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a) This problem is transformation of the independent variable. The transformation consists of a shift and time scaling. The resulting signal is shifted to the left by 5 and time scaled so the new times are divided by 2. | a) This problem is transformation of the independent variable. The transformation consists of a shift and time scaling. The resulting signal is shifted to the left by 5 and time scaled so the new times are divided by 2. | ||
| − | [[Image: | + | [[Image:xofttrans_Old Kiwi.doc]] |
b) This problem is finding the even and odd parts of a signal x[n]. x1[n] = (x[n] + x[-n])/2 is the even signal. It can be found by plotting x[n]/2 and x[-n]/2 then summing the two signals. This is shown below. Note that x1[n] is symmetric about the verticle axis. | b) This problem is finding the even and odd parts of a signal x[n]. x1[n] = (x[n] + x[-n])/2 is the even signal. It can be found by plotting x[n]/2 and x[-n]/2 then summing the two signals. This is shown below. Note that x1[n] is symmetric about the verticle axis. | ||
[[Image:x1ofn_Old Kiwi.doc]] | [[Image:x1ofn_Old Kiwi.doc]] | ||
| − | x2[n]= (x[n]-x[-n])/2 is the odd signal. It can be found by plotting x[n]/2 and -x[n]/2 and summing the two signals. This is shown below. Note that x2[n] satisfies the condition that x[n]=-x[-n]. | + | x2[n]= (x[n]-x[-n])/2 is the odd signal. It can be found by plotting x[n]/2 and -x[-n]/2 and summing the two signals. This is shown below. Note that x2[n] satisfies the condition that x[n]=-x[-n]. |
[[Image:x2ofn_Old Kiwi.doc]] | [[Image:x2ofn_Old Kiwi.doc]] | ||
Latest revision as of 13:50, 30 June 2008
a) This problem is transformation of the independent variable. The transformation consists of a shift and time scaling. The resulting signal is shifted to the left by 5 and time scaled so the new times are divided by 2.
b) This problem is finding the even and odd parts of a signal x[n]. x1[n] = (x[n] + x[-n])/2 is the even signal. It can be found by plotting x[n]/2 and x[-n]/2 then summing the two signals. This is shown below. Note that x1[n] is symmetric about the verticle axis. File:X1ofn Old Kiwi.doc
x2[n]= (x[n]-x[-n])/2 is the odd signal. It can be found by plotting x[n]/2 and -x[-n]/2 and summing the two signals. This is shown below. Note that x2[n] satisfies the condition that x[n]=-x[-n]. File:X2ofn Old Kiwi.doc
