Questions tagged [matrix]
is a mathematical object to be recorded in a [usually] rectangular array of elements of ring or field, which (table) is a set of rows and columns are located at the intersection of its elements. The number of rows and columns specify the size of the matrix.
44
questions with no upvoted or accepted answers
4
votes
0
answers
72
views
Designing a fast linear operator with $\pm 1$ entries with low condition number and low Hamming distance between consecutive rows
I need to design a matrix for compressive imaging where each row represents an $N$-pixel filter in a focal plane through which light is masked, summed, and measured (think of Rice's single-pixel ...
- 2,950
3
votes
0
answers
61
views
How can I explain the result of of multiplications by matrices
I have a vector $x$ with size $N \times 1$, it's multiplied with a $Z$ matrix $N \times N$, the resulted $N \times 1$ vector is $y = Zx$. I know that each value of $y_i$, where $i = 0, 1, 2, .., N-1$ ...
- 640
3
votes
0
answers
240
views
Distribution of a signal covariance matrix
A common estimation problem in signal processing assumes the following signal model
\begin{equation}
\mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n}
\end{equation}
where $\...
- 131
2
votes
0
answers
42
views
What is an analysis dictionary or operator in compressive sensing?
I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries.
Here are some papers that I have read so far:
https://www.hindawi.com/...
2
votes
0
answers
104
views
Normalized LMS with a posteriori Error and Woodburry's Matrix Inversion
I was going through this paper and the author mentioned that we can prove the following using the Matrix Inversion Lemma (AKA Woodburry's Matrix Inversion Identity): Using matrix inversion lemma we ...
- 131
2
votes
0
answers
248
views
Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori
I am implementing a Kalman filter (for a linear ODE system for now).
My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
2
votes
0
answers
132
views
Help Understanding Radial Gaussian Filter
I am currently reading through Mueller's "Fundamentals of Music Processing" and I am trying to understand audio segmentation through the use of self-similarity matrices.
Currently, my matrix looks ...
- 21
2
votes
0
answers
226
views
Can Cholesky outer product version result in negative square roots?
Say A is symmetric positive definite matrix , which means one necessary condition is diagonal entries of A are positive. If I do cholesky factorisation using outer product form, Can there be any ...
- 63
1
vote
1
answer
62
views
Matrix form of Overlap-add
We know overlap-add of a en-framed signal can be done easily by following code
...
1
vote
0
answers
49
views
Optimization Problem in Graph Signal Processing to find edge weights
I am working on an application which consists of cross-roads and roads that connects them. In my design, I am using graph signal processing to estimate the importance of the roads which means edge ...
- 11
1
vote
0
answers
87
views
Convolution between a vector and another symmetric vector
Let's have the vector $y = h * x$ where $*$ is the convolution operation, $h$ is the channel with length $N$ and $x$ is a symmetry vector which means $x = [x_M, x_{M-1}, ....,x_0, 0 , x_0, x_1, .... ...
- 640
1
vote
0
answers
83
views
Constructing a Hankel matrix for n4sid with multiple inputs\outputs
I am trying to construct a Hankel matrix to write my own code for n4sid algorithm (page 47 and 22).
$ \mathcal{H}= \underbrace{\begin{pmatrix} U_{0|2i-1}\\ Y_{0|2i-1} \end{pmatrix} / \sqrt{j} }_{2(m+l)...
- 207
1
vote
0
answers
143
views
Is FFT sub matrix degeneracy a problem in OFDMA for some type of noise?
Say that the discrete Fourier transform (DFT) is used in OFDMA. There are a number of degenerate (singular, non invertible) sub matrices of some DFT matrices. Does this result in any problems?
One ...
- 221
1
vote
0
answers
55
views
How to find parameters of Kalman filter using matrix information?
I'm trying to understand concepts on Kalman Filters. Consider the overdetermined system $Ax=y$;
$$\begin{bmatrix}1 \\ 1 \\ 1 \\1 \end{bmatrix} x = \begin{bmatrix} 3 \\ 5 \\ 4 \\ 8 \end{bmatrix}$$
Let $...
