Convolution with rectangular function












0














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.










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  • 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
    – Poujh
    2 days ago
















0














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.










share|cite|improve this question







New contributor




user71 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • 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
    – Poujh
    2 days ago














0












0








0







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.










share|cite|improve this question







New contributor




user71 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











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






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user71 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




user71 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









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share|cite|improve this question






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asked 2 days ago









user71

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user71 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






user71 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • 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
    – Poujh
    2 days ago


















  • 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
    – Poujh
    2 days ago
















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
– Poujh
2 days ago




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
– Poujh
2 days ago















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