User:Harishmukundan

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Harish Mukundan. Originally from Thrissur, Kerala, Flag of India India. Currently resides at Cambridge, Massachusetts, Flag of the United States United States. Active since November, 2005.


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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.