Centered Moving AverageΒΆ

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’.
\(L\) \(L \in \mathbb N\) \(L = 2M + 1, \quad M \in \mathbb{N}\) None None

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 \(N\) None

Single Steps using the Algorithm

References

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