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Of course, there is not necessarily exactly one instance of a target signal in a given signal. There could be one instance, more than one instance, or no instance of a target signal. Therefore, it is often more practical to identify all shifts corresponding to local maxima that are above a certain threshold.

The signal in [link] contains an instance of the template signal seen in [link] beginning at time t = s 1 as shown by the plot in [link] . Therefore,

s 1 = argmax t R f | | f | | , w S t g | | w S t g | | .

Pattern signal

This function shows tha pattern we are looking for in the signal below, which occurs at time t = s 1 .

Longer signal

This signal contains an instance of the above signal starting at time t = s 1 .

Absolute value of output

This signal shows a sketch of the absolute value of the matched filter output for the interval shown. Note that this was just an "eyeball approximation" sketch. Observe the pronounced peak at time t = s 1 .
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Practical applications

Image detection

Matched Filtering is used in image processing to detect a template image within a reference image. This has real-word applications in verifying fingerprints for security or in verifying someone's photo. As a simple example, we can turn to the ever-popular "Where's Waldo?" books (known as Wally in the UK!), where the reader is tasked with finding the specific face of Waldo/Wally in a confusing background rife with look-alikes! If we are given the template head and a reference image, we can run a two dimensional convolution of the template image across the reference image to obtain a three dimensional convolution map, [link] , where the height of the convolution map is determined by the degree of correlation, higher being more correlated. Finding our target then becomes a matter of determining the spot where the local surface area is highest. The process is demonstrated in [link] . In the field of image processing, this matched filter-based process is known as template matching .

Example of "Where's Waldo?" picture. Our Matched Filter Detector can be implemented to find a possible match forWaldo.

then we could easily develop a program to find the closest resemblance to the image of Waldo's head in the largerpicture. We would simply implement our same match filter algorithm: take the inner products at each shift and seehow large our resulting answers are. This idea was implemented on this same picture for a Signals and Systems Project at Rice University (click the link to learn more).

What are the advantages of the matched filter algorithm to image detection? What are the drawbacks of this method?

This algorithm is very simple and thus easy to code. However, it is susceptible to certain types of noise - for example, it would be difficult to find Waldo if his face was rotated, flipped, larger or smaller than expected, or distorted in some other way.

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Communications systems

Matched filter detectors are also commonly used in Communications Systems . In fact, they are the optimal detectors in Gaussian noise. Signals in the real-world are often distorted by the environment around them, sothere is a constant struggle to develop ways to be able to receive a distorted signal and then be able to filter itin some way to determine what the original signal was. Matched filters provide one way to compare a receivedsignal with two possible original ("template") signals and determine which one is the closest match to the receivedsignal.

Questions & Answers

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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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