A linear filter applies a linear operator to a time-varying input signal. Mathematically, it is a combination
H = ∑ h(k)Sk
of delays S and advances S-1[1].
Linear filters are very common in electronics and digital signal processing (see the article on electronic filters), but they can also be found in mechanical engineering and other technologies.
They are often used to eliminate unwanted frequencies from an input signal or to select a desired frequency among many others. There are a wide range of types of filters and filter technologies, of which this article will present an overview.
Regardless of whether they are electronic, electrical, or mechanical, or what frequency ranges or timescales they work on, the mathematical theory of linear filters is universal.
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