Skip to content

Linear Filter

Statistical Glossary

Linear Filter:

A linear filter is the filter whose output is a linear function of the input. Any output value of a linear filter is the weighted mean of input values. In other words, to form one element Math image of the output at time Math image , it is necessary to multiply the input values for time moments adjacent to Math image by coefficients and to sum up the products.

Mathematically, the output of a linear filter may be described by the expression

where

  • Math image is the output of the filter (the result of filtering);
  • Math image is the input of the filter (the original time series to be filtered);
  • Math image is the size of the “window” of the filter – the number of the input values affecting one output value;
  • Math image are “weights” that completely describe any linear filter.

In contrast to nonlinear filter , there is a well developed and conceptually rich mathematical theory of linear filters.

All the linear filters are subdivided into two broad categories – nonrecursive filters and recursive filters .

Examples of a linear filters are: the rectangular filter , the triangular filter , the Gaussian filter , the exponential filter , Kalman filter .

See also: Smoother (Smoothing Filter) , predicting filter

Browse Other Glossary Entries

Test Yourself

Planning on taking an introductory statistics course, but not sure if you need to start at the beginning? Review the course description for each of our introductory statistics courses and estimate which best matches your level, then take the self test for that course. If you get all or almost all the questions correct, move on and take the next test.

Data Analytics

Considering becoming adata scientist, customer analyst or our data science certificate program?

Analytics Quiz

Advanced Statistics Quiz

Statistics Quiz

Statistics

Looking at statistics for graduate programs or to enhance your foundational knowledge?

Statistics 1 Quiz

Regression Quiz

Regression Quiz

Biostatistics

Entering the biostatistics field? Test your skill here.

Biostatistics Quiz

Advanced Statistics Quiz

Statistics 2 Quiz

Stay Informed

Our Blog

Read up on our latest blogs

Certificates

Learn about our certificate programs

Courses

Find the right course for you

Contact Us

We'd love to answer your questions

Our mentors and academic advisors are standing by to help guide you towards the courses or program that makes the most sense for you and your goals.

300 W Main St STE 301, Charlottesville, VA 22903

(434) 973-7673

ourcourses@statistics.com

By submitting your information, you agree to receive email communications from Statistics.com. All information submitted is subject to our privacy policy. You may opt out of receiving communications at any time.