Calculating a periodic signal (way of solving this)?
$begingroup$
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
$endgroup$
|
show 1 more comment
$begingroup$
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
$endgroup$
$begingroup$
What is $Pi?$ Do you mean the number $pi?$
$endgroup$
– saulspatz
Dec 26 '18 at 16:47
$begingroup$
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
$endgroup$
– Agaeus
Dec 26 '18 at 18:20
$begingroup$
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
$endgroup$
– saulspatz
Dec 26 '18 at 20:46
$begingroup$
well yeah that's it saulspatz.
$endgroup$
– Agaeus
Dec 26 '18 at 21:55
1
$begingroup$
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
$endgroup$
– Paul Sinclair
Dec 27 '18 at 1:31
|
show 1 more comment
$begingroup$
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
$endgroup$
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
edited Dec 26 '18 at 22:34
saulspatz
15.6k31331
15.6k31331
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
asked Dec 26 '18 at 14:09
AgaeusAgaeus
626
626
$begingroup$
What is $Pi?$ Do you mean the number $pi?$
$endgroup$
– saulspatz
Dec 26 '18 at 16:47
$begingroup$
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
$endgroup$
– Agaeus
Dec 26 '18 at 18:20
$begingroup$
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
$endgroup$
– saulspatz
Dec 26 '18 at 20:46
$begingroup$
well yeah that's it saulspatz.
$endgroup$
– Agaeus
Dec 26 '18 at 21:55
1
$begingroup$
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
$endgroup$
– Paul Sinclair
Dec 27 '18 at 1:31
|
show 1 more comment
$begingroup$
What is $Pi?$ Do you mean the number $pi?$
$endgroup$
– saulspatz
Dec 26 '18 at 16:47
$begingroup$
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
$endgroup$
– Agaeus
Dec 26 '18 at 18:20
$begingroup$
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
$endgroup$
– saulspatz
Dec 26 '18 at 20:46
$begingroup$
well yeah that's it saulspatz.
$endgroup$
– Agaeus
Dec 26 '18 at 21:55
1
$begingroup$
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
$endgroup$
– Paul Sinclair
Dec 27 '18 at 1:31
$begingroup$
What is $Pi?$ Do you mean the number $pi?$
$endgroup$
– saulspatz
Dec 26 '18 at 16:47
$begingroup$
What is $Pi?$ Do you mean the number $pi?$
$endgroup$
– saulspatz
Dec 26 '18 at 16:47
$begingroup$
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
$endgroup$
– Agaeus
Dec 26 '18 at 18:20
$begingroup$
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
$endgroup$
– Agaeus
Dec 26 '18 at 18:20
$begingroup$
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
$endgroup$
– saulspatz
Dec 26 '18 at 20:46
$begingroup$
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
$endgroup$
– saulspatz
Dec 26 '18 at 20:46
$begingroup$
well yeah that's it saulspatz.
$endgroup$
– Agaeus
Dec 26 '18 at 21:55
$begingroup$
well yeah that's it saulspatz.
$endgroup$
– Agaeus
Dec 26 '18 at 21:55
1
1
$begingroup$
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
$endgroup$
– Paul Sinclair
Dec 27 '18 at 1:31
$begingroup$
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
$endgroup$
– Paul Sinclair
Dec 27 '18 at 1:31
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
$endgroup$
add a comment |
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%2f3052969%2fcalculating-a-periodic-signal-way-of-solving-this%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
$begingroup$
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
$endgroup$
add a comment |
$begingroup$
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
$endgroup$
add a comment |
$begingroup$
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
$endgroup$
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
answered Jan 3 at 21:57
alexjoalexjo
12.5k1430
12.5k1430
add a comment |
add a comment |
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%2f3052969%2fcalculating-a-periodic-signal-way-of-solving-this%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
$begingroup$
What is $Pi?$ Do you mean the number $pi?$
$endgroup$
– saulspatz
Dec 26 '18 at 16:47
$begingroup$
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
$endgroup$
– Agaeus
Dec 26 '18 at 18:20
$begingroup$
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
$endgroup$
– saulspatz
Dec 26 '18 at 20:46
$begingroup$
well yeah that's it saulspatz.
$endgroup$
– Agaeus
Dec 26 '18 at 21:55
1
$begingroup$
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
$endgroup$
– Paul Sinclair
Dec 27 '18 at 1:31