Understanding the Differences between 2D FFT and 2D DFT for Image Transforms

In summary, the person is confused about the third transform in a picture and why it appears distorted compared to the other two transforms. They mention that the distortion is related to discontinuous lines in a grid and ask for help understanding the relation. Another person suggests it could be a bug in their code and shares a link with an explanation of "rotation and edge effects" in the Fourier transform.
  • #1
nylonman
11
0
Confusion with 2D DFT

Hello everyone,

I'm trying to figure out why the third transform in the picture I attach here is different to the other ones, why it's 'distorted'. I know that it's related with the fact that if you copy the image in a grid the resulting image has discontinuous lines, unlike the other two transforms where the resulting lines are continuous, but I can't see the relation with the distortion.

Thank you for any help!
 

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  • #2
Could it just be a bug in your code?
 
  • #3

1. What is a 2D FFT and how does it work?

The 2D FFT (Fast Fourier Transform) is a mathematical algorithm used for analyzing and processing two-dimensional signals or images. It decomposes a two-dimensional signal into its frequency components, allowing for the identification of patterns and structures within the signal. It works by breaking down the signal into smaller sections, applying the Fourier transform to each section, and then combining the results to reconstruct the original signal.

2. What are some common sources of confusion when using a 2D FFT?

One common source of confusion when using a 2D FFT is understanding the relationship between the original signal and its frequency components. Another is correctly interpreting the results of the FFT and understanding how they relate to the original signal. Additionally, understanding the different parameters and settings that can affect the output of the 2D FFT can also be a source of confusion.

3. What types of signals or images can be analyzed using a 2D FFT?

A 2D FFT can be applied to any two-dimensional signal or image, including sound waves, images, and data sets. It is commonly used in fields such as signal processing, image processing, and data analysis to identify patterns and structures in the data.

4. How can I use a 2D FFT to improve my data analysis?

A 2D FFT can be used to identify hidden patterns and structures in data that may not be apparent when looking at the raw data. By decomposing the data into its frequency components, it can reveal underlying trends and relationships that can aid in data analysis and decision making.

5. Are there any limitations to using a 2D FFT?

While a 2D FFT can be a powerful tool for analyzing two-dimensional signals and images, it does have some limitations. It assumes that the signal is stationary, meaning that it does not change over time. It also assumes that the signal is periodic, meaning that it repeats itself. If these assumptions are not met, the results of the FFT may not accurately reflect the original signal.

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