Algorithm |
Overview and uses |
Pros |
Cons |
Additive smoothing |
used to smooth categorical data. |
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Butterworth filter |
Slower roll-off than a Chebyshev Type I/Type II filter or an elliptic filter |
- More linear phase response in the passband than Chebyshev Type I/Type II and elliptic filters can achieve.
- Designed to have a frequency response as flat as possible in the passband.
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- requires a higher order to implement a particular stopband specification
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Chebyshev filter |
Has a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters. |
- Minimizes the error between the idealized and the actual filter characteristic over the range of the filter
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Digital filter |
Used on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal |
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Elliptic filter |
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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.
- Also, provides an effective means of predicting future values of the time series (forecasting).[3]
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Kalman filter |
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Estimates of unknown variables it produces tend to be more accurate than those based on a single measurement alone |
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Kernel smoother |
- used to estimate a real valued function as the weighted average of neighboring observed data.
- most appropriate when the dimension of the predictor is low (p < 3), for example for data visualization.
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The estimated function is smooth, and the level of smoothness is set by a single parameter. |
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Kolmogorov–Zurbenko filter |
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- robust and nearly optimal
- performs well in a missing data environment, especially in multidimensional time and space where missing data can cause problems arising from spatial sparseness
- the two parameters each have clear interpretations so that it can be easily adopted by specialists in different areas
- Software implementations for time series, longitudinal and spatial data have been developed in the popular statistical package R, which facilitate the use of the KZ filter and its extensions in different areas.
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Laplacian smoothing |
algorithm to smooth a polygonal mesh.[4][5] |
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Local regression also known as "loess" or "lowess" |
a generalization of moving average and polynomial regression. |
- fitting simple models to localized subsets of the data to build up a function that describes the deterministic part of the variation in the data, point by point
- one of the chief attractions of this method is that the data analyst is not required to specify a global function of any form to fit a model to the data, only to fit segments of the data.
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- increased computation. Because it is so computationally intensive, LOESS would have been practically impossible to use in the era when least squares regression was being developed.
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Low-pass filter |
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Moving average |
- A calculation to analyze data points by creating a series of averages of different subsets of the full data set.
- a smoothing technique used to make the long term trends of a time series clearer.[3]
- the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series
- commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles.
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- has been adjusted to allow for seasonal or cyclical components of a time series
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Ramer–Douglas–Peucker algorithm |
decimates a curve composed of line segments to a similar curve with fewer points. |
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Savitzky–Golay smoothing filter |
- based on the least-squares fitting of polynomials to segments of the data
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Smoothing spline |
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Stretched grid method |
- a numerical technique for finding approximate solutions of various mathematical and engineering problems that can be related to an elastic grid behavior
- meteorologists use the stretched grid method for weather prediction
- engineers use the stretched grid method to design tents and other tensile structures.
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