# Centered Moving Average¶

Centered Moving Average algorithm replaces each original data value by the average over its neighbor values. The choice of filter width has a great impact on the final results. The basic formula (for filter width $$L = 2M+1$$) is stated as follows:

$\hat{x}[n] = \frac{1}{2M+1} \sum_{k=-M}^M x[n+k] \, \text{,}$

where $$x[n]$$ and $$\hat{x}[n]$$ denote raw data and processed data, respectively.

Input Parameters

Parameter Type Constraint Description Remarks
$$x[n]$$ $$x[n] \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Input data sequence of length $$N$$ The algorithm assumes that input data contains no outliers and improper values such as ‘nan’, ‘inf’, ‘null’.
$$L$$ $$L \in \mathbb N$$ $$L = 2M + 1, \quad M \in \mathbb{N}$$

Output Parameters

Parameter Type Constraint Description Remarks
$$\hat{x}[n]$$ $$\hat{x}[n] \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Output data sequence of length $$N$$

Tool Support

Single Steps using the Algorithm

References

• B. Jaehne, Digitale Bildverarbeitung, 5th ed. Berlin: Springer Verlag, 2002.
• K.D. Kammeyer and K. Kroschel, Digitale Signalverarbeitung, 5th ed. Stuttgart: Teubner, 2002.