Find the sampling matrix and sampling structure for R, G and B components

In summary, the conversation discusses lattices and their notation, as well as using matrices for image rotation. The speaker is seeking input on how to rotate matrices and is wary of links due to suspicious pop-ups.
  • #1
s3a
818
8
Homework Statement
The sub-questions of the question are on page 1 of this document ( https://www.docdroid.net/3iFwpy1/q2-plus-answers.pdf ), and the answers are on page 3 of the same document.
Relevant Equations
Three different pages in the same set of slides:
https://www.docdroid.net/gCTFghi/ft-msampling.pdf#page=80

https://www.docdroid.net/gCTFghi/ft-msampling.pdf#page=83

https://www.docdroid.net/gCTFghi/ft-msampling.pdf#page=84

Wikipedia article which provides the equation for the two-dimensional rotation matrix:
https://en.wikipedia.org/wiki/Rotation_matrix
Hello, everyone. :)

All I could gather is that, if I'm correct, lattices are spans of the column vectors of the matrix within the "LAT()" notation and the X and Y occurrences are unit placeholders (such as the pixel unit (since this is in the context of image processing)).

And, as an attempt to try to figure out how to do parts a and b, I'm trying to use the matrices from the Wikipedia link above to rotate the answers by –45° (and also +45°, just in case) (by left-multiplying the vectors and non-vector matrices with the rotation matrix), but doing that doesn't yield any vector or non-vector matrix from the slides which has the same ratio among its elements.

Any input would be GREATLY appreciated!
 
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  • #2
Can you type the formulas, in question, or at least provide screenshots. I do not trust these sites you are linking to. It has some suspicious pop-ups.
 
  • #3
Thread locked.
@s3a, please repost the pictures inline rather than as links to web sites. As @scottdave points out, that web set displays the images with some phishy popups.
 

1. What is a sampling matrix?

A sampling matrix is a mathematical representation of the sampling process used to convert analog signals, such as those from a camera's sensor, into digital signals.

2. Why is a sampling matrix needed for R, G, and B components?

R, G, and B components represent the red, green, and blue color channels of an image. A sampling matrix is needed to accurately capture and represent the color information in each channel.

3. How is the sampling matrix determined for R, G, and B components?

The sampling matrix for R, G, and B components is determined by the sampling rate, which is the frequency at which samples are taken, and the sampling resolution, which is the number of bits used to represent each sample.

4. What is the sampling structure for R, G, and B components?

The sampling structure for R, G, and B components is typically a grid pattern, where each pixel in the image corresponds to a specific location on the grid. The sampling rate and resolution determine the size and spacing of the grid.

5. How does the sampling matrix and sampling structure affect the quality of an image?

The sampling matrix and sampling structure play a crucial role in the quality of an image. A higher sampling rate and resolution can result in a more detailed and accurate representation of the image, while a lower sampling rate and resolution can lead to loss of information and a lower quality image.

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