ELEG 3124 Lecture Notes - Lecture 2: Rational Number

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Lec 2 8-25-16 even vs odd / periodic vs aperiodic / Complex exponential signal / sum of two periodic. Find the even and odd decomposition of the following signal. There is a positive real value t such that , where n is any real integer. And if the signal is defined for all possible values of t, The fundamental period denoted as is the smallest positive integer that satisfies. For example if ,then which means is not the smallest. We can check the answer by adding the odd and even components to see if we get the original signal positive integer and not the fundamental period. This means the sum of two periodic signals is periodic only if the ratio of the two individual periods can be expressed as a rational number. A complex exponential signal is periodic with a period of. This means the fundamental period of the sum of the signals is.

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