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.
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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
$\...
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On the use of Permutation matrix to perform iFFT
I have a question about using the permutation matrix for performing $iFFT$ for such matrix and then reshape it row-wise and column-wise way.
Let's say that we have a random matrix $x$ whose size is (...
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Effect of Adding the cyclic prefix on the toeplitz matrix in OFDM
Assuming we have $N$ symbols to transmit encoded in block $k$,
Performing $N$−iFFT at the transmitter, we now have
The resulted signal $x(k)$ has length of $N$. inserting a cyclic prefix $CP$ ...
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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. ...
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Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?
I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia.
If I understand correctly, you get the new value for each pixel by multiplying ...
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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 ...
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What is the difference between positive matrix coefficients and negative matrix coefficients of an audio?
I have turned an audio file into an one dimensional array by using audioread function in matlab and found several positive and negative fractional coefficient values.What is the basic difference of ...
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A good reference for matrix completion [closed]
Does anyone know a complete reference or book on matrix completion?
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Similarity or Relation between Walsh Hadamard Transform and Slant Transform
Is there any relation between Walsh Hadamard Transform and Slant Transform? Or is there any common property or similarity?
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Circular Convolution Matrix of $ {H}^{H} {H} $
We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
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Why discretize a continuous transition matrix in Kalman Filter?
In the Kalman filter toolbox at http://becs.aalto.fi/en/research/bayes/ekfukf/cwpa_demo.html the example code shows that a function lti_disc is called, which is essentially a matrix exponential ...
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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, ...
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Derivation of Toeplitz Matrix
I'm having a difficult time understanding why the matrix for LTI systems is a Toeplitz matrix. I can see why $h_{n,m} = h_{n' + q,m' + q}$ given that $n' = n - q$ and $m' = m - q$, and $$\sum_{m'= -\...
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Clarifying matrix notation from an ICA-CMN paper
In the paper I am referring (and here from citeseer), complex vectors $\mathbf{z}$ and matrix $\mathbf{M}$ were defined as follows
\begin{align}
{{\bf z}} &= \left[z_{1},z_{2},\ldots,z_{N}\right]^...
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How to reduce time consuming for calculating pseudo inverse of large matrix in matlab?
I have a matrix
P = randn(45875x65536 );
Pi = pinv (P);
I tried to run this code in matlab, but it takes long time
is it possible to split the matrix into ...
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Correlation of a signal
I have one sample for a signal. This sample is a vector of length 384. I need to calculate the correlation matrix for this signal,So I need many samples for the same signal.
How can i generate these ...
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Image processing - Why is sum of values of a blurring filter = 1?
Usually, blurring filters have the sum of all the values in the filter matrix equal to $1$.
Why is it so?
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How Is Mixed Norm ($ {L}_{1, 2 }$) Better than $ {L}_{1} $ Norm for Sparse Representation?
Using $ {l}_{1} $-norm regularization for the purpose of achieving sparsity of the solution has been successfully applied a lot. But many times, I found the paper using mixed-norm instead of $l_1$-...
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What is about the circular convolution in OFDM
In an OFDM system, serial-to-parallel conversion for data is done, then the DFT is performed and then adding the cyclic prefix (CP).
My question is related to that step of adding a CP. As I know, ...
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how to set Equalizer's coefficient using generalized eigenvector.
In that paper https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2012-72 .. Equation 3,
$J(w) = w^HBw/w^HCw$ ..
$B$ and $C$ are matrices, $w$ the filter coefficients vector ...
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In OFDM, does $N N^H$ equal $I$?
I'm still new in OFDM and reading about it, but I have a question.
In OFDM system, when having $N$ data symbol assigned to sub-carriers, $N$ should be orthogonal with each others, which means $NN=0$....
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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 ...
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What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?
I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
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Ifft through Matrix multiplication
I am still new to MATLAB, so apologies if I sound lazy to you. I am attempting to model a transformation as a set of matrix operations. I start with a vector, up-sample it by $U$ (up-sampling rate), ...
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Estimating a Matrix from Scaled Permuted Matrix
The problem is the non- negative matrix factorization of a matrix. Let me explain my problem I have an original matrix $A=\begin{bmatrix}
0.248437 &0.25198098 & 0.25396825 & 0.25077881\\
0....
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Is sparsity induced penalty in source separation "Entrywise matrix norms"?
I am reading this paper where they introduce norm penalties for source separation. In table 1, the $\log/ l_1$ type is $\sum_{g} log(\epsilon + \lVert H_{g} \rVert_1)$. I wonder this $\lVert H_{g} \...
