Matched filter

matched filteringmatched-filteringNorth filters
In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.wikipedia
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Pulse compression

Pulse compression is an example of matched filtering.
To detect the incoming signal, matched filtering is commonly used.

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.
A receiver. Knowing the shape of the desired received signal (a pulse), an optimal receiver can be designed using a matched filter.

Linear filter

linearlinear filtersfilter
The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.
They can easily be designed to give a matched filter for any arbitrary pulse shape.

Signal-to-noise ratio

signal to noise ratioSNRsignal-to-noise
The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.
Matched filter

Whittle likelihood

The matched filter may be derived in a variety of ways, but as a special case of a least squares procedure it may also be interpreted as a maximum likelihood method in the context of a (coloured) Gaussian noise model and the associated Whittle likelihood.
This expression also is the basis for the common matched filter.

Discrete Fourier transform

DFTcircular convolution theoremFourier transform
This method is, in fact, a simple version of the discrete Fourier transform (DFT).
It is the cross correlation of the input sequence, x_n, and a complex sinusoid at frequency k/N. Thus it acts like a matched filter for that frequency.

Estimation theory

parameter estimationestimationestimated
Additionally, matched filters can be used in parameter estimation problems (see estimation theory).
Matched filter

Periodogram
Matched filter

Gravitational-wave astronomy

gravitational wave astronomyfirst direct gravitational wave observationgravitational wave observation
Matched filters play a central role in gravitational-wave astronomy.
Matched filter

Digital filter

filterdigitaldigital filters
Digital filter
Matched filter

filtered back projectionfiltered backprojectionsinograms
Matched filter

SAMV (algorithm)

SAMViterative Sparse Asymptotic Minimum Variance
SAMV
This imaging problem is a single-snapshot application, and algorithms compatible with single-snapshot estimation are included, i.e., Matched filter (MF, similar to the periodogram or backprojection, which is often efficiently implemented as fast Fourier transform (FFT)), IAA, and a variant of the SAMV algorithm (SAMV-0).

MUSIC (algorithm)

MUltiple SIgnal ClassificationMUSICMUSIC (Multiple Signal Classification)
MUltiple SIgnal Classification (MUSIC), a popular parametric superresolution method
Matched filter

Wiener filter

WienerWiener–Kolmogorov filterWiener filtering
Wiener filter
matched filter

Least mean squares filter

Least Mean SquaresLeast Mean Squares (LMS) filterLMS
Least mean squares (LMS) filter
matched filter

Cross-correlation

cross correlationcorrelationcorrelating
In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.

Signal

signalselectrical signalelectrical signals
In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.

Convolution

convolvedconvolvingkernel
This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template.

Complex conjugate

complex conjugationconjugateconjugation
This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template.

Stochastic process

stochastic processesrandom processstochastic
The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.

Noise (signal processing)

noisenoisybackground noise
The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.

Digital image processing

image processingimageprocessing
Two-dimensional matched filters are commonly used in image processing, e.g., to improve SNR for X-ray.

Discrete time and continuous time

discrete-timediscrete timecontinuous-time
The following section derives the matched filter for a discrete-time system.

Impulse response

impulseImpulse Response Functionsimpulse-response function.
Though we most often express filters as the impulse response of convolution systems, as above (see LTI system theory), it is easiest to think of the matched filter in the context of the inner product, which we will see shortly.

Linear time-invariant system

linear time-invariantLTIlinear time invariant
Though we most often express filters as the impulse response of convolution systems, as above (see LTI system theory), it is easiest to think of the matched filter in the context of the inner product, which we will see shortly.