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The most prevalent remedy for this so called spectral

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the signal. The most prevalent remedy for this so-called “spectral leakage” is windowing, whereby the sampled signal is weighted prior to Fourier analysis is a way that de-emphasizes samples taken near the start and end of the sample interval. This has the effect of attenuating the apparent discontinuity in the signal. It can also be viewed as replacing the gate function mentioned above with another function with lower sidelobes. Reducing the sidelobe level comes at the expense of broadening the main lobe and degrading the frequency resolution. Various tradeoffs have to be weighed when selecting the spectral window. Popular choices include the Hann window, which has a sinusoidal shape, and the Hamming window, which is like the Hann window except with a pedestal. 1.4.2 Probability theory Probability is a concept that governs the outcomes of experiments that are indeterministic, i.e., random or unpre- dictable. Noise in radar systems is an example of a random process and can only be described probabilistically. The unpredictability of noise is a consequence of the complexity of the myriad processes that contribute to it. Radar signals may reflect both random and deterministic processes, depending on the nature of the target, but the sum of signal plus noise is always a random process, and we need probability theory to understand it. We should consider the operation of a radar as the performance of an experiment with outcomes that cannot be predicted because it is simply impossible to determine all of the conditions under which the experiment is performed. Such an experiment is called a random experiment. Although the outcomes cannot be predicted, they nevertheless exhibit statistical regularity that can be appreciated after the fact. If a large number of experiments are performed under similar conditions, a frequency distribution of all the outcomes can be constructed. Because of the statistical regularity of the experiment, the distribution will converge on a limit as the number of trials increases. We can assign a probability P ( A ) to an outcome A as the relative frequency of occurrence of that outcome in the limit of an infinite number of trials. For any A , 0 P ( A ) 1 . This is the frequentist interpretation of statistics. Other interpretations 19
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of probability related to the plausibility of events as determined using information theory also exist but are beyond the scope of this text. Random variables Since the outcome of a radar experiment is finally a set of numbers, we are interested in random variables that label all the possible outcomes of a random experiment numerically. A random variable is a function that maps the outcomes of a random experiment to numbers. Particular numbers emerging from an experiment are called realizations of the random variables. Random variables come in discrete and continuous forms.
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