Weighted Forward Moving AverageΒΆ
Local Algorithm - One-Dimensional Algorithm
Weighted Forward Moving Average algorithm is based on the Forward Moving Average algorithm. Differently, varying weights are assigned to the values within the filter width. The basic formula (for filter width \(L = M+1\)) is stated as follows:
\[\hat{x}[n] = \frac{1}{M+1} \sum_{k=0}^M w[k] x[n+k] \, \text{,}\]
where \(x[n]\), \(\hat{x}[n]\) and \(w[k]\) denote raw data, processed data and weights, 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’. |
| \(L\) | \(L \in \mathbb N\) | \(L = M + 1, \quad M \in \mathbb{N}\) | ||
| \(w[k]\) | \(w[k] \in \mathbb{R}^L\) | \(w[k] \geq 0, \quad \sum w[k] = 1\) | Weighting vector of of length \(L\) |
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