Difference between revisions of "Lmd eta three pion hlu"
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==Form of side-band subtraction histograms== | ==Form of side-band subtraction histograms== | ||
Question: Suppose there is an original function (e.g. Gaussian), what is the form of the function after bin-by-bin side-band subtraction | Question: Suppose there is an original function (e.g. Gaussian), what is the form of the function after bin-by-bin side-band subtraction | ||
| − | Answer: Suppose the function is y=f(x). The side-band subtraction makes a new function: | + | |
| + | Answer: Suppose the function is y=f(x). The side-band subtraction makes a new function:<math>y\prime=g(x)=f(x)-\frac{(f(x+\Delta x)+f(x-\Delta x)}{2}=\frac{1}{2}(f(x)-f(x-\Delta x))-\frac{1}{2}(f(x+\Delta x)-f(x))=\frac{\Delta x}{2}f\prime(x)-\frac{\Delta x}{2}f\prime(x+\Delta x)=\frac{(\Delta x)^2}{2}f\prime\prime(x)</math> | ||
| + | |||
| + | ===Test of the formula=== | ||
==reference== | ==reference== | ||
Revision as of 21:02, 10 March 2014
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Form of side-band subtraction histograms
Question: Suppose there is an original function (e.g. Gaussian), what is the form of the function after bin-by-bin side-band subtraction
Answer: Suppose the function is y=f(x). The side-band subtraction makes a new function:<math>y\prime=g(x)=f(x)-\frac{(f(x+\Delta x)+f(x-\Delta x)}{2}=\frac{1}{2}(f(x)-f(x-\Delta x))-\frac{1}{2}(f(x+\Delta x)-f(x))=\frac{\Delta x}{2}f\prime(x)-\frac{\Delta x}{2}f\prime(x+\Delta x)=\frac{(\Delta x)^2}{2}f\prime\prime(x)</math>
