Trying to interpret Fourier transform correctly, using the Heaviside function as an example.
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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
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up vote
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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 |
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