A Study on Low-Pass Filter for Finite Length Data (2nd Report)

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  • 有限長データ用ローパスフィルタの研究（第2報）
  • ユウゲンチョウ データヨウ ロー パス フィルタ ノ ケンキュウ ダイ2ホウ サイショウ 2ジョウ キジュン ニ ヨル ロー パス フィルタ
  • - Low-Pass Filters Based on A Least-Squares Criterion -
  • －最小2乗基準によるローパスフィルタ－

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A low-pass filter is almost always applied to data of finite length. Therefore, unexpected vibration occurs at the data end of the low-pass filter output. To solve this problem, the previous report of this paper has proposed that two types of low-pass filters (i.e. spacial and frequency) can be used in a point symmetric extension method. To make the above proposal more specific, a point symmetric extension method was applied to reduce an abnormal value occurring in the filtered data at the data end where the center of the point symmetric method is applied. Before that, the data end was replaced by the generalized low-pass filtered output. Consequently this paper proposes a method to determine the center point of this point symmetric extension based on the sum of squared errors between the primary and the filtered output. This new method also uses a spatial low-pass filter and a frequency low-pass filter. The method is applicable not only to a low-pass filter that uses a point symmetric extension method but also to all other types of low-pass filters for minimizing the sum of squared errors between primary and filtered data.

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