Why is the maximum signal frequency here labeled as 1/2? Does it depend on the units, and what are they?
Yes, it does depend on the units. Here, on the frequency domain diagram, the units I've chosen are "samples per pixel".
Each pixel in the original image is a sample, so the sampling frequency is 1 (sample per pixel). Then the Nyquist frequency is 1/2 the sampling rate, so 1/2 * 1 (samples per pixel). This Nyquist frequency is the maximum frequency at the point furthest from the origin on the frequency domain.
This is a bit abstract, but one nice effect of this choice of units is that the maximum signal frequency is 1/2 regardless of the physical size or pixel resolution of the image. Why?
Staffyirenng
All this said, it is a helpful exercise to reason about what the sampling frequency and Nyquist frequency are while considering the actual size of the photograph and number of pixels in the image.
As an example, assume the width of the photograph is 3 centimeters, and it has a pixel resolution of N \cross N. What are the sampling frequency and Nyquist frequency of the photograph, in SI units?
Why is the maximum signal frequency here labeled as 1/2? Does it depend on the units, and what are they?
Yes, it does depend on the units. Here, on the frequency domain diagram, the units I've chosen are "samples per pixel".
Each pixel in the original image is a sample, so the sampling frequency is 1 (sample per pixel). Then the Nyquist frequency is 1/2 the sampling rate, so 1/2 * 1 (samples per pixel). This Nyquist frequency is the maximum frequency at the point furthest from the origin on the frequency domain.
This is a bit abstract, but one nice effect of this choice of units is that the maximum signal frequency is 1/2 regardless of the physical size or pixel resolution of the image. Why?
All this said, it is a helpful exercise to reason about what the sampling frequency and Nyquist frequency are while considering the actual size of the photograph and number of pixels in the image.
As an example, assume the width of the photograph is 3 centimeters, and it has a pixel resolution of N \cross N. What are the sampling frequency and Nyquist frequency of the photograph, in SI units?