One problem that any rendering system must deal with, no matter which approach it takes, is the sampling problem.

Shannon used Nyquist's approach when he proved the sampling theorem in 1948, but Nyquist did not work on sampling per se.

Cameras that use a beam-splitter single-shot 3CCD approach, three-filter multi-shot approach, Color co-site sampling or Foveon X3 sensor do not use anti-aliasing filters, nor demosaicing.

Eric R. Bittner's group at the University of Houston has advanced a statistical variant of this approach that uses Bayesian sampling technique to sample the quantum density and compute the quantum potential on a structureless mesh of points.

An alternative approach that often works better in such situations, known as Gibbs sampling, involves choosing a new sample for each dimension separately from the others, rather than choosing a sample for all dimensions at once.

However, due to the need for frequent blood sampling, this approach has been largely replaced by breath testing.

A novel approach, recently cleared by the US FDA, is sampling cortisol in saliva over 24 hours, which may be equally sensitive, as late night levels of salivary cortisol are high in Cushingoid patients.

According to music writers, the genre's works are mostly album-oriented and distinguished by its musicianship and production, incorporating " organic " elements of classic soul music with the use of live instrumentation, in contrast to the more single-oriented, hip hop-based, and producer-driven sampling approach of contemporary R & B.

Although there were many individuals trying to lead United States industries towards a more comprehensive approach to quality, the U. S. continued to apply the Quality Control ( QC ) concepts of inspection and sampling to remove defective product from production lines, essentially ignoring advances in QA for decades.

The adaptive sampling Markov state model approach significantly increases the efficiency of simulation as it avoids computation inside the local energy minimum itself, and is amenable to distributed computing ( including on GPUGRID ) as it allows for the statistical aggregation of short, independent simulation trajectories.

However, the tendency of Pacific White-sided Dolphins to approach boats complicates precise estimates via sampling.

In high dimensions, it is necessary to use a different approach, typically a Markov chain Monte Carlo method such as Metropolis sampling or Gibbs sampling.

Produced by music legend Ian Molly Meldrum, and written by singing star Johnny Young, the single encompassed high production values and a psychedelic approach in its use of instruments such as a sitar, sampling of a children's choir, and its 6-minute running time ( unusually long for the time ).

This article takes a generalized abstract mathematical approach to signal sampling and reconstruction.

However if a CD ( the CD Red Book standard is 44. 1 kHz 16 bit ) is to be made from a recording, then doing the initial recording using a sampling rate of 44. 1 kHz is obviously one approach.

Whereas a confidence interval's size is entirely due to sampling error, and will approach a zero-width interval at the true population parameter as sample size increases, a tolerance interval's size is due partly to sampling error and partly to actual variance in the population, and will approach the population's probability interval as sample size increases.

The approach is strongly related to density networks which use importance sampling and a multi-layer perceptron to form a non-linear latent variable model.

In the former purpose ( that of approximating a posterior probability ), variational Bayes is an alternative to Monte Carlo sampling methods — particularly, Markov chain Monte Carlo methods such as Gibbs sampling — for taking a fully Bayesian approach to statistical inference over complex distributions that are difficult to directly evaluate or sample from.

A sufficient condition for recovering s ( t ) ( and therefore S ( ƒ )) from just these samples is that the non-zero portion of s ( t ) be confined to a known interval of duration P, which is the frequency domain dual of the Nyquist – Shannon sampling theorem.

It can therefore be played using a compatible player, although sometimes one must force a different sampling rate to hear it correctly.

The required phase delay D for a given fundamental frequency F < sub > 0 </ sub > is therefore calculated according to D = F < sub > s </ sub >/ F < sub > 0 </ sub > where F < sub > s </ sub > is the sampling frequency.

When selecting a subject for a case study, researchers will therefore use information-oriented sampling, as opposed to random sampling.

On the other hand, Sinc functions and Airy functions-which are not only the point spread functions of rectangular and circular apertures, respectively, but are also cardinal functions commonly used for functional decomposition in interpolation / sampling theory 1990-do correspond to converging or diverging spherical waves, and therefore could potentially be implemented as a whole new functional decomposition of the object plane function, thereby leading to another point of view similar in nature to Fourier optics.

