if given a LTI response to a signal is shown in x1n and the

if given a LTI response to a signal is shown in x1[n] and the results are y2[n] how do you find the results when given x2[n] and x3[n] ? In other words how do I find the equation given x1[n] and its resultant y1[n]? I\'m guessing that\'s how you find the results when given x2[n] and x3[n]??

Solution

Given that, for an LTI system

x1(n) <---------> y1(n)

Now if input is x2(n) or x3(n),

Then find the relationship between x1(n) and x2(n), i.e by performing which mathematical transformation we get x2(n) by from x1(n), then check the properties of LTI signals that how ouptut changes for this transformation of input signal. Then apply the same for y1(n) and get y2(n).