About Me

Harish Mukundan. Originally from Thrissur, Kerala,   India. Currently resides at Cambridge, Massachusetts,   United States. 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

See Also

• Personal Website

My Personal Stuff

Example

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

${\displaystyle f(x)=\int _{x-1}^{x+1-\mu }s(\tau )\,d\tau \ =\int _{-1}^{+1}s(x+\tau )\,d\tau \,}$

${\displaystyle f_{s}\approx {\frac {U}{D}},}$

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

${\displaystyle f(t-1)=\int _{-2}^{0}s(t+\tau )\,d\tau =\int _{0}^{+2}s(t-\tau )\,d\tau \,}$

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