We may therefore speak of sampling strategies or data analysis strategies.

However, the Provincial government's engineering consultants advised that sampling of the water behind the 2200 plug before removal of the sampling valve, showed the water that the chemistry behind the plug had become more neutral with respect to sulphate levels and pH since construction of the plug, and therefore the simple concrete plug could last much longer than 60-70 years.

Thus, when sampling to avoid aliasing on a high-frequency axis, the other texture axes will be similarly downsampled and therefore potentially blurred.

To record a bandwidth of 250 kHz therefore requires a sampling frequency in excess of 500 kHz.

The direct measurements of arterial oxygen tension only offer a static glimpse, and repeated measurements from invasive procedures such as sampling arterial blood for oxygen will disturb the patient ’ s sleep ; therefore, noninvasive methods are preferred such as pulse oximetry, transcutaneous oxygen monitoring, transcutaneous carbon dioxide, and pulse transit time.

The fact that the 01 / W's samples were recorded at a slightly lower sampling rate, therefore reducing sample size, plus the advantage of having more ROM memory to actually store more of each sample meant that more of the nuance of the samples was heard.

Only a small percentage of the US population is being surveyed, and therefore the data are subject to sampling errors.

In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population are less likely to be included than others.

One of hip-hop's first superproducers, Marley Marl was an early innovator in the art of sampling, developing new techniques that resulted in some of the sharpest beats and hooks in rap's Golden Age.

Other arrangements of pixels are possible, with some sampling patterns even changing the shape ( or kernel ) of each pixel across the image.

It can also be achieved by sampling ( e. g. buying stocks of each kind and sector in the index but not necessarily some of each individual stock ), and there are sophisticated versions of sampling ( e. g. those that seek to buy those particular shares that have the best chance of good performance ).

For the most part, statistical inference makes propositions about populations, using data drawn from the population of interest via some form of random sampling.

For some target populations this process may be easy, for example, sampling the employees of a company by using payroll list.

The continuous signal varies over time ( or space in a digitized image, or another independent variable in some other application ) and the sampling process is performed by measuring the continuous signal's value every T units of time ( or space ), which is called the sampling interval.

# Increase the sampling rate, to above twice some or all of the frequencies that are aliasing.

WCC member churches include most of the Orthodox Churches ; numerous Protestant churches, including the Anglican Communion, some Baptists, many Lutheran, Methodist, and Presbyterian and other Reformed, a sampling of united and independent churches, and some Pentecostal churches ; and some Old Catholic churches.

The early view that " black " and " white " mantas were different species was also discounted through a study of mitochondrial DNA in 2001, which however did reveal some general geographic patterns: Based on limited sampling, west Pacific mantas formed one clade, east Pacific and some Caribbean mantas formed a second clade, and finally the remaining Caribbean mantas formed a third clade.

The wavelets forming a continuous wavelet transform ( CWT ) are subject to the uncertainty principle of Fourier analysis respective sampling theory: Given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event.

In many developed nations there are now emissions regulations which have dramatically decreased the emissions and thus alleviated some concerns, although the lack of continuous sampling of dioxin emissions causes concern about the understatement of emissions.

In some cases, scanning is accomplished by moving the sensor e. g. when using Color co-site sampling or rotate the whole camera ; a digital rotating line camera offers images of very high total resolution.

Various algorithms can be used to choose these individual samples, depending on the exact form of the multivariate distribution: some possibilities are adaptive rejection sampling, a one-dimensional Metropolis – Hastings step, or slice sampling.

The product of two " beat tracks " of slightly different speeds overlaid, producing an audible moiré pattern ; if the beats of one track correspond to where in space a black dot or line exists and the beats of the other track correspond to the points in space where a camera is sampling light, because the frequencies are not exactly the same and aligned perfectly together, beats ( or samples ) will align closely at some moments in time and far apart at other times.

In some cases it is desirable to have a sampling frequency more than twice the desired system bandwidth so that a steep digital filter and a less steep analog anti-aliasing filter can be used in exchange for a steep analog anti-aliasing filter.

Although cluster sampling and stratified sampling bear some superficial similarities, they are substantially different.