I'm still confused about how to read and create visual frequency spectrums. Is the first term of f(x) stuck only at frequency x because of its term? Is the actual amplitude only based on the constant factor multiplied to the sinusoidal term? Does each term only have one frequency they are at in the frequency spectrum graph?
mpotoole
Exactly. $f(x)$ is the sum of two terms: $\sin(2\pi k x)$ and $\frac{1}{3} \sin(2\pi 3k x)$. To compute the frequency spectrum, we pull out (i) the frequency of each term (in this case it's $k$ and $3k$), and (ii) the amplitude of each term (in this case it's $1$ and $\frac{1}{3}$. The value of the spectrum at $k$ is therefore $1$, and the value at $3k$ is $\frac{1}{3}$.
I'm still confused about how to read and create visual frequency spectrums. Is the first term of f(x) stuck only at frequency x because of its term? Is the actual amplitude only based on the constant factor multiplied to the sinusoidal term? Does each term only have one frequency they are at in the frequency spectrum graph?
Exactly. $f(x)$ is the sum of two terms: $\sin(2\pi k x)$ and $\frac{1}{3} \sin(2\pi 3k x)$. To compute the frequency spectrum, we pull out (i) the frequency of each term (in this case it's $k$ and $3k$), and (ii) the amplitude of each term (in this case it's $1$ and $\frac{1}{3}$. The value of the spectrum at $k$ is therefore $1$, and the value at $3k$ is $\frac{1}{3}$.