# The most prevalent remedy for this so called spectral

This preview shows pages 20–22. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern