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Unformatted text preview: number of periods of each of the two components.) In this case, lcm(8, 10) = 40 If (x[n], y[n]) = (x[n+40], y[n+40]) then clearly also x[n]+y[n] = x[n+40]+y[n+40] The fundamental period of x[n]+y[n] equals 40 (not a submultiple thereof). This is always the case with sums of sinusoids of different frequencies, and in this problem it can be verified directly by examining a vector of 40 consecutive samples of x[n]+y[n]. Sheet1 Page 2 (v) z[n] = x[n]^2 ==> z[n] = cos(3*pi*n/4+2*pi/3)^2 = 0.5 * cos(2 * (3*pi*n/4+2*pi/3) ) + 0.5 z[n] = 0.5 * cos(3*pi*n/2+4*pi/3) + 0.5 z[n] is periodic with period 4. Note that the period of z[n] is half the period of x[n]....
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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08