Systems&Signals Find and sketch the system output y(t)

AI Thread Summary
To find the system output y(t) given the input x(t) and the impulse response h(t) = u(t), one can use the convolution method. The input x(t) can be expressed as a sum of time-shifted impulses, allowing the output y(t) to be derived by summing the responses of these impulses through the system's impulse response. Alternatively, tools like Mathematica can be utilized to perform the convolution if the equations for x(t) and h(t) are defined. The key takeaway is that understanding the relationship between the input and impulse response is crucial for determining the output. Convolution is the mathematical operation that facilitates this process.
goaliejoe35
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Suppose that the system of figure (a) has the input x(t) given in Figure (b). The impulse response is the unit step function h(t) = u(t). Find and sketch the system output y(t).
http://qaboard.cramster.com/answer-board/image/a4d35f0d5eef154398161f9124b69a59.jpg

http://qaboard.cramster.com/answer-board/image/4e19bec6ce63932d6e85f12071ffe5ff.jpg

Could someone please explain this to me? I have no idea how to do it.

I thought maybe write an equation for x(t), but I am not sure. All I need is someone to push me in the right direction.

Thanks.
 
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Hi goaliejoe35...here's how u find out y(t) without having to write the equation for x(t). Basically what h(t) means is that if x(t)=input were an impulse (a function whose value is 1 at t=0 and 0 otherwise) instead of what is given in the figure, then the system represented by the box gives an output of h(t)=u(t)=step function. Since the actual input given in the pic can be decomposed as a sum of time shifted impulses, h(t)s of these time shifted impulses can be summed together to form y(t). Mathematically known as convolution. Check this out for an example on convolution:
http://cnx.org/content/m11541/latest/

To take the easier way, you could use a tool such as mathematica(although u have to write an equation to represent x(t) and h(t)) to perform the convolution and find out the output.
x(t) = 2u(t)-3u(t-1)+u(t+2);
h(t)=u(t);
 
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