Longest common subsequence problem: Difference between revisions

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[[Image:KaiserWindow.jpg|right]]
Your Basal Metabolic rate (BMR) is the number of calories the body burns a day while inside a resting state. The Basal Metabolic Rate is a function of the Gender, Age, Height, plus Weight. This number is essentially the number of calories which you would burn should you did nothing yet sit on the sofa and watch TV all day long. Generally speaking, If you are a Male, a BMR is higher than a Female's BMR. Also, being young, heavier, and/or taller usually heighten the BMR.<br><br>There are many sites that create it easy to find out how countless calories we require for fat maintenance plus fat reduction. Just type [http://safedietplansforwomen.com/bmr-calculator bmr calculator] into a search engine plus follow the procedures they provide you. BMR stands for basal metabolic rate, plus acquiring this amount will enable give we an idea of how countless calories you need to consume for your particular goals. You'll be asked to answer several questions regarding the activity level plus possibly even the degree of weight reduction we wish to achieve. Some BMR calculators usually go thus far as to offer the amounts of proteins, carbohydrates plus fats you should consume also. They're a very useful tool!<br><br>The basal metabolic rate (BMR)Your basal metabolic rate is significant whenever planning a weight loss program. It shows the rate your body burns calories really for standard metabolic functions, i.e. how various calories would you burn for a day should you only lie inside bed. "Lying in bed" isn't surprisingly exact naturally, considering should you are thinking or having conversation whilst in bed, a body can nevertheless burn more calories than your BMR. The BMR shows merely the minimum calories necessary to stay alive.<br><br>Horsegram is powdered to a nice consistency. Heat sour buttermilk plus add 100 gm of horsegram powder to this and create a consistent paste. Apply this paste onto fat deposits on the body plus massage vigorously in upward strokes. Horsegram is known to minimize body fat really effectively.Take hot water shower after half an hr. Use 'eladhi choornam' rather of soap. Add a limited drops of water for this choornam plus prepare a thick paste plus use it for bathing purposes.<br><br>Same goes to our body. Do we understand why certain persons eat so little yet not seeing any encouraging fat reduction results? Each 1 of us has our own power indicator, the bmr which is the amount of calories required by our body to let us have the vitality to work daily activities like strolling, doing home chores, functioning, driving plus etc. BMR also based found on the individual person's age, muscle mass, physic rating, body fat %, visceral fat and body water %.<br><br>The BMI Calculator or BMI is a practical tool, but, it's based on fat and refuses to measure fat vs muscle. There may be a amount of individuals whose BMI is actually ok, yet have still have too much fat due to a loss of muscle when you reach this age group. So, one suggested idea is to consider a waist to cool ratio. Measuring the waistline initially, as a guide ladies ought to be 32inches (80cm) or less and guys could be 37inches (94cm) or less. Anything over means you're at a high risk of diabetes plus heart disease. Now measure a hips plus divide your waist measuring by a hip measuring. Guys you should be no high than 0.9, women no high than 0.8.<br><br>So, in the event you are 40-year-old woman whom is 55 and 150 lb, plus we get light exercise, you require 1,959 calories to maintain a weight. To lose a pound a week, we want to eat about 1,460 calories a day. If thats too difficult (and it happens to be very low), try upping a exercise. Then youll reach eat 1,700 calories a day.
The '''Kaiser window''', also known as the '''Kaiser-Bessel window''', was developed by James Kaiser at [[Bell Laboratories]]. It is a one-parameter family of [[window function]]s used for [[digital signal processing]], and is defined by the formula
,<ref name="f.harris">
{{cite journal
  | doi = 10.1109/PROC.1978.10837
  | last = Harris
  | first = Fredric j.
  | coauthors =
  | title = On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform
  | journal = Proceedings of the IEEE
  | volume = 66
  | issue = 1
  | pages = 73–74
  |date=Jan 1978
  | url=http://web.mit.edu/xiphmont/Public/windows.pdf}} Article on FFT windows which introduced many of the key metrics used to compare windows.</ref><ref>{{cite journal|last=Kaiser|first=James F.|coauthors=Ronald W. Schafer|title=On the Use of the I0-Sinh Window for Spectrum Analysis|journal=IEEE Transactions on Acoustics, Speech and Signal Processing|date=February 1980|volume=ASSP-28|issue=1|pages=105–107}}</ref>''':'''
:<math>
 
w[n] =
 
\left\{
\begin{matrix}
 
\frac{I_0\left(\pi \alpha \sqrt{1 - \left(\frac{2n}{N-1}-1\right)^2}\right)} {I_0(\pi \alpha)},
& 0 \leq n \leq N-1 \\ \\
 
0 & \mbox{otherwise}, \\
 
\end{matrix}
\right.
</math>
 
where:
* ''N'' is the length of the sequence.
* ''I''<sub>0</sub> is the zeroth order [[Modified Bessel function]] of the first kind.
* ''α'' is an arbitrary, non-negative real number that determines the shape of the window. In the frequency domain, it determines the trade-off between main-lobe width and side lobe level, which is a central decision in window design.
 
