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However, in most fielded systems, unwanted clutter and interference sources mean that the noise level changes both spatially and temporally. In this case, a changing threshold can be used, where the threshold level is raised and lowered to maintain a constant probability of false alarm. This is known as constant false alarm rate (CFAR) detection.
The normal deviate mapping (or normal quantile function, or inverse normal cumulative distribution) is given by the probit function, so that the horizontal axis is x = probit(P fa) and the vertical is y = probit(P fr), where P fa and P fr are the false-accept and false-reject rates.
The false discovery rate (FDR) is then simply the following: [1] = = [], where [] is the expected value of . The goal is to keep FDR below a given threshold q . To avoid division by zero , Q {\displaystyle Q} is defined to be 0 when R = 0 {\displaystyle R=0} .
where [] is the input as a function of the independent variable , and [] is the filtered output. 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.
Polyspace – Uses abstract interpretation, a formal methods based technique, [17] to detect and prove the absence of certain run time errors in source code for C/C++, and Ada; SPARK Toolset including the SPARK Examiner – Based on the SPARK language, a subset of Ada.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
For an optimized detector for digital signals the priority is not to reconstruct the transmitter signal, but it should do a best estimation of the transmitted data with the least possible number of errors. The receiver emulates the distorted channel. All possible transmitted data streams are fed into this distorted channel model.
Polyspace is a static code analysis tool for large-scale analysis by abstract interpretation to detect, or prove the absence of, certain run-time errors in source code for the C, C++, and Ada programming languages. The tool also checks source code for adherence to appropriate code standards.