Sketching Signal Over Time | Homework Statement & Equations

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Homework Statement



The problem is to sketch the signal over time:
x(t)=1+δ(t-2)+δ(t+2)+δ(5)

Homework Equations


N/A


The Attempt at a Solution


I'm not too sure how to begin this. Would it look like a square wave with different "peaks" over time?
 
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it would look like a constant value with a few peaks

however \delta (5) doesn't make sense, it should be a function of t
 
lanedance said:
it would look like a constant value with a few peaks

however \delta (5) doesn't make sense, it should be a function of t

well wouldn't that be just a constant value of 5 added across the whole signal?
 
don't think so, the delta function \delta (t) is zero everywhere except at t=0, hence why it doesn't make much sense
 
lanedance said:
don't think so, the delta function \delta (t) is zero everywhere except at t=0, hence why it doesn't make much sense

I check it again, I did write it correctly. So assuming that's right, would it be a linear looking like increasing as time increased?
 
well as I said it doesn't make sense, but if you have to work with it, I think delta(5) = 0
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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