com /article/CA90388.html?1=1 (3650 words)

	University of Bradford/School of Life Sciences/Vision Sciences/CorticalUndersamplingInHumanAmblyopia
		In preliminary investigations, we have tested a hypothesis that the visual deficits experienced by subjects with amblyopia have their origins in the loss of functional neural density at the level of the visual cortex.
		Together with our collaborators from Indiana University, we have (1) developed a computational model of cortical undersampling (2) examined the consequences of sample deletion when a sinusoidal grating is input; (3) collected detailed drawings from a large number of amblyopes documenting their perception of sinusoidal gratings.
		Test hypothesis that neural undersampling within the hypercolumn area of cortical area V1 will lead to spatial misperceptions similar in nature to those observed by human amblyopes.
	www.brad.ac.uk /acad/lifesci/optometry/index.php?n=Projects.CorticalUndersamplingInHumanAmblyopia (323 words)

	DV - Columns - Aliasing In Detail
		With the advent of low-cost, undersampled HD camcorders, it's time to revisit the topic and reconsider how we measure camera resolution.
		Undersampling and its companion artifact, aliasing, aren't just a problem in HD, but the demands of packing too many pixels into too tiny of a chip make them more common in small HD cameras.
		Aliasing is an artifact of undersampling, and we'll get into much more detail about it in a minute.
	www.dv.com /columns/columns_item.php?category=Archive&articleId=187202363 (1452 words)

	Technical Report # 121 (Site not responding. Last check: 2007-10-16)
		In Section 1 of this chapter we review the existing models of peripheral vision, most of which are based on the appealing conception that peripheral vision is just a spatially scaled version of central vision.
		The results show that, although the optical system of the eye is the dominant factor limiting central vision, spatial undersampling by the optic nerve cells of the retina limits resolution in the periphery.
		Neural undersampling of the retinal image leads to perceptual aliasing and spurious detection of patterns up to an order of magnitude finer than the Nyquist limit.
	www.cogs.indiana.edu /publications/techreps1994/121.html (235 words)

	Amazon.com: undersampling: Books (Site not responding. Last check: 2007-10-16)
		An auditory method of demonstrating aliasing with an analysis of the results of undersampling a fixed frequency sinusoidal signal by Ronald W Parker (Unknown Binding - 1988)
		ADC degradation levels at and beyond B. By contrast, with undersampling (RS = 2B,,), the ADC degrada- tions for wideband Gaussian...
		Undersampling generates artifacts caused by the sampling frequency or process (i.
	www.amazon.com /s?ie=UTF8&rh=i:books,k:undersampling&page=1 (1168 words)

	CCD University
		A good rule of thumb to avoid undersampling is to divide your seeing in half and choose a pixel size that provides that amount of sky coverage.
		Under excellent seeing conditions, a camera with 24µ pixels on a telescope of 2000 mm focal length will produce images that are very close to being undersampled.
		Consider the case, for a moment, where all the light of a star was contained in a single pixel.
	www.ccd.com /ccd113.html (962 words)

	slide 5 (Site not responding. Last check: 2007-10-16)
		For a two-dimensional signal such as the retinal image, the penalty of undersampling is that the neural image may misrepresent both the spatial frequency and the orientation of the stimulus pattern, and if the pattern is moving then the direction of motion may also be misrepresented.
		In the cartoon at the right I've coded the strength of individual neural responses by the luminance of the circles at each sample point and, as you can see, the neural image indicates the presence of an obliquely oriented pattern with a lower spatial frequency than is actually present on the retina.
		This misrepresentation of the spatial features of the stimulus caused by undersampling is called 'aliasing' and so, according to this 'Sampling Theory of Visual Resolution', the limit to visual resolution is marked by the onset of aliasing.
	www.opt.indiana.edu /people/faculty/thibos/NAPS/slide5.html (202 words)

	Sampling and Reconstruction of Periodic Signals \| DSP-FPGA.com
		However, for signals which do not extend to dc, the minimum required sampling rate is a function of the bandwidth of the signal as well as its position in the frequency spectrum.
		First, using the criteria of sampling at a frequency that is twice the signal bandwidth instead of twice the highest signal frequency, assumes that the input analog signal is indeed limited to that bandwidth.
		Third, it is important to remember, that even though undersampling implies a lower sampling rate, the input bandwidth of the analog waveform must still be accommodated.
	www.dsp-fpga.com /articles/neagoe_and_fugerer (3339 words)

	Digital Photography Essentials #002 @Digital Outback Photo
		Once the minimum spatial resolution capability of the optical system is determined, the consequences of spatial oversampling or undersampling of the projected features must be considered.
		This kind of incorrect data resulting from undersampling is called "spatial aliasing".
		In its most obvious form, spatial aliasing causes the Moire patterns that form when a digital camera images a subject whose features project onto the image plane at a spacing close to the pixel pitch.
	www.outbackphoto.com /dp_essentials/dp_essentials_02/essay.html (950 words)

	The Nyquist Sampling Rate
		Actually, you get samples that are consistent with a lower frequency sine wave, and if you had that data in a file (just the sampled points, the large dots) you would have no way of knowing that the signal had not been sampled correctly (i.e.
		that whoever generated the data had undersampled.) and you would be justified in thinking that the apparent low frequency sine wave (see the large dots) was the actual signal recorded.
		The consequences of undersampling are that a frequency higher than the Nyquist limit is aliased into another signal with a frequency within the Nyquist limit.
	www.facstaff.bucknell.edu /mastascu/eLessonsHTML/Signal/SignalNoteNyquistSampling.htm (851 words)

	Aliasing and Sampling at Frequencies Above the Nyquist Frequency- Developer Zone - National Instruments
		Undersampling is essentially sampling too slowly, or sampling at a rate below the Nyquist frequency for a particular signal of interest.
		Undersampling leads to aliasing and the original signal cannot be properly reconstructed.
		However, undersampling also requires less memory, so it may be useful in certain applications, see "Undersampling to Obtain Frequencies Above the Nyquist Frequency" below.
	zone.ni.com /devzone/cda/tut/p/id/3000 (1131 words)

	How to use undersampling \| Automotive DesignLine
		Undersampling can be an extremely valuable tool, but care must be taken to ensure good performance
		If so, this can be a big benefit compared to baseband sampling, where we would otherwise need to use an A/D converter with a sampling rate of about 150 MHz.
		In order to apply undersampling successfully, a careful frequency plan must be developed.
	www.automotivedesignline.com /196702493?cid=RSSfeed_automotivedesignline_autodlRSS (573 words)

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