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
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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