User:Harishmukundan

About Me
Harish Mukundan. Originally from Thrissur, Kerala, 🇮🇳. Currently resides at Cambridge, Massachusetts, 🇺🇸. Active since November, 2005.

Articles Created

 * St. Thomas College, Thrissur
 * Ocean Engineering & Ocean Science
 * List of commercial airlines in India
 * Deshpande Center for Technological Innovation
 * Vortex Induced Vibration

Articles Significantly Modified

 * Thrissur
 * IIT Madras
 * Arts and entertainment in India
 * Sand festival

Example
The following definition is a moving (or "sliding") average of input data $$s(x)\,$$. A constant factor of 1/2 is omitted for simplicity:


 * $$f(x) = \int_{x-1}^{x+1-\mu} s(\tau)\, d\tau\ = \int_{-1}^{+1} s(x + \tau) \,d\tau\,$$


 * $$f_s \approx \frac{U}{D},$$

where x could represent a spatial coordinate, as in image processing. But if $$x\,$$ represents time $$(t)\,$$, then a moving average defined that way is non-causal (also called non-realizable), because $$f(t)\,$$ depends on future inputs, such as $$s(t+1)\,$$. A realizable output is


 * $$f(t-1) = \int_{-2}^{0} s(t + \tau)\, d\tau = \int_{0}^{+2} s(t - \tau) \, d\tau\,$$

which is a delayed version of the non-realizable output.