Midtens

Midtens are a term used in some fictional and experimental literatures to refer to a class of data units that summarize central tendency within short subsequences of a signal or time series.

Construction: For a sequence x1, x2, ..., xN and a window size k, the midten sequence m_t is defined for t = 1 to N − k + 1 by m_t = (x_t + x_{t+1} + ... + x_{t+k−1}) / k. This moving-average–like operation yields a downsampled representation that emphasizes the middle values of the window. Midten sequences can be used as inputs to further processing or as compact features.

Variants: Weighted midten uses a weighting that emphasizes central samples; robust midten replaces the arithmetic mean with the median (or a trimmed mean); geometric midten uses the geometric mean. These variants adjust sensitivity to outliers and scale.

Applications: Midtens are described as useful for signal smoothing, downsampling, and feature extraction in sensors. They can serve as a preprocessing step for data compression, pattern recognition, or preliminary edge or trend detection in signals and images.

History and usage: The term "midtens" has appeared in a number of niche texts and hypothetical frameworks and is not a standard term in mainstream signal processing. It is often used for illustrative purposes or as a teaching device to discuss central-tendency summarization in sliding windows.

Example: Sequence 1, 3, 5, 7, 9 with window size 3 yields midten values 3, 5, 7. This illustrates how a midten sequence preserves the central tendency of local segments while reducing length.