Convolution with rectangular function
$begingroup$
I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$.
I have followed those steps:
$y(t)=x(t){*}h(t)$
$=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$
$=4[u(t)-u(t+8)] { * } e^{-4(t-4)}u(t-4)$
$=4[u(t){*}e^{-4(t-4)}u(t-4)] - 4[u(t+8){*}e^{-4(t-4)}u(t-4)]$
I got stuck after this point. I have an exam in a week. Thanks in advance for the help.
functions convolution
asked Dec 25 '18 at 17:51
user71user71
1
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add a comment |
$begingroup$
I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$.
I have followed those steps:
$y(t)=x(t){*}h(t)$
$=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$
$=4[u(t)-u(t+8)] { * } e^{-4(t-4)}u(t-4)$
$=4[u(t){*}e^{-4(t-4)}u(t-4)] - 4[u(t+8){*}e^{-4(t-4)}u(t-4)]$
I got stuck after this point. I have an exam in a week. Thanks in advance for the help.
functions convolution
asked Dec 25 '18 at 17:51
user71user71
1
$endgroup$
$begingroup$
1. What exactly causes you problem ? <br> 2. I don't really understand what you're doing. Aren't you supposed to set up integrals ? <br> 3. I don't know if it helps, but the following method made convolution integrals a lot easier for me : apps.dtic.mil/dtic/tr/fulltext/u2/a602143.pdf
$endgroup$
– Poujh
Dec 25 '18 at 19:44
add a comment |
$begingroup$
I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$.
I have followed those steps:
$y(t)=x(t){*}h(t)$
$=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$
$=4[u(t)-u(t+8)] { * } e^{-4(t-4)}u(t-4)$
$=4[u(t){*}e^{-4(t-4)}u(t-4)] - 4[u(t+8){*}e^{-4(t-4)}u(t-4)]$
I got stuck after this point. I have an exam in a week. Thanks in advance for the help.
functions convolution
asked Dec 25 '18 at 17:51
user71user71
1
$endgroup$
I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$.
I have followed those steps:
$y(t)=x(t){*}h(t)$
$=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$
$=4[u(t)-u(t+8)] { * } e^{-4(t-4)}u(t-4)$
$=4[u(t){*}e^{-4(t-4)}u(t-4)] - 4[u(t+8){*}e^{-4(t-4)}u(t-4)]$
I got stuck after this point. I have an exam in a week. Thanks in advance for the help.
functions convolution
functions convolution
asked Dec 25 '18 at 17:51
user71user71
1
asked Dec 25 '18 at 17:51
user71user71
1
asked Dec 25 '18 at 17:51
user71user71
1
asked Dec 25 '18 at 17:51
user71user71
1
asked Dec 25 '18 at 17:51
user71user71
1
1
$begingroup$
1. What exactly causes you problem ? <br> 2. I don't really understand what you're doing. Aren't you supposed to set up integrals ? <br> 3. I don't know if it helps, but the following method made convolution integrals a lot easier for me : apps.dtic.mil/dtic/tr/fulltext/u2/a602143.pdf
$endgroup$
– Poujh
Dec 25 '18 at 19:44
add a comment |
$begingroup$
1. What exactly causes you problem ? <br> 2. I don't really understand what you're doing. Aren't you supposed to set up integrals ? <br> 3. I don't know if it helps, but the following method made convolution integrals a lot easier for me : apps.dtic.mil/dtic/tr/fulltext/u2/a602143.pdf
$endgroup$
– Poujh
Dec 25 '18 at 19:44
$begingroup$
1. What exactly causes you problem ? <br> 2. I don't really understand what you're doing. Aren't you supposed to set up integrals ? <br> 3. I don't know if it helps, but the following method made convolution integrals a lot easier for me : apps.dtic.mil/dtic/tr/fulltext/u2/a602143.pdf
$endgroup$
– Poujh
Dec 25 '18 at 19:44
$begingroup$
1. What exactly causes you problem ? <br> 2. I don't really understand what you're doing. Aren't you supposed to set up integrals ? <br> 3. I don't know if it helps, but the following method made convolution integrals a lot easier for me : apps.dtic.mil/dtic/tr/fulltext/u2/a602143.pdf
$endgroup$
– Poujh
Dec 25 '18 at 19:44
add a comment |
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$begingroup$
1. What exactly causes you problem ? <br> 2. I don't really understand what you're doing. Aren't you supposed to set up integrals ? <br> 3. I don't know if it helps, but the following method made convolution integrals a lot easier for me : apps.dtic.mil/dtic/tr/fulltext/u2/a602143.pdf
$endgroup$
– Poujh
Dec 25 '18 at 19:44