# Nyquist Rate (Sampling Frequency) for ${f}^{2} \left( x, y \right)$

We are given that $$f(x,y)$$ is highest frequency is $$\omega$$ what will be the frequency sample rate if we want to restore the function of the form $$g(x,y)=f^2(x,y)$$

Would it be correct to say that because $$\sin^2x=1-\cos 2x$$, we will have to sample it at $$4\pi$$ ?

• $f(x,y)$ is a function of two variables. If you are referring to "signal functions" then this is likely to be $y_1 = f(t), y_2 = g(t)$. On whether your reasoning is correct, I can tell you that it is down the right track (although, that is not exactly $\sin^2(x)$) but what if the input signal is not a simple sinusoid?
– A_A
Jan 23, 2019 at 18:27
• @A_A it is an image
– gbox
Jan 23, 2019 at 19:07
• Nice twist. What are your thoughts about $f(x,y)$ being a squared "image"? What is the role of spatial resolution in this case?
– A_A
Jan 23, 2019 at 19:31
• @A_A Sorry, I do not understand $f(x,y)$ is let say an $N$ by $N$ matrix of 256 gray values. So it is a sampling $N^2$ times, I think
– gbox
Jan 23, 2019 at 20:03