Mixing
![Is strong law of large numbers an improvement of weak law of large numbers? [on hold]](https://lh6.googleusercontent.com/-2VRrQn9dfZc/AAAAAAAAAAI/AAAAAAAAAAA/ABtNlbDXC1BXRGIU0vkLBUJ_j4DmiXYJgg/s72-c-mo/photo.jpg?sz=32)
Autocorrelation and spectral density in MATLAB
$begingroup$
This question is twofold.
We have an LTI system that is a first degree Butterworth LP filter with the power TF
where fu = 110Hz and f1 = 90Hz
The input X(t) has the autocorrelation: R_X(tau) = 5e^{-600|tau|}
1) How can I calculate the power spectral density of the output in MATLAB? FFT? How do I represent the autocorrelation as a vector?
2) How can I simulate the system and plot the output in MATLAB?
matlab correlation
asked Apr 12 '14 at 11:11
dingaridingari
94212
$endgroup$
migrated from stackoverflow.com Apr 13 '14 at 22:13
This question came from our site for professional and enthusiast programmers.
add a comment |
$begingroup$
This question is twofold.
We have an LTI system that is a first degree Butterworth LP filter with the power TF
where fu = 110Hz and f1 = 90Hz
The input X(t) has the autocorrelation: R_X(tau) = 5e^{-600|tau|}
1) How can I calculate the power spectral density of the output in MATLAB? FFT? How do I represent the autocorrelation as a vector?
2) How can I simulate the system and plot the output in MATLAB?
matlab correlation
asked Apr 12 '14 at 11:11
dingaridingari
94212
$endgroup$
migrated from stackoverflow.com Apr 13 '14 at 22:13
This question came from our site for professional and enthusiast programmers.
$begingroup$
mathworks.se/help/signal/ug/psd-estimate-using-fft.html
$endgroup$
– tashuhka
Apr 12 '14 at 13:57
$begingroup$
possible duplicate of Calculate autocorrelation using FFT in matlab
$endgroup$
– tashuhka
Apr 12 '14 at 13:58
$begingroup$
I thought I had posted this in math.stackexhange, oh well.
$endgroup$
– dingari
Apr 12 '14 at 17:12
add a comment |
$begingroup$
This question is twofold.
We have an LTI system that is a first degree Butterworth LP filter with the power TF
where fu = 110Hz and f1 = 90Hz
The input X(t) has the autocorrelation: R_X(tau) = 5e^{-600|tau|}
1) How can I calculate the power spectral density of the output in MATLAB? FFT? How do I represent the autocorrelation as a vector?
2) How can I simulate the system and plot the output in MATLAB?
matlab correlation
asked Apr 12 '14 at 11:11
dingaridingari
94212
$endgroup$
This question is twofold.
We have an LTI system that is a first degree Butterworth LP filter with the power TF
where fu = 110Hz and f1 = 90Hz
The input X(t) has the autocorrelation: R_X(tau) = 5e^{-600|tau|}
1) How can I calculate the power spectral density of the output in MATLAB? FFT? How do I represent the autocorrelation as a vector?
2) How can I simulate the system and plot the output in MATLAB?
matlab correlation
matlab correlation
asked Apr 12 '14 at 11:11
dingaridingari
94212
asked Apr 12 '14 at 11:11
dingaridingari
94212
asked Apr 12 '14 at 11:11
dingaridingari
94212
asked Apr 12 '14 at 11:11
dingaridingari
94212
asked Apr 12 '14 at 11:11
dingaridingari
94212
94212
migrated from stackoverflow.com Apr 13 '14 at 22:13
This question came from our site for professional and enthusiast programmers.
migrated from stackoverflow.com Apr 13 '14 at 22:13
This question came from our site for professional and enthusiast programmers.
$begingroup$
mathworks.se/help/signal/ug/psd-estimate-using-fft.html
$endgroup$
– tashuhka
Apr 12 '14 at 13:57
$begingroup$
possible duplicate of Calculate autocorrelation using FFT in matlab
$endgroup$
– tashuhka
Apr 12 '14 at 13:58
$begingroup$
I thought I had posted this in math.stackexhange, oh well.
$endgroup$
– dingari
Apr 12 '14 at 17:12
add a comment |
$begingroup$
mathworks.se/help/signal/ug/psd-estimate-using-fft.html
$endgroup$
– tashuhka
Apr 12 '14 at 13:57
$begingroup$
possible duplicate of Calculate autocorrelation using FFT in matlab
$endgroup$
– tashuhka
Apr 12 '14 at 13:58
$begingroup$
I thought I had posted this in math.stackexhange, oh well.
$endgroup$
– dingari
Apr 12 '14 at 17:12
$begingroup$
mathworks.se/help/signal/ug/psd-estimate-using-fft.html
$endgroup$
– tashuhka
Apr 12 '14 at 13:57
$begingroup$
mathworks.se/help/signal/ug/psd-estimate-using-fft.html
$endgroup$
– tashuhka
Apr 12 '14 at 13:57
$begingroup$
possible duplicate of Calculate autocorrelation using FFT in matlab
$endgroup$
– tashuhka
Apr 12 '14 at 13:58
$begingroup$
possible duplicate of Calculate autocorrelation using FFT in matlab
$endgroup$
– tashuhka
Apr 12 '14 at 13:58
$begingroup$
I thought I had posted this in math.stackexhange, oh well.
