Wiener filter - definition
Wiener filter - definition
The Wiener Filter is an optimum digital filter or analogue filter used in the theory of signal processing to minimise the mean square error between the original signal and its estimate from the distorted version. Developed by Norbert Wiener, this filter belongs to the class of statistical filters and bases its operation on knowledge of the statistical characteristics of the signal and noise. Its primary objective is to reconstruct the signal as faithfully as possible in the presence of additive noise with a known power spectrum.
From a technical point of view, the Wiener filter implements an inverse filtering operation in the frequency domain or correlation in the time domain, while taking into account the presence of the noise and the characteristics of the source signal. It operates as a signal-matched filter, taking into account distortion and noise, which distinguishes it from classical low-pass or bandpass filters, which are not designed based on the estimation error optimisation criterion.
In its digital version, the Wiener filter can be implemented as an FIR or IIR filter, depending on the characteristics of the task and the available data. A key feature of its implementation is the need to know the autocorrelation function of the signal and the mutual correlation function between the input signal and the expected output. In practical applications, an adaptive version of the Wiener filter, e.g. the Least Mean Squares (LMS) algorithm, is often used to adapt to changing signal-noise conditions in real time.
Applications of the Wiener filter include noise reduction in data transmission, image processing, communication systems, radar, sonar and in medical diagnostics, where it is necessary to extract a signal from a distorted or incomplete measurement. Thanks to its ability to take into account the statistical properties of signals, it is regarded as one of the most effective tools in the field of estimation and optimal filtering.
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