laplace transform of impulse function












0












$begingroup$


The laplace tranform of the following function impulse function is



$$int_{0}^{infty}delta(t).e^{-st},dt$$
$$=int_{0}^{infty}delta(t),dt=1$$
(area under unit impulse is always 1)
$$=1.int_{0}^{infty}e^{-st},dt$$
$$=1.frac{1}{S}$$
$$=frac{1}{S}$$
but the correct answer is 1, I don't know why.










share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    You can't integrate a factor only and take it out from the integral.
    $endgroup$
    – Sergio Enrique Yarza Acuña
    Aug 12 '17 at 6:46










  • $begingroup$
    Also $int_0^infty delta(t) e^{-st}dt$ is not a very good notation. You should say instead that $int_{-infty}^infty delta(t) e^{-st}dt = e^{-st}|_{s=0} = 1$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:06
















0












$begingroup$


The laplace tranform of the following function impulse function is



$$int_{0}^{infty}delta(t).e^{-st},dt$$
$$=int_{0}^{infty}delta(t),dt=1$$
(area under unit impulse is always 1)
$$=1.int_{0}^{infty}e^{-st},dt$$
$$=1.frac{1}{S}$$
$$=frac{1}{S}$$
but the correct answer is 1, I don't know why.










share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    You can't integrate a factor only and take it out from the integral.
    $endgroup$
    – Sergio Enrique Yarza Acuña
    Aug 12 '17 at 6:46










  • $begingroup$
    Also $int_0^infty delta(t) e^{-st}dt$ is not a very good notation. You should say instead that $int_{-infty}^infty delta(t) e^{-st}dt = e^{-st}|_{s=0} = 1$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:06














0












0








0





$begingroup$


The laplace tranform of the following function impulse function is



$$int_{0}^{infty}delta(t).e^{-st},dt$$
$$=int_{0}^{infty}delta(t),dt=1$$
(area under unit impulse is always 1)
$$=1.int_{0}^{infty}e^{-st},dt$$
$$=1.frac{1}{S}$$
$$=frac{1}{S}$$
but the correct answer is 1, I don't know why.










share|cite|improve this question









$endgroup$




The laplace tranform of the following function impulse function is



$$int_{0}^{infty}delta(t).e^{-st},dt$$
$$=int_{0}^{infty}delta(t),dt=1$$
(area under unit impulse is always 1)
$$=1.int_{0}^{infty}e^{-st},dt$$
$$=1.frac{1}{S}$$
$$=frac{1}{S}$$
but the correct answer is 1, I don't know why.







calculus






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 12 '17 at 6:44









TapasXTapasX

192




192








  • 2




    $begingroup$
    You can't integrate a factor only and take it out from the integral.
    $endgroup$
    – Sergio Enrique Yarza Acuña
    Aug 12 '17 at 6:46










  • $begingroup$
    Also $int_0^infty delta(t) e^{-st}dt$ is not a very good notation. You should say instead that $int_{-infty}^infty delta(t) e^{-st}dt = e^{-st}|_{s=0} = 1$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:06














  • 2




    $begingroup$
    You can't integrate a factor only and take it out from the integral.
    $endgroup$
    – Sergio Enrique Yarza Acuña
    Aug 12 '17 at 6:46










  • $begingroup$
    Also $int_0^infty delta(t) e^{-st}dt$ is not a very good notation. You should say instead that $int_{-infty}^infty delta(t) e^{-st}dt = e^{-st}|_{s=0} = 1$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:06








2




2




$begingroup$
You can't integrate a factor only and take it out from the integral.
$endgroup$
– Sergio Enrique Yarza Acuña
Aug 12 '17 at 6:46




$begingroup$
You can't integrate a factor only and take it out from the integral.
$endgroup$
– Sergio Enrique Yarza Acuña
Aug 12 '17 at 6:46












$begingroup$
Also $int_0^infty delta(t) e^{-st}dt$ is not a very good notation. You should say instead that $int_{-infty}^infty delta(t) e^{-st}dt = e^{-st}|_{s=0} = 1$
$endgroup$
– reuns
Aug 12 '17 at 7:06




$begingroup$
Also $int_0^infty delta(t) e^{-st}dt$ is not a very good notation. You should say instead that $int_{-infty}^infty delta(t) e^{-st}dt = e^{-st}|_{s=0} = 1$
$endgroup$
– reuns
Aug 12 '17 at 7:06










1 Answer
1






active

oldest

votes


















0












$begingroup$

Hint. Note that by the sampling property of the delta function (which is actually a distribution)
$$int_{-infty}^{+infty}f(t)delta(t-t_0)dt=f(t_0).$$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    @reuns Yes, it is better to recall that.
    $endgroup$
    – Robert Z
    Aug 12 '17 at 7:13










  • $begingroup$
    To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:22











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2391019%2flaplace-transform-of-impulse-function%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0












$begingroup$

Hint. Note that by the sampling property of the delta function (which is actually a distribution)
$$int_{-infty}^{+infty}f(t)delta(t-t_0)dt=f(t_0).$$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    @reuns Yes, it is better to recall that.
    $endgroup$
    – Robert Z
    Aug 12 '17 at 7:13










  • $begingroup$
    To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:22
















0












$begingroup$

Hint. Note that by the sampling property of the delta function (which is actually a distribution)
$$int_{-infty}^{+infty}f(t)delta(t-t_0)dt=f(t_0).$$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    @reuns Yes, it is better to recall that.
    $endgroup$
    – Robert Z
    Aug 12 '17 at 7:13










  • $begingroup$
    To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:22














0












0








0





$begingroup$

Hint. Note that by the sampling property of the delta function (which is actually a distribution)
$$int_{-infty}^{+infty}f(t)delta(t-t_0)dt=f(t_0).$$






share|cite|improve this answer











$endgroup$



Hint. Note that by the sampling property of the delta function (which is actually a distribution)
$$int_{-infty}^{+infty}f(t)delta(t-t_0)dt=f(t_0).$$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Aug 12 '17 at 7:12

























answered Aug 12 '17 at 7:06









Robert ZRobert Z

95.1k1063134




95.1k1063134












  • $begingroup$
    @reuns Yes, it is better to recall that.
    $endgroup$
    – Robert Z
    Aug 12 '17 at 7:13










  • $begingroup$
    To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:22


















  • $begingroup$
    @reuns Yes, it is better to recall that.
    $endgroup$
    – Robert Z
    Aug 12 '17 at 7:13










  • $begingroup$
    To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
    $endgroup$
    – reuns
    Aug 12 '17 at 7:22
















$begingroup$
@reuns Yes, it is better to recall that.
$endgroup$
– Robert Z
Aug 12 '17 at 7:13




$begingroup$
@reuns Yes, it is better to recall that.
$endgroup$
– Robert Z
Aug 12 '17 at 7:13












$begingroup$
To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
$endgroup$
– reuns
Aug 12 '17 at 7:22




$begingroup$
To make it clear, you can define it as $int_{-infty}^infty delta(t) f(t)dt overset{def}= lim_{epsilon to 0^+} int_{-infty}^infty frac{1_{|t| < epsilon}}{2 epsilon} f(t)dt$
$endgroup$
– reuns
Aug 12 '17 at 7:22


















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2391019%2flaplace-transform-of-impulse-function%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

android studio warns about leanback feature tag usage required on manifest while using Unity exported app?

SQL update select statement

'app-layout' is not a known element: how to share Component with different Modules