Trying to interpret Fourier transform correctly, using the Heaviside function as an example.
up vote
0
down vote
favorite
I'm new to Fourier transforms. Say $f(t) = H(5-|t|)$, with $H$ the Heaviside function. Then $F(omega) = dfrac{2sin(5omega)}{omega}$. I understand how we get this result. I'd just like to know how to interpret the graphs below. If I understand correctly, the second plot, $F(omega)$, tells us how 'common' the frequencies (represented on the $x$-axis of the second plot) are in $f(t)$, the first plot. But why is there a spike at $0$ in $F(omega)$? Does this mean the frequency of $0$ is common in $f(t)$? What does this mean? And why is there a peak at $1$ and $-1$ and why is $F(omega) = 0$ for $omega = 5$? I just don't get how to interpret the information the plot of $F(omega)$ gives about $f(t)$.
analysis fourier-analysis fourier-transform
asked Nov 18 at 13:33
Surzilla
1238
add a comment |
up vote
0
down vote
favorite
I'm new to Fourier transforms. Say $f(t) = H(5-|t|)$, with $H$ the Heaviside function. Then $F(omega) = dfrac{2sin(5omega)}{omega}$. I understand how we get this result. I'd just like to know how to interpret the graphs below. If I understand correctly, the second plot, $F(omega)$, tells us how 'common' the frequencies (represented on the $x$-axis of the second plot) are in $f(t)$, the first plot. But why is there a spike at $0$ in $F(omega)$? Does this mean the frequency of $0$ is common in $f(t)$? What does this mean? And why is there a peak at $1$ and $-1$ and why is $F(omega) = 0$ for $omega = 5$? I just don't get how to interpret the information the plot of $F(omega)$ gives about $f(t)$.
analysis fourier-analysis fourier-transform
asked Nov 18 at 13:33
Surzilla
1238
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm new to Fourier transforms. Say $f(t) = H(5-|t|)$, with $H$ the Heaviside function. Then $F(omega) = dfrac{2sin(5omega)}{omega}$. I understand how we get this result. I'd just like to know how to interpret the graphs below. If I understand correctly, the second plot, $F(omega)$, tells us how 'common' the frequencies (represented on the $x$-axis of the second plot) are in $f(t)$, the first plot. But why is there a spike at $0$ in $F(omega)$? Does this mean the frequency of $0$ is common in $f(t)$? What does this mean? And why is there a peak at $1$ and $-1$ and why is $F(omega) = 0$ for $omega = 5$? I just don't get how to interpret the information the plot of $F(omega)$ gives about $f(t)$.
analysis fourier-analysis fourier-transform
asked Nov 18 at 13:33
Surzilla
1238
I'm new to Fourier transforms. Say $f(t) = H(5-|t|)$, with $H$ the Heaviside function. Then $F(omega) = dfrac{2sin(5omega)}{omega}$. I understand how we get this result. I'd just like to know how to interpret the graphs below. If I understand correctly, the second plot, $F(omega)$, tells us how 'common' the frequencies (represented on the $x$-axis of the second plot) are in $f(t)$, the first plot. But why is there a spike at $0$ in $F(omega)$? Does this mean the frequency of $0$ is common in $f(t)$? What does this mean? And why is there a peak at $1$ and $-1$ and why is $F(omega) = 0$ for $omega = 5$? I just don't get how to interpret the information the plot of $F(omega)$ gives about $f(t)$.
analysis fourier-analysis fourier-transform
analysis fourier-analysis fourier-transform
asked Nov 18 at 13:33
Surzilla
1238
asked Nov 18 at 13:33
Surzilla
1238
asked Nov 18 at 13:33
Surzilla
1238
asked Nov 18 at 13:33
Surzilla
1238
asked Nov 18 at 13:33
Surzilla
1238
1238
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3003534%2ftrying-to-interpret-fourier-transform-correctly-using-the-heaviside-function-as%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