- 111
1
vote
0
answers
217
views
What is the order of the output of HoughCircles in OpenCV, when having several circles on a frame?
So I am trying to use stereo vision to calculate the depth of several red balls. With the function HoughCircles, I get an output at one frame from one of the cameras like for example:
...
- 11
1
vote
0
answers
252
views
correlation matrix vs. correlation function?
Can someone help me understand the difference between a 1-dim autocorrelation function and a 2-dim autocorrelation matrix of a random process aka time series?
My Leon-Garcia textbook defines CX(τ) and ...
- 111
1
vote
0
answers
90
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. ...
1
vote
0
answers
2k
views
The rank of Fundamental Matrix
This question is regarding two view geometry where a point lying in the image plane of the first frame/ position of the camera is mapped onto the image plane of the second frame/ position of the ...
- 283
1
vote
0
answers
203
views
1D as a 2D FFT - am I understand it properly
in one of my question about non $ 2^L $ points FFT I got answer with advice to read about that in following book:
Rabiner, Lawrence R., and Bernard Gold. "Theory and application of digital signal ...
- 359
1
vote
0
answers
275
views
What is the best way to determine the process noise matrix $\mathbf Q$ of a Kalman filter?
It seems like most of the resources online suggest to determine the values of the process noise matrix $\mathbf Q$ through trial and error. However sometimes trial and error doesn't work, so I would ...
1
vote
0
answers
29
views
Emulate signal loss of a pixellated detector in Python?
I have a matrix 64x64 where each cell represents the pixel of a pixellated detector.
The spacial response of this detector decreases by going further from its center (that is, coordinates "31,31" or "...
- 111
1
vote
0
answers
122
views
Sensor Data Fusion with Orientation Sensors in 3D Euclidian Space
Preconditions
For measuring the position of a mobile device in 3D space, I utilize two sensors with different characteristics that measure device orientation.
Sensor A (a combined sensor of ...
- 226
1
vote
0
answers
54
views
Matrix expansion into bases
I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should ...
- 61
1
vote
0
answers
118
views
How to replace Hadamard Product and Column wise addition with new Matrix operation?
Let
$$
A=
\begin{bmatrix}
a_{1,1} & a_{1,2} & a_{1,3}\\
a_{2,1} & a_{2,2} & a_{2,3}\\
a_{3,1} & a_{3,2} & a_{3,3}\\
\end{bmatrix}
$$
and
$$
B=
\begin{...
- 115
1
vote
0
answers
79
views
Solving an Array Signal Processing Estimation Problem based on the Rayleigh Quotient
The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by
$$
R(\mathbf{C},\mathbf{a}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
- 233
1
vote
0
answers
388
views
How to understand energy function in thin plate splines?
guys! I have carried out some experiments using matlab warp tools from here. But the results are not good, so I decide to read its original paper Principal Warps: Thin-Plate Splines and the ...
- 145
0
votes
0
answers
41
views
What is the possible application of eigenvalues?
I am a PhD in mathematics. Recently, we made an attempt to compute the eigenvalues of non-normalized discrete sine and cosine transforms. Surprisingly, the issue regarding three particular types, DCT-...
- 345
0
votes
0
answers
86
views
Python - Discrete deconvolution using Toeplitz matrix
Lets say I have 2 vectors (1D signals that are sigmoids): $s$ and $m$, both related through the relation: $m = s * r$, my goal here is to recover the vector $r$ (should be a gaussian $\rightarrow$ ...
- 75
0
votes
0
answers
40
views
model of a quasi static block fading channel in MIMO system
can I know what is the model of a quasi static block fading channel in a MIMO system, in function of angle of departure and arrival?
0
votes
0
answers
9
views
Converting 2 variables (obtained by ICA decomposition) named A_ffdiag and W_ffdiag into mixing/unmixing matrix
I have two variables as a result of an ICA (Independent Component analysis) decomposition (decomposed using joint diagonalization algorithm which uses frobenius norm formulation) named A_ffdiag and ...
