Register allocation: Difference between revisions

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→‎Spilling: verb spill but operation is gerund spilling; section confuses logical registers, hardware registers, and variables; needs a lot more work
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{{merge to|spectral density estimation|date=September 2013}}
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The '''periodogram''' is an estimate of the [[spectral density]] of a signal.  The term was coined by [[Arthur Schuster]] in 1898<ref name="Perry">[http://onlinelibrary.wiley.com/doi/10.1029/TM003i001p00013/pdf Schuster, A., "On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena," ''Terrestrial Magnetism'', 3, 13-41, 1898.] </ref> as in the following quote:<ref>{{cite book | url = http://books.google.com/books?id=v-EOAAAAIAAJ&q=schuster+%22convenient+to+have+a+word+for+some+representation+of+a+variable+quantity%22&dq=schuster+%22convenient+to+have+a+word+for+some+representation+of+a+variable+quantity%22&pgis=1 | title = The Annals of Mathematical Statistics | year = 1972 }}</ref>
 
{{cquote|THE PERIODOGRAM. It is convenient to have a word for some representation of a variable quantity which shall correspond to the 'spectrum' of a luminous radiation. I propose the word periodogram, and define it more particularly in the following way:
Let
:::<math>\frac{T}{2}a = \int_{t_1}^{t_1+T}f(t)\cos(kt)dt</math>
:::<math>\frac{T}{2}b = \int_{t_1}^{t_1+T}f(t)\sin(kt)dt</math>
where ''T'' may for convenience be chosen to be equal to some integer multiple of 
:::<math>\frac{2\pi}{k}</math>,
and plot a curve with <math>{2\pi}/k</math> as [[abscissae]] and
:::<math>r = \sqrt{a^2+b^2}</math>
as [[ordinate]]s; this curve, or, better, the space between this curve and the axis of abscissæ, represents the periodogram of f(t).}}
 
Note that the term ''periodogram'' may also be used to describe the quantity <math>r^2</math>,<ref name="Box">Box, George and Jenkins, Gwilym (1970) ''Time series analysis: Forecasting and control'', San Francisco: Holden-Day.</ref> which is its common meaning in astronomy (as in "the modulus-squared of the [[discrete Fourier transform]] of the time series (with the appropriate normalisation)"<ref name="Vaughan">Simon Vaughan and Philip Uttley (2006), "Detecting X-ray QPOs in active galaxies",Advances in Space Research, Volume 38, Issue 7, pp. 1405-1408</ref>). See Scargle (1982) for a detailed discussion in this context.<ref name="Scargle">Scargle (1982), ''Astrophysical Journal'', Part 1, vol. 263, Dec. 15, 1982, p. 835-853</ref>
 
A '''spectral plot''' refers to a smoothed version of the periodogram.<ref>[http://www.itl.nist.gov/div898/handbook/eda/section3/eda33r.htm Spectral Plot], from the [[NIST]] Engineering Statistics Handbook.</ref><ref>[http://www.itl.nist.gov/div898/software/dataplot/refman1/ch2/spectral.pdf Short explanation] of the relation between the spectral plot and the periodogram.</ref> [[Smoothing]] is performed to reduce the effect of measurement noise.
 
In practice, the periodogram is often computed from a finite-length digital sequence using the [[fast Fourier transform]] (FFT). The raw periodogram is not a good spectral estimate because of [[spectral bias]] and the fact that the variance at a given [[frequency]] does not decrease as the number of samples used in the computation increases.  
 
The spectral bias problem arises from a sharp truncation of the sequence, and can be reduced by first multiplying the finite sequence by a [[window function]] which truncates the sequence gradually rather than abruptly.
 
The variance problem can be reduced by smoothing the periodogram. Various techniques to reduce spectral bias and variance are the subject of [[spectral estimation]].
 
One such technique to solve the variance problems is also known as the ''method of averaged periodograms''<ref name="Engelberg">Engelberg, S. (2008), ''Digital Signal Processing: An Experimental Approach'',  Springer, Chap. 7 p. 56</ref> or as [[Bartlett's method]]. The idea behind it is, to divide the set of N samples into L sets of M samples, compute the [[discrete Fourier transform]] (DFT) of each set, square it to get the power spectral density and compute the average of all of them. This leads to a decrease in the standard deviation as <math> \frac{1}{\sqrt{L}}. </math>
 
== See also ==
 
*[[Fourier transform]]
*[[Least-squares spectral analysis]]
*[[Seasonality]]
*[[Spherical harmonics]]
*[[Welch method]]
 
== References ==
{{reflist}}
 
[[Category:Frequency domain analysis]]
[[Category:Fourier analysis]]

Latest revision as of 09:03, 25 October 2014

Have you been thinking to obtain fine jewellery for yourself? If you'd like to make the most of the deals available on the net? Well, when it comes to shopping jewellery there are many options to choose from. You can go for diamonds, pearls, gold, silver in addition to similar options and combinations. But the majority of of such jewellery comes to the high price which is the reason that they cannot be afforded by all. If you are contemplating buying designer jewellery at low cost then you should go for Thomas Sabo. This brand offers all that you want a reasonable tag.



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December - Blue Topaz: This stone represent those that are living life and obtaining the fun in everything. These person is outgoing, lively and that will laugh in any way types of adversities. You tend to celebrate success, wealth and life.

Lac beads can be discovered in varying shapes pertaining to instance round beads, square beads, heart shaped beads, bell beads, and egg shaped beads females began feeling other unusual shapes. Beaded lac beads with works of mirrors, cut-stones, metal rings, tiny small beads and other accessories give these lac beads a royal take a look. Many jewelries such as earrings, necklaces, bracelets, Pendants can become using lac beads. Certainly making jewelry, these lac beads may possibly used to wear homes. For example, during Christmas these beads very well to decorate Christmas forests. Lac beads are very unique and other from kinds of pills. For people who visit search of wholesale beads, lac beads can result in be a most wonderful choice.

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Routine exposure to humid conditions will possess the jewelry damaged if considerably more plenty of oxygen. To forestall this, really should have all your jewelry safely tucked away in plastic bags or cloth handbags. Take care of total state person jewelry. Don't let them look neglected and in poor cut.

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