# Weighted Backward Moving AverageΒΆ

Weighted Backward Moving Average algorithm is based on the Backward 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:

$\hat{x}[n] = \frac{1}{M+1} \sum_{k=-M}^0 w[k] x[n+k] \, \text{,}$

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