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Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components (resistors, capacitors, inductors, and linear amplifiers) will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies (their frequency response), they are sometimes known as frequency filters.
Non real-time implementations of linear time-invariant filters need not be causal. Filters of more than one dimension are also used such as in image processing. The general concept of linear filtering also extends into other fields and technologies such as statistics, data analysis, and mechanical engineering.
Linearfilters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters...
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements...
interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear...
specification, but Butterworth filters have a more linear phase response in the passband than Chebyshev Type I/Type II and elliptic filters can achieve. A transfer...
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...
types of electronic filters are linearfilters, regardless of other aspects of their design. See the article on linearfilters for details on their design...
matched filter is the optimal linearfilter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise. Matched filters are...
An adaptive filter is a system with a linearfilter that has a transfer function controlled by variable parameters and a means to adjust those parameters...
the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed...
an advantage over recursive filters such as IIR filter (Infinite Impulse Response) in applications that require a linear phase response because it will...
signal processing, a Bessel filter is a type of analog linearfilter with a maximally flat group delay (i.e., maximally linear phase response), which preserves...
as analog filters. Digital filters can often be made very high order, and are often finite impulse response filters, which allows for linear phase response...
estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean...
Chebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband...
encoded, notably in the sRGB color space, so luminance is not linear. Thus to apply a linearfilter, one must first gamma decode the values – and if resampling...
In photography, a polarizing filter can be used to filter out reflections. The common types of polarizers are linear polarizers and circular polarizers...
by Gösta Granlund, by adding a reference direction. The Gabor filter is a linearfilter used for texture analysis, which essentially means that it analyzes...
system is a time-varying linear-phase filter via the decimator and interpolator. The lowpass filter consists of two polyphase filters, one for the decimator...
In signal processing, a digital biquad filter is a second order recursive linearfilter, containing two poles and two zeros. "Biquad" is an abbreviation...
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