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1D as a 3D FFT - what’s wrong here?
I implemented the algorithm to calculate 2D DFT derived from 1D DFT.
It works great, and makes my calculations much more efficiency then regular 1D DFT.
But now I want to make 3D DFT derived from 1D ...
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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 ...
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FFT - mixed radix - bit reversal
I wonder what is bit reversal for mixed radix FFT. Is there any algorithm that compute the bit reversal for various mixed radix FFT?
Here should be mention why I want that. For example if I have ...
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3D world homography matrix calculation
I have a matrix in (x,y,z) coordinates and also i have a transformed version like (x_new,y_new,z_new).
I need to calculate a transformation matrix that can transform (x,y,z) to (x_new,y_new,z_new). ...
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AWGN channel matrix
For my current project work, I need to create an AWGN channel in MATLAB. There is a built-in function in MATLAB named 'awgn'. But that returns the value of received signal after passing through awgn ...
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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 ...
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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 ...
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How to calculate the Diagonal loading factor evaluate calculate the inversion of a covariance matrix
I am programming a Generalised Likelihood Ratio Test (GLRT) detector. When it comes to inverting a covariance matrix $Ri$, I need to do a diagonal loading to fix the problem of sigularity of this ...
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Can I start testing my NMF with extension on sample that have only one source?
I am testing my supervised NMF algorithm to extract signal from observation that have only one source inside. I am new here and I wonder this is very weak model or not? Is it acceptable in signal ...
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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 ...
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Relationship between matrix rank and beamforming
I always encounter the term matrix rank in papers related to beamforming. I am only familiar with the basics of beamforming (delay sum beamformer, basic capon). Can someone explain the significance of ...
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Noise estimation SNR matrix
I have a signal matrix which is a $256\times 192$, and I want to calculate the SNR considering that my $259\times 192$ matrix is an average of a $256\times 192\times 330$ matrix, where $330$ is the ...
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The Least Norm Solution of Under Determined Linear System
Suppose I have a matrix
$$A=
\begin{pmatrix}
1 & 0 & 1 & 0\\
0 & 1 & 1& 0\\
\end{pmatrix}
$$
where the variables are channel information like assume $X_1$, $X_2$, $X_3$ ...
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Linear Systems, Sparse Solutions, and $4 \times 4$ Sudoku Algorithm [closed]
I am unable to understand the paper Linear Systems, Sparse Solutions, and Sudoku. I have to form a $4 \times 4$ Sudoku using the algorithm in this paper. Can somebody please provide me the algorithm ...
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How to prepare and plot unequally spaced, irregular data to a contour plot or similar with MATLAB
I've got a data set of hot-wire measurement velocity amplitudes at a given frequency bin (time data that has already been transformed to the frequency domain and I am just considering data for a given ...
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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 ...
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Sensing matrix for compressed sensing
What are the differences between random binary sensing matrix and
random Gaussian sensing matrix?
What the advantages and disadvantages of each matrix?
How can I choose the suitable matrix for a ...
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In 1D DCT, why is the input a vector?
The question is specific to this document: Image Compression.
It is chapter 6 from book "A First Course in Applied Mathematics" by Jorge Rebaza. It is, a to the point explaination of DCT that is ...
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The inverse of an orthogonal matrix is its transpose
In the following statement I don't understand the case for $\ i = j$:
Let $\mathbf A$ be an $\ m \times \ n$ orthogonal matrix where $\ a_i$ is the $\ i^{th}$ column vector. The $\ ij^{th} $ element ...
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How to solve this entropy integral?
I am having the entropy integral below where $\mathbf x$ is a $N$ dimensional Gaussian vector having variance as $\mathbf P$ and mean zero,
$$ -\int\frac {\exp\left(\frac{1}{2}\mathbf x^T\mathbf P^{-...
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How can I get the uncertainties for peaks on an image?
When pick the peak points on an image, e.g. the matrix made by peak in matlab as this one,
I can use max to get the index of ...
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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 ...
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2D Convolution as a Doubly Block Circulant Matrix Operating on a Vector
I was reading Fundamental Image Processing, Chapter 5 (Image Transforms), I encountered the following problem:
Given the arrays $x_1(m,n)$ and $x_2(m,n)$ as follows:
Write their convolution $x_3(m,n)...
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Deriving the Matrix Inversion Lemma for RLS Equations vs the Woodbury Derivation
Can any one help me in deriving the matrix inversion lemma rule for RLS algorithm?
I don't know how to start with. Many books have just stated but they haven't derived it.
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