# 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 radarchirp radarintra-pulse modulation**

Pulse compression is an example of matched filtering.

To detect the incoming signal, matched filtering is commonly used.

### Radar

**radar stationradarsradar system**

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

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

### Radon transform

**filtered back projectionfiltered backprojectionsinograms**

Filtered Backprojection (Radon transform)

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**

### 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.