In statistics, the moving average is usually defined for discrete data sets. Is there a moving average concept for continuous randomly fast-oscillating functions? I am seeking for the moving average determined in terms of integrals rather than sums.
Solved – Moving average for continuous functions
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Best Answer
You could simply use the mean value of the function in each window.
A "backward-looking" moving average with window size $w$ is $$ \mbox{MA}_w^\text{b}(t) = \frac{1}{w} \int_{t-w}^t f(x)dx , $$ and a "centered" moving average is $$ \mbox{MA}_w^\text{c}(t) = \frac{1}{w} \int_{t-w/2}^{t+w/2} f(x)dx . $$