Some advanced topics in filter design
Advanced topics in signal processing
Discrete-time signal processing
Discrete-time signal processing
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Introduction to signal processing
Introduction to signal processing
Multiresolution moment filters: theory and applications
IEEE Transactions on Image Processing
Savitzky-Golay smoothing and differentiation filter for even number data
Signal Processing
A multiscale polynomial filter for adaptive smoothing
Digital Signal Processing
Towards Generic Detection of Unusual Events in Video Surveillance
AVSS '09 Proceedings of the 2009 Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance
Expert Systems with Applications: An International Journal
GPS/Galileo Multipath Mitigation Using the First Side Peak of Double Delta Correlator
Wireless Personal Communications: An International Journal
Time-domain analysis of the Savitzky-Golay filters
Digital Signal Processing
Full length article: Differentiation by integration using orthogonal polynomials, a survey
Journal of Approximation Theory
Using microtomography, image analysis and flow simulations to characterize soil surface seals
Computers & Geosciences
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The Savitzky-Golay (SG) filters are generally used for smoothing and differentiation in many fields. The properties of the SG smoothing filters have been well studied. However, the properties of the SG differentiation filters or SG digital differentiators (SGDD, for the first order differentiation) are not developed well somehow, although they have been widely used. In the paper, the properties of the SGDD are discussed in detail. The effects of the SGDD on a noise-free single Gaussian line and a noise-free Gaussian doublet are studied via simulation. The results indicate that the contrast and resolution loss of the SGDD depends on the ratio of the width of signal derivative and filter length. The linear SGDD is not preferable for preserving small details of signal derivative from this study. The cubic and quintic SGDD with the choice of appropriate filter length are recommended in order to maintain the resolution of signal derivative.