Exponential Moving Average

An Exponential Moving Average (EMA) is a first-order IIR Filter that weights recent samples more heavily than older ones. Each output is a blend of the current input and the previous output:

$$y[n]=\alpha \cdot x[n]+(1-\alpha )\cdot y[n-1]$$

• where $\alpha \in (0,1)$ controls how quickly the average responds; a larger $\alpha$ reacts faster to changes, a smaller $\alpha$ smooths more aggressively.

Asymmetric EMA

Instead of a single $\alpha$, use separate values for growth and decay:

$$\alpha =\{\begin{array}{ll}{\alpha }_{grow}& x[n]>y[n-1]\\ {\alpha }_{decay}& x[n]<y[n-1]\end{array}$$

Useful in signal tracking where reacting quickly to a rising signal but holding on longer to a falling one reduces false “signal gone” declarations.