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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 - Yoav Benjamini, Ruth Heller & Daniel Yekutieli - Rousseeuw Prize for Statistics ceremony lecture from 2024. False Discovery Rate: Corrected & Adjusted P-values - MATLAB/GNU Octave implementation and discussion on the difference between corrected and adjusted FDR p-values. Understanding False Discovery Rate - blog post
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.
The few systems that calculate the majority function on an even number of inputs are often biased towards "0" – they produce "0" when exactly half the inputs are 0 – for example, a 4-input majority gate has a 0 output only when two or more 0's appear at its inputs. [1] In a few systems, the tie can be broken randomly. [2]
Cyclic codes are not only simple to implement but have the benefit of being particularly well suited for the detection of burst errors: contiguous sequences of erroneous data symbols in messages. This is important because burst errors are common transmission errors in many communication channels , including magnetic and optical storage devices.
where p(r | x) denotes the conditional joint probability density function of the observed series {r(t)} given that the underlying series has the values {x(t)}. In contrast, the related method of maximum a posteriori estimation is formally the application of the maximum a posteriori (MAP) estimation approach.
The degree of freedom used in the chi-squared probability density function is a positive number related to the target model. Values of m {\displaystyle m} between 0.3 and 2 have been found to closely approximate certain simple shapes, such as cylinders or cylinders with fins.