TAILIEUCHUNG - Statistical Description of Data part 9

In § we learned something about the construction and application of digital filters, but little guidance was given on which particular filter to use. That, of course, depends on what you want to accomplish by filtering. One obvious use for low-pass filters is to smooth noisy data. The premise of data smoothing is that one is measuring a variable that is both slowly varying and also corrupted by random noise. | 650 Chapter 14. Statistical Description of Data Savitzky-Golay Smoothing Filters In we learned something about the construction and application of digital filters but little guidance was given on which particular filter to use. That of course depends on what you want to accomplish by filtering. One obvious use for low-pass filters is to smooth noisy data. The premise of data smoothing is that one is measuring a variable that is both slowly varying and also corrupted by random noise. Then it can sometimes be useful to replace each data point by some kind of local average of surrounding data points. Since nearby points measure very nearly the same underlying value averaging can reduce the level of noise without much biasing the value obtained. We must comment editorially that the smoothing of data lies in a murky area beyond the fringe of some better posed and therefore more highly recommended techniques that are discussed elsewhere in this book. If you are fitting data to a parametric model for example see Chapter 15 it is almost always better to use raw data than to use data that has been pre-processed by a smoothing procedure. Another alternative to blind smoothing is so-called optimal or Wiener filtering as discussed in and more generally in . Data smoothing is probably most justified when it is used simply as a graphical technique to guide the eye through a forest of data points all with large error bars or as a means of making initial rough estimates of simple parameters from a graph. In this section we discuss a particular type of low-pass filter well-adapted for data smoothing and termed variously Savitzky-Golay 1 least-squares 2 or DISPO Digital Smoothing Polynomial 3 filters. Rather than having their properties defined in the Fourier domain and then translated to the time domain Savitzky-Golay filters derive directly from a particular formulation of the data smoothing problem in the time domain as we will now see. Savitzky-Golay filters .

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