$endgroup$
– dingari
Apr 12 '14 at 17:12
$begingroup$
I thought I had posted this in math.stackexhange, oh well.
$endgroup$
– dingari
Apr 12 '14 at 17:12
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
To calculate the Autocorrelation of the output:
R_y = xcorr(y); % with Y(f) = X(f).H(f) or y(t) = x(t)*h(t)
To calculate the P.S.D of the output:
PSD_y = fft (R_y);
To reprensent them graphically, you can use plot
if you do not have the x(t) or X(f) expressions, you could use this relation:
PSD_y (f) = PSD_x (f) . |H(f)|^2 % with PSD_x (f) = fft(R_x);
$endgroup$
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
you meanPSD_y = abs(fft(y)).^2possibly with zero paddingPSD_y = abs(fft(y, 2*length(y))).^2
$endgroup$
– reuns
Oct 11 '16 at 0:12
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%2f752473%2fautocorrelation-and-spectral-density-in-matlab%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
$begingroup$
To calculate the Autocorrelation of the output:
R_y = xcorr(y); % with Y(f) = X(f).H(f) or y(t) = x(t)*h(t)
To calculate the P.S.D of the output:
PSD_y = fft (R_y);
To reprensent them graphically, you can use plot
if you do not have the x(t) or X(f) expressions, you could use this relation:
PSD_y (f) = PSD_x (f) . |H(f)|^2 % with PSD_x (f) = fft(R_x);
$endgroup$
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
you meanPSD_y = abs(fft(y)).^2possibly with zero paddingPSD_y = abs(fft(y, 2*length(y))).^2
$endgroup$
– reuns
Oct 11 '16 at 0:12
add a comment |
$begingroup$
To calculate the Autocorrelation of the output:
R_y = xcorr(y); % with Y(f) = X(f).H(f) or y(t) = x(t)*h(t)
To calculate the P.S.D of the output:
PSD_y = fft (R_y);
To reprensent them graphically, you can use plot
if you do not have the x(t) or X(f) expressions, you could use this relation:
PSD_y (f) = PSD_x (f) . |H(f)|^2 % with PSD_x (f) = fft(R_x);
$endgroup$
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
you meanPSD_y = abs(fft(y)).^2possibly with zero paddingPSD_y = abs(fft(y, 2*length(y))).^2
$endgroup$
– reuns
Oct 11 '16 at 0:12
add a comment |
$begingroup$
To calculate the Autocorrelation of the output:
R_y = xcorr(y); % with Y(f) = X(f).H(f) or y(t) = x(t)*h(t)
To calculate the P.S.D of the output:
PSD_y = fft (R_y);
To reprensent them graphically, you can use plot
if you do not have the x(t) or X(f) expressions, you could use this relation:
PSD_y (f) = PSD_x (f) . |H(f)|^2 % with PSD_x (f) = fft(R_x);
$endgroup$
To calculate the Autocorrelation of the output:
R_y = xcorr(y); % with Y(f) = X(f).H(f) or y(t) = x(t)*h(t)
To calculate the P.S.D of the output:
PSD_y = fft (R_y);
To reprensent them graphically, you can use plot
if you do not have the x(t) or X(f) expressions, you could use this relation:
PSD_y (f) = PSD_x (f) . |H(f)|^2 % with PSD_x (f) = fft(R_x);
answered Apr 12 '14 at 11:29
user51886
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
you meanPSD_y = abs(fft(y)).^2possibly with zero paddingPSD_y = abs(fft(y, 2*length(y))).^2
$endgroup$
– reuns
Oct 11 '16 at 0:12
add a comment |
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
you meanPSD_y = abs(fft(y)).^2possibly with zero paddingPSD_y = abs(fft(y, 2*length(y))).^2
$endgroup$
– reuns
Oct 11 '16 at 0:12
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
I have the autocorrelation of X, but I don't know the actual x. How can I do this given the autocorrelation?
$endgroup$
– dingari
Apr 12 '14 at 11:50
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
see my updated answer, and let me know if it worked. thx
$endgroup$
– user51886
Apr 12 '14 at 13:59
$begingroup$
you mean
PSD_y = abs(fft(y)).^2 possibly with zero padding PSD_y = abs(fft(y, 2*length(y))).^2$endgroup$
– reuns
Oct 11 '16 at 0:12
$begingroup$
you mean
PSD_y = abs(fft(y)).^2 possibly with zero padding PSD_y = abs(fft(y, 2*length(y))).^2$endgroup$
– reuns
Oct 11 '16 at 0:12
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%2f752473%2fautocorrelation-and-spectral-density-in-matlab%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
$begingroup$
mathworks.se/help/signal/ug/psd-estimate-using-fft.html
$endgroup$
– tashuhka
Apr 12 '14 at 13:57
$begingroup$
possible duplicate of Calculate autocorrelation using FFT in matlab
$endgroup$
– tashuhka
Apr 12 '14 at 13:58
$begingroup$
I thought I had posted this in math.stackexhange, oh well.
$endgroup$
– dingari
Apr 12 '14 at 17:12