Transfer Function, what does s Stand for
$begingroup$
Trying to understand what the variable s is for transfer functions (if there is a common accepted use of it). In the problem space I am working in, control theory, I believe I have seen definitions of "short period poles", "complex Laplace transform variable", and at
http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf it describes s as s = sigma + j * omega (I guess as a complex variable). Any insight into one of these being correct or if I am missing a better common use, that would be appreciated.
laplace-transform control-theory
asked Dec 12 '18 at 15:44
DannyDanny
12
$endgroup$
add a comment |
$begingroup$
Trying to understand what the variable s is for transfer functions (if there is a common accepted use of it). In the problem space I am working in, control theory, I believe I have seen definitions of "short period poles", "complex Laplace transform variable", and at
http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf it describes s as s = sigma + j * omega (I guess as a complex variable). Any insight into one of these being correct or if I am missing a better common use, that would be appreciated.
laplace-transform control-theory
asked Dec 12 '18 at 15:44
DannyDanny
12
$endgroup$
$begingroup$
Check out the Wikipedia Transfer Function page. I don't know what a "short period pole" is, but the other two definitions seem correct to me (even if not providing much insight).
$endgroup$
– NickD
Dec 12 '18 at 15:55
$begingroup$
Thanks, I appreciate the second opinion, you'd be surprised how hard it is to google any variation of "transfer function s" since every webpage has an s in it :)
$endgroup$
– Danny
Dec 12 '18 at 15:58
1
$begingroup$
No doubt that $s$ is a complex variable in Laplace transform. Decomposing it into $sigma+jomega$ way is dangerous because it tends to say (what you find in old books) that setting $sigma=0$ you can reach the Fourier Transform. The best way to consider the $s$ in a Laplace Transform is as a purely formal parameter.
$endgroup$
– Jean Marie
Dec 12 '18 at 19:53
$begingroup$
Thank you Jean! Great answer :D
$endgroup$
– Danny
Dec 12 '18 at 21:38
add a comment |
$begingroup$
Trying to understand what the variable s is for transfer functions (if there is a common accepted use of it). In the problem space I am working in, control theory, I believe I have seen definitions of "short period poles", "complex Laplace transform variable", and at
http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf it describes s as s = sigma + j * omega (I guess as a complex variable). Any insight into one of these being correct or if I am missing a better common use, that would be appreciated.
laplace-transform control-theory
asked Dec 12 '18 at 15:44
DannyDanny
12
$endgroup$
Trying to understand what the variable s is for transfer functions (if there is a common accepted use of it). In the problem space I am working in, control theory, I believe I have seen definitions of "short period poles", "complex Laplace transform variable", and at
http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf it describes s as s = sigma + j * omega (I guess as a complex variable). Any insight into one of these being correct or if I am missing a better common use, that would be appreciated.
laplace-transform control-theory
laplace-transform control-theory
asked Dec 12 '18 at 15:44
DannyDanny
12
asked Dec 12 '18 at 15:44
DannyDanny
12
asked Dec 12 '18 at 15:44
DannyDanny
12
asked Dec 12 '18 at 15:44
DannyDanny
12
asked Dec 12 '18 at 15:44
DannyDanny
12
12
$begingroup$
Check out the Wikipedia Transfer Function page. I don't know what a "short period pole" is, but the other two definitions seem correct to me (even if not providing much insight).
$endgroup$
– NickD
Dec 12 '18 at 15:55
$begingroup$
Thanks, I appreciate the second opinion, you'd be surprised how hard it is to google any variation of "transfer function s" since every webpage has an s in it :)
$endgroup$
– Danny
Dec 12 '18 at 15:58
1
$begingroup$
No doubt that $s$ is a complex variable in Laplace transform. Decomposing it into $sigma+jomega$ way is dangerous because it tends to say (what you find in old books) that setting $sigma=0$ you can reach the Fourier Transform. The best way to consider the $s$ in a Laplace Transform is as a purely formal parameter.
