6
votes
Calculate 1D Power Spectrum from 2D Images
I am just reading Quantitative characterization of surface topography using spectral analysis and recalled seeing your post today. The paper makes distinction between $C^{iso}$ (radially averaged) and ...
- 195
6
votes
Accepted
How does MATLAB recover picture from magnitude spectrum alone?
Your code uses the phase for the reconstruction. Have a look at the output of fft2(x); they are complex numbers, i.e. the contain phase and magnitude. Have a look at this code:
...
- 6,238
4
votes
Accepted
Efficient implementation of 2-d circularly symmetric low-pass filter
Approximation by the real part of a weighted sum of separable complex Gaussian component kernels
Figure 1. The proposed scheme illustrated as 1-d real convolutions ($*$) and additions ($+$), for cut-...
- 13.7k
3
votes
Accepted
How to represent impulse function in 2D?
So dealing with generalized functions like the Dirac delta requires some care, and when dealing with N-dimensional versions you need to be very explicit with your notation to keep things straight.
I'...
- 2,710
3
votes
Zero padding and 2D Fourier transforms: how does zero-padding affect phase?
Symmetric zero-padding (in the center of an image around the N/2,N/2 sample) does not affect the FFT phase result. Or after an 2d fftshift before the 2DFFT, symmetric zero-padding around the edges (...
- 35.7k
3
votes
Accepted
Compute the two-dimensional DFT
No you are not doing the separation correctly :
The horizontal 1D-DFT of the rows of input will be:
$ H_1 = \begin{matrix}
2 & 0 & 0 & 0 \\
2 & 0 & 0 & 0 \\
2 & 0 &...
- 28.4k
3
votes
Accepted
Mathematical Approach to Detect If a 2D Signal Is Separable
Let's assume our data is in finite dimension.
So $ x \left[ m, n \right] \in \mathbb{R}^{M \times N} $. So it can be written as a matrix $ X \in \mathbb{R}^{M \times N} $.
Using the SVD Decomposition ...
- 20.5k
3
votes
Why does this plot correspond to this function?
The axes in your plot seem to be indexes into an array, as if you were using stem3(Z) instead of stem3(X,Y,Z).
Check the ...
- 5,024
2
votes
Accepted
Why does this plot correspond to this function?
Formally, you are correct. But the question says "should look like this". And not "should be equal too". Apparently, the graph drawn is just a hint of the solution, and one should correctly set the $x$...
- 32.3k
2
votes
Accepted
A PID that can handle 2 inputs for my application
If you require two outputs, which belong to a movement in x and the other in y direction, you could start with the assumption, that both movements are independent an simply implement two PID ...
- 112
2
votes
Accepted
2D Convolution in MATLAB Causes Artifacts (Boundary Issues)
If I understood right this is a duplicate question but I cannot find the link let me re-type the answer. Given that you want to implement a 2D discrete convolution of two images of sizes $N_1 \times ...
- 28.4k
2
votes
Accepted
Understanding 2D FFT result of an image having a pattern
I found that FFT output depends on aspect ratio of the input image. Fourier pattern is perpendicular to the input image pattern only if the input image has same width and height.
- 151
2
votes
Accepted
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?
One way to interpret the DFT, that I personally find most useful, is by comparing it to the DTFT (Discrete Tome Fourier Transform, which has an infinite input domain) of a repeated function. That is, ...
- 2,770
2
votes
Accepted
Applying a 2D Convolution Using 2D FFT
You may follow the answers to the following questions which implements the paper you linked above:
Kernel Convolution in Frequency Domain - Cyclic Padding (Exact same paper).
2D Frequency Domain ...
- 20.5k
1
vote
2D Fourier transform of an element-wise product of two matrices
Yes. It's the 2D circular convolution of the Fourier transform of each matrix. I.e. $\mathcal F \{A \odot B\} = \mathcal F\{A\} * \mathcal F\{B\}$.
This is basically the same property as with the 1D ...
- 13.3k
1
vote
How can extract the cosine transform formula used for 2D by scipy.fft.dct
I'd take bets that the 2D-DCT is just separable into identical row-wise and column-wise DCTs. Anything else would be surprising.
Anyways, you know the 2D-DCT is a reversible linear operation: It ...
- 32.5k
1
vote
Accepted
How could I approach determining if this 2D system represented as a 2D summation formula is linear?
I'm actually starting this out not knowing the answer, although I have my suspicions. I think it'll be a linear system, but I'm not sure. Here's your starting point: you define the system $y = h(x)$ ...
- 13.3k
1
vote
how to interpret the 2D FFT
Yes, due to the separability of the kernel :
$$e^{-j \left(\frac{2\pi}{N_1} n_1 k_1 + \frac{2\pi}{N_2} n_2 k_2 \right) } = e^{-j \frac{2\pi}{N_1} n_1 k_1} \cdot e^{-j \frac{2\pi}{N_2} n_2 k_2}$$
the ...
- 28.4k
1
vote
Accepted
Show That a 2D Linear Transform $ T \left( \cdot \right) $ Is Homogeneous
The idea here is that any Linear Operator is Homogeneous though not every Homogeneous Operator is Linear.
The classic proof indeed is to build the zero term as a sum (Difference) of 2 other elements ...
- 20.5k
1
vote
Accepted
How is 2D convolution calculated?
Technically, shifting the kernel above the still image, or shifting the image "below" the centered kernel are equivalent. This is because convolution of a kernel and an image is a commutative ...
- 32.3k
1
vote
On the symmetry of a $2$-dimensional discrete-time signal
What you have displayed is true for which it's odd symmetric for only one of the variables $n1,n2$ and even-symmetric for th other.
For 1D signals, an even-symmetric signal has the property that
$$ h[...
- 28.4k
1
vote
Accepted
Scale Image by using FFT
Up-Scaling an image can be performed in the frequency-domain, as usual.
Given an image of $N \times M$, interpolation by integer factor $K$, using frequency-domain, is obtained by enlarging the $N \...
- 28.4k
1
vote
MATLAB phase of 2D rectangular pulse's Fourier transform
The issue is that the phase value found is between $-\pi$ and $\pi$ (or $0$ and $2\pi$) but it needs to be "unwrapped" to be continuous.
In 1D, the unwrap function ...
- 26k
1
vote
Accepted
Linearity and shift-invariance of 2-D system on lattice
Well, actually you only need to insert the system $H$ into the definition of linearity and check, if it holds:
$$\begin{align}H\{af_1[x]+bf_2[x]\}&=\sum_y\phi[y](af_1[x-y]+bf_2[x-y])\\
&= a\...
- 6,238
1
vote
Easy way to get rid of noise in a hand drawing
Why don't you just count the numbers of pixels in each connected structure (by an appropriate definition of connected), and set a threshold on the number of pixels? If it is e.g. below 10 px, it is ...
- 1,736
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