Is there an analogue of the Fourier transform based on hyperbolic trig functions?
1
$begingroup$
Is there something analogous to Fourier series or the Fourier transform but which is based on hyperbolic trig functions rather than $sin, cos$, and $exp$?
fourier-analysis hyperbolic-functions
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
$endgroup$
add a comment |
1
$begingroup$
Is there something analogous to Fourier series or the Fourier transform but which is based on hyperbolic trig functions rather than $sin, cos$, and $exp$?
fourier-analysis hyperbolic-functions
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
$endgroup$
$begingroup$
In some sense the analogue is the Laplace transform, that is the analytic continuation of the Fourier transform
$endgroup$
– reuns
Dec 19 '18 at 10:47
add a comment |
1
1
1
$begingroup$
Is there something analogous to Fourier series or the Fourier transform but which is based on hyperbolic trig functions rather than $sin, cos$, and $exp$?
fourier-analysis hyperbolic-functions
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
$endgroup$
Is there something analogous to Fourier series or the Fourier transform but which is based on hyperbolic trig functions rather than $sin, cos$, and $exp$?
fourier-analysis hyperbolic-functions
fourier-analysis hyperbolic-functions
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
asked Dec 19 '18 at 10:34
eternalGoldenBraideternalGoldenBraid
739314
739314
$begingroup$
In some sense the analogue is the Laplace transform, that is the analytic continuation of the Fourier transform
$endgroup$
– reuns
Dec 19 '18 at 10:47
add a comment |
$begingroup$
In some sense the analogue is the Laplace transform, that is the analytic continuation of the Fourier transform
$endgroup$
– reuns
Dec 19 '18 at 10:47
$begingroup$
In some sense the analogue is the Laplace transform, that is the analytic continuation of the Fourier transform
$endgroup$
– reuns
Dec 19 '18 at 10:47
$begingroup$
In some sense the analogue is the Laplace transform, that is the analytic continuation of the Fourier transform
$endgroup$
– reuns
Dec 19 '18 at 10:47
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
});
}
});
draft saved
draft discarded
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%2f3046248%2fis-there-an-analogue-of-the-fourier-transform-based-on-hyperbolic-trig-functions%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
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
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%2f3046248%2fis-there-an-analogue-of-the-fourier-transform-based-on-hyperbolic-trig-functions%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
$begingroup$
In some sense the analogue is the Laplace transform, that is the analytic continuation of the Fourier transform
$endgroup$
– reuns
Dec 19 '18 at 10:47