Determining the Periodicity of the Sum of Periodic Signals

Determining the Periodicity of the Sum of Periodic Signals...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Determining the periodicity of the sum of periodic signals Let x(t) = x 1 (t) + x 2 (t) + … x N (t) where x j (t) is a periodic signal with fundamental period T j seconds, j = 1,2…N. To determine whether x(t) is periodic , form the ratios T 1 / T j , j=2,…N. If every one of the ratios is a rational number, then x(t) is periodic. Otherwise, it is not periodic. If x(t) is periodic, we determine its fundamental period as below
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: : 1. Convert the ratios T 1 / T j , j = 2,…N to a ratio of integers, with common factors between numerator and denominator canceled out. Now the ratios will be of the form N j / D j , for j=2,…N. 2. Find the least common multiple (LCM) of the D j ‘s. Let this number be K. 3. The fundamental period of x(t), T, is then given by T = K T 1 seconds...
View Full Document

This note was uploaded on 07/14/2010 for the course EE 3320 taught by Professor Rajasekaran during the Spring '10 term at Temasek Polytechnic.

Ask a homework question - tutors are online