Filters used in signal processing that are optimal in some sense.
In signal processing, the output of the matched filter is given by correlating a known delayed signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.[1][2] This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.
Matched filters are commonly used in radar, in which a known signal is sent out, and the reflected signal is examined for common elements of the out-going signal. Pulse compression is an example of matched filtering. It is so called because the impulse response is matched to input pulse signals. Two-dimensional matched filters are commonly used in image processing, e.g., to improve the SNR of X-ray observations.
Matched filtering is a demodulation technique with LTI (linear time invariant) filters to maximize SNR.[3]
It was originally also known as a North filter.[4]
^Woodward, P. M. (1953). Probability and information theory with applications to radar. London: Pergamon Press.
^Turin, G. L. (1960). "An introduction to matched filters". IRE Transactions on Information Theory. 6 (3): 311–329. doi:10.1109/TIT.1960.1057571. S2CID 5128742.
^After D.O. North who was among the first to introduce the concept: North, D. O. (1943). "An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems". Report PPR-6C, RCA Laboratories, Princeton, NJ. Re-print: North, D. O. (1963). "An analysis of the factors which determine signal/noise discrimination in pulsed-carrier systems". Proceedings of the IEEE. 51 (7): 1016–1027. doi:10.1109/PROC.1963.2383. See also: Jaynes, E. T. (2003). "14.6.1 The classical matched filter". Probability theory: The logic of science. Cambridge: Cambridge University Press.
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