Numerical comparison of Savitzky-Golay filter and Least Square filter

Abstract

Modern communication relies heavily on accurate reproduction and transmission of waves which confront with noise. In this thesis we study two numerical methods to reduce noise from observed wave data : Savitzky-Golay filter and Least Square filter. QR decomposition is used to develop a Savitzky-Golay filter and Lagrangian multiplier method is applied to get Least square filter. Numerical results are given and the differences between Savitzky-Golay filter and Least square filter are compared. ; 현대 communication은 waves의 정확한 reproduction과 transmission에 의존한다. 그러나 waves는 noise에 직면한다. 이 논문에서는 관찰된 wave data로부터 noise를 줄이는 두가지 수치적 방법: Savitzky-Golay filter와 Least Square filter를 제시한다. QR decomposition은 Savitzky-Golay filter를 나타내는데 사용되어지고, Lagrangian multiplier 방법은 Least Square filter를 얻을때에 적용되어진다. 끝으로, 수치적 결과들이 주어지고 Savitzky-Golay filter와 Least square filter 사이의 차이점이 비교되어진다.