- 1
0
votes
0
answers
47
views
Signal Processing on non-Euclidean domains
I have a very simple yet fundamental question.
Suppose I have a vector of data $x \in \mathbb{R}^N$. Without additional information, I guess the majority of people think this vector as defined over ...
- 103
0
votes
0
answers
46
views
Estimating Correlation Matrices
I am trying to obtain the correlation matrices of two random signals. Both of them, $ X $ and $ Y $, are white Gaussian Noise, with unitary variance. However, they are correlated, with correlation ...
- 677
0
votes
0
answers
56
views
Matrix multiplication computational complexity based on radix 2
I am wondering, can we use Radix 2 based computational-complexity calculation for any matrix multiplication whose size is $N$ x $N$ ?? where $N$ = $2^K$ and $K > 1$ is an integer ?? Or it can only ...
- 598
0
votes
0
answers
22
views
Stability of $x(n) = A x(n-1)+b$
I am looking at the following system:
$x(n) = A x(n-1) + b$
where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform?
If ...
- 15
0
votes
0
answers
86
views
unitary matrix complexity multiplication
Having a unitary matrix $X$ whose size is $n \times n$ and a vector $z$ whose length is $n$, and let's have:
$$y = X^H {\rm diag}(z)X$$
where $X^H$ is the conjugate transpose of $X$.
My question,...
- 639
0
votes
0
answers
59
views
Expectation of a constant diagonal matrix
Is the expected value of a diagonal matrix with constant entries equal to the mean value of the entries?
My question stems from the following observation in a paper.
Given a real diagonal matrix
$\...
- 359
0
votes
0
answers
65
views
Matlab: How to implement expectation of product of hermitian matrix
I want to implement the following equation in Matlab:
$\mathbf {R}_\mathbf {z}^a(\tilde{f}) = \mathbb {E} \left[\mathbf {z}(\tilde{f}) \mathbf {z}^H(\tilde{f}+a) \right]$, $ \tilde{f} \in \left[0, ...
- 1
0
votes
0
answers
22
views
Join 2 NMF models where dictionaries has hierarchical structure
I have two NMF models $A = W_1A_{dict}$ and $B = W_2B_{dict}$ (where the $W$ represents weight coefficient matrix). What is a good way to join two NMFs if I know each column of $B_{dict}$ is summed up ...
- 189
0
votes
0
answers
2k
views
How to calculate the scale, rotation angle and translation between 2 images if we know the homography result matrix?result
I got the result of findHomorgraphy in OpenCv. As below:
Homography transform matrix:
[-1.1534205416542787 0.7834287271121142 527.9064589440736
-0.2415444621693116 0.16412191792642924 ...
- 11
0
votes
0
answers
443
views
Generating Wavelet family matrixes
We have unnormalized Haar matrix which, is for example,
H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1]
After normalizing it, we use for haar transform. I know how to ...
0
votes
0
answers
30
views
Are there condition numbers associated with the STFT, DWT?
Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1.
Is it possible to represent the STFT and DWT as ...
- 33
0
votes
0
answers
1k
views
How to Prevent overflow/saturation in fixed point implementation of Fast Data Projection Algorithm
I am trying to implement an algorithm in real-time on a Fixed point DSP (The Blackfin from Analog Devices). The algorithm does a lot of stuff, but in the middle it performs an algorithm called "Fast ...
- 1,241
0
votes
0
answers
574
views
3 Band Wavelet Transform In MATLAB
I am currently working on an audio watermarking project in MATLAB. I currently have a code I am using to construct a nxn 3 Band Wavelet Transform matrix. However, when I try to construct a matrix that ...
- 65
0
votes
1
answer
467
views
Incoherence: Compressed Sensing (CS) vs Matrix Completion (MC)
I am seeking a clarification of the concept of Incoherence within the MC framework.
Specifically,
1) the literature mentions the application of a "strong incoherence" given a set of assumptions. ...
- 445