Questions tagged [2d]
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68 questions
0 votes
0 answers
30 views
reconstruct a signal - help with understanding a question
I need your help with the following question: I can see tht there is kind of a convolution here together with sampling, but I can not understand how to solve it. It is quite difficult for me to see ...
- 11
1 vote
1 answer
97 views
What is the Fourier Transform integral equation for a 1D signal and how can it be expanded into 2D, 3D, and 4D?
I know that is the 1D Fourier Transform (FT), and the 2D FT is and 3D FT is , but I am not sure whether these expressions are in fact Fourier transform integral equations for a 1D signal, expanded ...
- 13
2 votes
1 answer
501 views
2D Fourier transform of an element-wise product of two matrices
I wonder if there is any known formula to describe a 2D Fourier transform of an element-wise product, i.e., Hadamard product, of two matrices. Let $\odot$ is the Hadamard product operator, and there ...
- 53
1 vote
0 answers
144 views
Discrete Fourier transform of a 2D exponential decay
The Discrete Fourier transform of a 1D discrete decay function $d[n]=e^{-a n}$ is simply computed as the sum of a geometric series: $$\tilde{d}[k] = \sum_{n=0}^{N-1}e^{-a n}e^{2 j \pi n k/N} = \frac{1-...
- 11
1 vote
0 answers
565 views
range-doppler map of FMCW radar
I have created a 2D matrix with L as the number of samples and K as the number of chirps. Now I am trying to plot the Range-Doppler response which doesn't correspond to the correct range and velocity ...
- 11
1 vote
0 answers
159 views
calibrating camera using 3d objects such as rubik's cube?
Hello all hope everyone is doing fine. I have a vision related problem where I want to calibrate my camera using a 3d object such as rubik's cube with known dimensions. I have a cube with 60mm length, ...
- 11
2 votes
0 answers
76 views
Geometric Transformation of Distorted Grid Lines Using Image Processing
If the grid-lines in the image (attached: distort1.jpeg) are distorted and squares in image appears distorted a bit. What would be the best and easy approach to convert them to perfect squares (as ...
- 21
1 vote
1 answer
302 views
Why does the 2D-DFT of a sinus gradient not show energy along the diagonal straigh lines and only vertical/horizontal from the diagonal point?
I have been experimenting a little bit with simple examples of the 2D DFT to get a better sense for it's interpretation. For this purpose I have been using sinus gratings with the following code: <...
- 327
5 votes
1 answer
3k views
Applying a 2D Convolution Using 2D FFT
So I was following the article Victor Podlozhnyuk (nVidia) - FFT Based 2D Convolution (Page 7). I have expanded the kernel to the correct way they have done it. However when it comes to the part on ...
- 95
0 votes
0 answers
339 views
How to get the phase of a 2D sine wave?
I am trying to find the phase of a generic 2D sine wave with the 2D FFT. The formula for the phase is arctan(im/re). So I made 22 sine waves with phases ranging from 0 to 2 pi (by cropping the ...
- 1
1 vote
1 answer
463 views
How can extract the cosine transform formula used for 2D by scipy.fft.dct
For the 1D cosine transform the documentation is clear in here, and I can reproduce it easily: The formula is: $$y_k= 2 \sum_{n=0}^{N-1}x_n \cos \left( \frac{\pi k(2n + 1)}{2N}\right)$$ and here it is ...
- 443
1 vote
0 answers
557 views
2D Deconvolution using a non-gaussian mask using C++
I am currently working on a project, where we record an electron beam profile using a target. The obtained image is a result of convolution of the actual beam profile and the aperture wherein the ...
- 11
2 votes
2 answers
151 views
How could I approach determining if this 2D system represented as a 2D summation formula is linear?
I have a given 2D system: $$y(m,n) = \sum_{k_1=-\infty}^{m} \sum_{k_2=-\infty}^{n} x(k_1,k_2)$$ My usual approach to determining if a system is linear is to test if it is homogeneous and additive. ...
- 123
1 vote
0 answers
118 views
Calculate sampling lattice matrix in 2D
The pattern in which the sample points are distributed in 2 dims, is called a sampling lattice, and can be defined by a generator matrix.. In 2 dimensions, the generator matrix consists of 2 vectors. ...
0 votes
1 answer
612 views
how to interpret the 2D FFT
I know how to compute the 1D FFT (and interpret values from 0 to Nyq). When computing the 2D FFT, do we compute the FFT of row[1] then the FFT of row[2] then the FFT of row[3] up to the last row. ...
