The object of this report is to survey noise theory and to formulate the statistics of noise ensembles created by transforming other noise en¬sembles. The transformations discussed are addition, multiplication, differentiation, linear combination of derivatives, integration with respect to a weighting function, and function with a noise argument. The formu¬lations of transformed statistics are quite general (for example, the n'th probability distribution of the product of possibly dependent noise signals is given), providing comprehensive solutions of a large number of elemen¬tary problems. Problems in a general setting display the ease with which the answers can be formulated, while solving specific problems tends to emphasize evaluation techniques. No paper giving comprehensive solutions for these elementary transofrmations was found to be available in the literature.
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