Smoothing - Smoothing Algorithms

Smoothing Algorithms

One of the most common algorithms is the "moving average", often used to try to capture important trends in repeated statistical surveys. In image processing and computer vision, smoothing ideas are used in scale space representations. The simplest smoothing algorithm is the "rectangular" or "unweighted sliding-average smooth". This method replaces each point in the signal with the average of "m" adjacent points, where "m" is a positive integer called the "smooth width". Usually m is an odd number. The triangular smooth is like the rectangular smooth except that it implements a weighted smoothing function.

Some specific smoothing and filter types are:

• Additive smoothing
• Butterworth filter
• Digital filter
• Kalman filter
• Kernel smoother
• Laplacian smoothing
• Stretched grid method
• Low-pass filter
• Recursive filter
• Savitzky–Golay smoothing filter based on the least-squares fitting of polynomials to segments of the data
• Local regression also known as "loess" or "lowess"
• Smoothing spline
• Ramer–Douglas–Peucker algorithm
• Moving average a form of average which has been adjusted to allow for seasonal or cyclical components of a time series. Moving average smoothing is a smoothing technique used to make the long term trends of a time series clearer.
• Exponential smoothing used to reduce irregularities (random fluctuations) in time series data, thus providing a clearer view of the true underlying behaviour of the series. It also provides an effective means of predicting future values of the time series (forecasting).
• Kolmogorov–Zurbenko_filter