When ''N'' is an odd number, the peak value of the window is &nbsp;<math>\scriptstyle w[(N-1)/2] = 1,</math>&nbsp; and when ''N'' is even, the peak values are &nbsp;<math>\scriptstyle w[N/2-1]\ =\ w[N/2]\ <\ 1.</math>
 
==Fourier transform==
Underlying the discrete sequence is this continuous-time function and its Fourier transform''':'''
 
:<math>\underbrace{\frac{I_0\left(\pi \alpha \sqrt{1 - \left(\frac{2t}{(N-1)T}\right)^2}\right)} {I_0(\pi \alpha)}}_{w_0(t)}
\quad \stackrel{\mathcal{F}}{\Longleftrightarrow}\quad
\underbrace{\frac{(N-1)T\cdot\sinh\left(\pi \sqrt{\alpha^2-\left((N-1)T\cdot f\right)^2}\right)}{I_0(\pi \alpha)\cdot\pi \sqrt{\alpha^2-\left((N-1)T\cdot f\right)^2}}}_{W_0(f)}.
</math>
 
[[Image:Kaiser-Window-Spectra.jpg|right|thumb|452px|Fourier transforms of Kaiser windows for typical values of parameter α]]
The maximum value of ''w''<sub>''0''</sub>(''t'') is ''w''<sub>''0''</sub>(0)&nbsp;=&nbsp;1.&nbsp; The ''w''[n] sequence defined above are the samples of''':'''
 
:<math>w_0\left(t-\tfrac{(N-1)T}{2}\right)\cdot \operatorname{rect}\left(\tfrac{t-(N-1)T/2}{NT}\right),</math>&nbsp; &nbsp; sampled at intervals of '''T''',
 
and where rect() is the [[rectangle function]].&nbsp; The first null after the main lobe of ''W''<sub>''0''</sub>(''f'') occurs at''':'''
 
:<math>f = \frac{\sqrt{1+\alpha^2}}{NT},</math>&nbsp; &nbsp; &nbsp; which in units of DFT bins is just &nbsp;<math>\scriptstyle \sqrt{1+\alpha^2}.</math><ref>{{cite doi|10.1109/TASSP.1980.1163349}}</ref>
 
''α'' controls the tradeoff between main-lobe width and side-lobe area.&nbsp; As ''α'' increases, the main lobe of ''W''<sub>''0''</sub>(''f'') increases in width, and the side lobes decrease in amplitude, as illustrated in the figure at right.&nbsp; ''α''&nbsp;=&nbsp;0 corresponds to a rectangular window. For large ''α'', the shape of the Kaiser window (in both time and frequency domain) tends to a [[Gaussian function|Gaussian]] curve.&nbsp; The Kaiser window is nearly optimal in the sense of its peak's concentration around frequency ''0'' (Oppenheim ''et al.'', 1999).
 
==Kaiser-Bessel derived (KBD) window==
[[File:Kbd-window.jpg|right]]
A related window function is the '''Kaiser-Bessel derived (KBD)''' window, which is designed to be suitable for use with the [[modified discrete cosine transform]] (MDCT). The KBD window function is defined in terms of the Kaiser window of length ''M''+1, by the formula''':'''
:<math>
d_n =
 
\left\{\begin{matrix}
 
\sqrt{\frac{\sum_{i=0}^{n} w[i]} {\sum_{i=0}^M w[i]}}
& \mbox{if } 0 \leq n < M \\ \\
 
\sqrt{\frac{\sum_{i=0}^{2M-1-n} w[i]} {\sum_{i=0}^M w[i]}}
& \mbox{if } M \leq n < 2M \\ \\
 
0 & \mbox{otherwise}. \\
 
\end{matrix}
\right.
</math>
 
This defines a window of length 2''M'', where by construction ''d''<sub>''n''</sub> satisfies the Princen-Bradley condition for the MDCT (using the fact that ''w''<sub>''M''−''n''</sub> = ''w''<sub>''n''</sub>): ''d''<sub>''n''</sub><sup>2</sup>&nbsp;+&nbsp;''d''<sub>''n''&nbsp;+&nbsp;''M''</sub><sup>2</sup>&nbsp;=&nbsp;1 (interpreting ''n'' and ''n''&nbsp;+&nbsp;''M'' [[modular arithmetic|modulo]] 2''M''). The KBD window is also symmetric in the proper manner for the MDCT: ''d''<sub>''n''</sub>&nbsp;=&nbsp;''d''<sub>2''M''−1−''n''</sub>.
 
