This question deals with an example found in Signals and Systems, 2ed, page 99, ex 2.7. But I can summarize it here:(adsbygoogle = window.adsbygoogle || []).push({});

EDIT - my latex doesn't seem to work ...

[tex]

x(t) = (1, 0 < t < T) or (0, otherwise)

[/tex]

[tex]

h(t) = (t, 0 < t < 2T) or (0, otherwise)

[/tex]

I realize there are five bounds to consider: (t<0, 0 <t <T, T < t < 2T, 2T < t <3T, 3T < t)

However, for instance,

[tex]

\\int_T^0 x(\tau) h(t-\tau) d\tau = \\int_T^0 h(t-\tau) d\tau = t\tau - \tau^2/2 (from 0 to T)

[/tex]

does not equal the example's answer of

[tex]

t^2/2

[/tex]

nor does

(integrate from 2T to 3T)

[tex]

\\int_2*T^3*T x(\tau) h(t-\tau) d\tau = \\int_T^0 h(t-\tau) d\tau = t\tau - \tau^2/2 (from 2T to 3T)

[/tex]

does not equal the example's answer of

[tex]

-t^2/2 + Tt + 3/2*T^2

[/tex]

So my question is this:

Once I realize the bounds that the convolution must be evaluated for, how do i convert the bounds so that I can integrate them and derive the correct answer?

edit- x(tau) is a square pulse of height 1, from 0 to T (not tau but T)

and

h(t-tau) is a downward sloping right trianlge (90degree corner on the left) with a base from t-2T to t.

Thank you for your time.

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# Homework Help: CT Convolutions and their bounds

Can you offer guidance or do you also need help?

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