Problem 2: Given x1[n] and x2[n] are real power signals with power of Px1 and Px2 respectively. Find the power of the following: a) x1(n) + jx2[n] b) x1 [n-m] m is an integer. c) c1x1[n] + jc2x2[n] c1 and c2 are constants. d) x[m-n) m is an integer.
Solution
given the power signals
X 1 [n] = P x1
X 2 [n] = P x2
a).we know from the properity of conjuagte
j X 2 [n] = -X 2 [n]
and power = (-X 2 [n]) 2 is same as the previous
so, X 1 [n]+ j X 2 [n] = P x1 +P x2
b). we know that from the property of shift invariance of
X 1 [n-m] = shift in each and every value of output but the power value doesnt change since alla values change
X 2 [n-m] = Px1
c). from the property of linearity and from the solution 1,
C 1X 1 [n] +J C 2 X 2 [n] = C 1 P x1 + C 2 P x2
d). x[m-n] = even for the shift as power doesn\'t change so power reamins the same
P x
.
Problem 2- Given x1-n- and x2-n- are real power signals with power of.docx
1. Problem 2: Given x1[n] and x2[n] are real power signals with power of Px1 and Px2
respectively. Find the power of the following: a) x1(n) + jx2[n] b) x1 [n-m] m is an integer. c)
c1x1[n] + jc2x2[n] c1 and c2 are constants. d) x[m-n) m is an integer.
Solution
given the power signals
X 1 [n] = P x1
X 2 [n] = P x2
a).we know from the properity of conjuagte
j X 2 [n] = -X 2 [n]
and power = (-X 2 [n]) 2
is same as the previous
so, X 1 [n]+ j X 2 [n] = P x1 +P x2
b). we know that from the property of shift invariance of
X 1 [n-m] = shift in each and every value of output but the power value doesnt change since alla
values change
X 2 [n-m] = Px1
c). from the property of linearity and from the solution 1,
C 1X 1 [n] +J C 2 X 2 [n] = C 1 P x1 + C 2 P x2
d). x[m-n] = even for the shift as power doesn't change so power reamins the same
P x
![Problem 2: Given x1[n] and x2[n] are real power signals with power of Px1 and Px2
respectively. Find the power of the following: a) x1(n) + jx2[n] b) x1 [n-m] m is an integer. c)
c1x1[n] + jc2x2[n] c1 and c2 are constants. d) x[m-n) m is an integer.
Solution
given the power signals
X 1 [n] = P x1
X 2 [n] = P x2
a).we know from the properity of conjuagte
j X 2 [n] = -X 2 [n]
and power = (-X 2 [n]) 2
is same as the previous
so, X 1 [n]+ j X 2 [n] = P x1 +P x2
b). we know that from the property of shift invariance of
X 1 [n-m] = shift in each and every value of output but the power value doesnt change since alla
values change
X 2 [n-m] = Px1
c). from the property of linearity and from the solution 1,
C 1X 1 [n] +J C 2 X 2 [n] = C 1 P x1 + C 2 P x2
d). x[m-n] = even for the shift as power doesn't change so power reamins the same
P x](https://image.slidesharecdn.com/problem2-givenx1-n-andx2-n-arerealpowersignalswithpowerof-230131045250-487d4b35/85/problem-2-given-x1n-and-x2n-are-real-power-signals-with-power-ofdocx-1-320.jpg)
