Hi! I need help understanding this signal Originally I thought the signal was this But it's actually this Can anyone help me understand how they got this graph? I thought since x[n] is one when n>=0, I pay attention to u[1-t] from 0 to 1.
This is completely arbitrary. You need to tell us what x[n] is for us to explain the graph. We assume u[n] is the step function and x[n] is some other arbitrary signal. Without its definition, these plots are completely meaningless I think you may be misunderstanding the concept of the unit step function
this is just the original signal - x[n] - multiplied by a modified step function. u[1-n] is a step function that is time reversed around n=1. So u[1-n] = 1 for n<=1 and u[1-n] = 0 for n > 1 (instead of one for n>=0). So for g[n] = x[n]u[1-n], g[n] = x[n] for n <= 1 (where u[1-n] = 1), and g[n] = 0 for n>1 (where u[1-n] = 0).
So x[n]u[1-n] is simply a pointwise multiplication of this given x[n] with u[1-n]. u[1-n] has a value of 1 for all n<=1, and a value of 0 for n >1. So with this given x[n], the result will be almost the same as x[n] (since you are multiplying most sample values by 1), except for the resulting function changes to 0 at n = 2,3, since u[1-n] = 0 at these two points. This gives you the result that you originally posted.