===Applications===
The KBD window is used in the [[Advanced Audio Coding]] digital audio format.
 
==Notes==
<references />
 
==References==
* {{cite book | author=Oppenheim, A. V.; Schafer, R. W.; and Buck J. R. | title=Discrete-time signal processing | location=Upper Saddle River, N.J. | publisher=Prentice Hall | year=1999 | isbn=0-13-754920-2}}
* Kaiser, J. F. (1966). Digital Filters. In Kuo, F. F. and Kaiser, J. F. (Eds.), ''System Analysis by Digital Computer'', chap. 7. New York, Wiley.
* Craig Sapp, [http://ccrma.stanford.edu/courses/422/projects/kbd/ Kaiser-Bessel Derived Window Examples and C-language Implementation], ''Music 422 / EE 367C: Perceptual Audio Coding'' (Stanford University course page, 2001).
 
==External links==
 
[[Category:Signal processing]]

Latest revision as of 06:30, 18 November 2014

Your Basal Metabolic rate (BMR) is the number of calories the body burns a day while inside a resting state. The Basal Metabolic Rate is a function of the Gender, Age, Height, plus Weight. This number is essentially the number of calories which you would burn should you did nothing yet sit on the sofa and watch TV all day long. Generally speaking, If you are a Male, a BMR is higher than a Female's BMR. Also, being young, heavier, and/or taller usually heighten the BMR.

There are many sites that create it easy to find out how countless calories we require for fat maintenance plus fat reduction. Just type bmr calculator into a search engine plus follow the procedures they provide you. BMR stands for basal metabolic rate, plus acquiring this amount will enable give we an idea of how countless calories you need to consume for your particular goals. You'll be asked to answer several questions regarding the activity level plus possibly even the degree of weight reduction we wish to achieve. Some BMR calculators usually go thus far as to offer the amounts of proteins, carbohydrates plus fats you should consume also. They're a very useful tool!

The basal metabolic rate (BMR)Your basal metabolic rate is significant whenever planning a weight loss program. It shows the rate your body burns calories really for standard metabolic functions, i.e. how various calories would you burn for a day should you only lie inside bed. "Lying in bed" isn't surprisingly exact naturally, considering should you are thinking or having conversation whilst in bed, a body can nevertheless burn more calories than your BMR. The BMR shows merely the minimum calories necessary to stay alive.

Horsegram is powdered to a nice consistency. Heat sour buttermilk plus add 100 gm of horsegram powder to this and create a consistent paste. Apply this paste onto fat deposits on the body plus massage vigorously in upward strokes. Horsegram is known to minimize body fat really effectively.Take hot water shower after half an hr. Use 'eladhi choornam' rather of soap. Add a limited drops of water for this choornam plus prepare a thick paste plus use it for bathing purposes.

Same goes to our body. Do we understand why certain persons eat so little yet not seeing any encouraging fat reduction results? Each 1 of us has our own power indicator, the bmr which is the amount of calories required by our body to let us have the vitality to work daily activities like strolling, doing home chores, functioning, driving plus etc. BMR also based found on the individual person's age, muscle mass, physic rating, body fat %, visceral fat and body water %.

The BMI Calculator or BMI is a practical tool, but, it's based on fat and refuses to measure fat vs muscle. There may be a amount of individuals whose BMI is actually ok, yet have still have too much fat due to a loss of muscle when you reach this age group. So, one suggested idea is to consider a waist to cool ratio. Measuring the waistline initially, as a guide ladies ought to be 32inches (80cm) or less and guys could be 37inches (94cm) or less. Anything over means you're at a high risk of diabetes plus heart disease. Now measure a hips plus divide your waist measuring by a hip measuring. Guys you should be no high than 0.9, women no high than 0.8.

So, in the event you are 40-year-old woman whom is 55 and 150 lb, plus we get light exercise, you require 1,959 calories to maintain a weight. To lose a pound a week, we want to eat about 1,460 calories a day. If thats too difficult (and it happens to be very low), try upping a exercise. Then youll reach eat 1,700 calories a day.

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