Filter (signal processing)

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, , computer graphics, and structural dynamics. There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be: non-linear or linear time-variant or time-invariant, also known as shift invariance. If the filter operates in a spatial domain then the characterization is space invariance. causal or non-causal: A filter is non-causal if its present output depends on future input. Filters processing time-domain signals in real time must be causal, but not filters acting on spatial domain signals or deferred-time processing of time-domain signals. analog or digital discrete-time (sampled) or continuous-time passive or active type of continuous-time filter infinite impulse response (IIR) or finite impulse response (FIR) type of discrete-time or digital filter. Linear continuous-time circuit is perhaps the most common meaning for filter in the signal processing world, and simply "filter" is often taken to be synonymous. These circuits are generally designed to remove certain frequencies and allow others to pass. Circuits that perform this function are generally linear in their response, or at least approximately so. Any nonlinearity would potentially result in the output signal containing frequency components not present in the input signal.

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Nonlinear filter

In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage R(t) at any moment is the square of the input voltage r(t); or which is the input clipped to a fixed range [a,b], namely R(t) = max(a, min(b, r(t))).

Electronic filter topology

Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected. Filter design characterises filter circuits primarily by their transfer function rather than their topology. Transfer functions may be linear or nonlinear. Common types of linear filter transfer function are; high-pass, low-pass, bandpass, band-reject or notch and all-pass.

All-pass filter

An all-pass filter is a signal processing filter that passes all frequencies equally in gain, but changes the phase relationship among various frequencies. Most types of filter reduce the amplitude (i.e. the magnitude) of the signal applied to it for some values of frequency, whereas the all-pass filter allows all frequencies through without changes in level. A common application in electronic music production is in the design of an effects unit known as a "phaser", where a number of all-pass filters are connected in sequence and the output mixed with the raw signal.

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