I think I heard this being said in class but I want to make sure: Is this the same as saying there are at least two data points within each period of the signal?
motoole2
Yes exactly. I want to ensure that my sample rate is double that of the maximum frequency.
Let's use an example to work through this. Suppose that I have a signal $g(x) = A \sin(10*x)$ and the domain is $x \in [0, 2\pi]$; therefore $f_{max} = 10$. I would need to sample this function at double the highest frequency to avoid aliasing, i.e., $f_s = 20$. In other words, I need two samples within each period of this sinusoidal signal to ensure that I am sampling at the Nyquist frequency (or higher).
I think I heard this being said in class but I want to make sure: Is this the same as saying there are at least two data points within each period of the signal?
Yes exactly. I want to ensure that my sample rate is double that of the maximum frequency.
Let's use an example to work through this. Suppose that I have a signal $g(x) = A \sin(10*x)$ and the domain is $x \in [0, 2\pi]$; therefore $f_{max} = 10$. I would need to sample this function at double the highest frequency to avoid aliasing, i.e., $f_s = 20$. In other words, I need two samples within each period of this sinusoidal signal to ensure that I am sampling at the Nyquist frequency (or higher).