$endgroup$
– Jean Marie
Dec 12 '18 at 19:53
$begingroup$
Thank you Jean! Great answer :D
$endgroup$
– Danny
Dec 12 '18 at 21:38
add a comment |
$begingroup$
Check out the Wikipedia Transfer Function page. I don't know what a "short period pole" is, but the other two definitions seem correct to me (even if not providing much insight).
$endgroup$
– NickD
Dec 12 '18 at 15:55
$begingroup$
Thanks, I appreciate the second opinion, you'd be surprised how hard it is to google any variation of "transfer function s" since every webpage has an s in it :)
$endgroup$
– Danny
Dec 12 '18 at 15:58
1
$begingroup$
No doubt that $s$ is a complex variable in Laplace transform. Decomposing it into $sigma+jomega$ way is dangerous because it tends to say (what you find in old books) that setting $sigma=0$ you can reach the Fourier Transform. The best way to consider the $s$ in a Laplace Transform is as a purely formal parameter.
$endgroup$
– Jean Marie
Dec 12 '18 at 19:53
$begingroup$
Thank you Jean! Great answer :D
$endgroup$
– Danny
Dec 12 '18 at 21:38
$begingroup$
Check out the Wikipedia Transfer Function page. I don't know what a "short period pole" is, but the other two definitions seem correct to me (even if not providing much insight).
$endgroup$
– NickD
Dec 12 '18 at 15:55
$begingroup$
Check out the Wikipedia Transfer Function page. I don't know what a "short period pole" is, but the other two definitions seem correct to me (even if not providing much insight).
$endgroup$
– NickD
Dec 12 '18 at 15:55
$begingroup$
Thanks, I appreciate the second opinion, you'd be surprised how hard it is to google any variation of "transfer function s" since every webpage has an s in it :)
$endgroup$
– Danny
Dec 12 '18 at 15:58
$begingroup$
Thanks, I appreciate the second opinion, you'd be surprised how hard it is to google any variation of "transfer function s" since every webpage has an s in it :)
$endgroup$
– Danny
Dec 12 '18 at 15:58
1
1
$begingroup$
No doubt that $s$ is a complex variable in Laplace transform. Decomposing it into $sigma+jomega$ way is dangerous because it tends to say (what you find in old books) that setting $sigma=0$ you can reach the Fourier Transform. The best way to consider the $s$ in a Laplace Transform is as a purely formal parameter.
$endgroup$
– Jean Marie
Dec 12 '18 at 19:53
$begingroup$
No doubt that $s$ is a complex variable in Laplace transform. Decomposing it into $sigma+jomega$ way is dangerous because it tends to say (what you find in old books) that setting $sigma=0$ you can reach the Fourier Transform. The best way to consider the $s$ in a Laplace Transform is as a purely formal parameter.
$endgroup$
– Jean Marie
Dec 12 '18 at 19:53
$begingroup$
Thank you Jean! Great answer :D
$endgroup$
– Danny
Dec 12 '18 at 21:38
$begingroup$
Thank you Jean! Great answer :D
$endgroup$
– Danny
Dec 12 '18 at 21:38
add a comment |
0
active
oldest
votes
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3036841%2ftransfer-function-what-does-s-stand-for%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3036841%2ftransfer-function-what-does-s-stand-for%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
$begingroup$
Check out the Wikipedia Transfer Function page. I don't know what a "short period pole" is, but the other two definitions seem correct to me (even if not providing much insight).
$endgroup$
– NickD
Dec 12 '18 at 15:55
$begingroup$
Thanks, I appreciate the second opinion, you'd be surprised how hard it is to google any variation of "transfer function s" since every webpage has an s in it :)
$endgroup$
– Danny
Dec 12 '18 at 15:58
1
$begingroup$
No doubt that $s$ is a complex variable in Laplace transform. Decomposing it into $sigma+jomega$ way is dangerous because it tends to say (what you find in old books) that setting $sigma=0$ you can reach the Fourier Transform. The best way to consider the $s$ in a Laplace Transform is as a purely formal parameter.
$endgroup$
– Jean Marie
Dec 12 '18 at 19:53
$begingroup$
Thank you Jean! Great answer :D
$endgroup$
– Danny
Dec 12 '18 at 21:38