2d fourier analysis of shapes

In summary, the conversation discusses a question on a graphical 2d Fourier transform that is often included in old exams for a physical measuring techniques course. The solution involves taking the transform of the surrounding shape, the grid, and the shape of the grid. This approach does not have a specific name and is not mentioned in the course literature or on the internet. However, there is a promising resource that may provide more information on this approach.
  • #1
hadoque
43
1
I'm studying for a re-examn in a physical measuring techniques course that includes some Fourier analysis. On old exams there are always a question about a graphical 2d Fourier transform. It can be an ellipse containing a grid of circels, or something like that. In the solutions he takes the transform of the surrounding shape, the grid and the shape of the grid.
I can't find any information about this approach the course litterature (The Fourier Transform & Its Applications) nor on the internet. Does this approach have a name, and does anyone know of information about this?

Thanks
 
Physics news on Phys.org
  • #2
For anybody with a similar question:
https://www.ncurproceedings.org/ojs/index.php/NCUR2012/article/download/241/207
looks promising.
 

1. What is 2D Fourier analysis of shapes?

2D Fourier analysis is a mathematical technique used to analyze the shape and spatial frequencies of an object or image in two dimensions. It involves breaking down the shape into its constituent sine and cosine components, which can reveal information about its orientation, size, and complexity.

2. How is 2D Fourier analysis different from 1D Fourier analysis?

In 1D Fourier analysis, the shape or signal is analyzed along a single axis. In 2D Fourier analysis, the shape is analyzed in both the x and y dimensions, providing a more complete understanding of its features and characteristics.

3. What types of shapes can be analyzed using 2D Fourier analysis?

2D Fourier analysis can be applied to any type of shape, including simple geometric shapes, natural objects, and complex patterns. It is particularly useful for analyzing irregular or asymmetric shapes.

4. What information can be obtained from 2D Fourier analysis of shapes?

2D Fourier analysis can provide information about the orientation, size, and complexity of a shape. It can also reveal any repeating patterns or symmetries present in the shape.

5. How is 2D Fourier analysis used in practical applications?

2D Fourier analysis has a wide range of practical applications, including image processing, pattern recognition, and shape analysis in fields such as biology, geology, and engineering. It is also used in the design of filters and other signal processing techniques.

Similar threads

Replies
11
Views
806
Replies
1
Views
2K
  • Topology and Analysis
Replies
1
Views
4K
  • STEM Academic Advising
Replies
2
Views
2K
  • STEM Academic Advising
Replies
4
Views
1K
  • STEM Academic Advising
Replies
6
Views
743
Replies
2
Views
767
  • Electrical Engineering
Replies
4
Views
3K
  • Beyond the Standard Models
Replies
14
Views
3K
  • Mechanical Engineering
Replies
1
Views
3K
Back
Top