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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9 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: ...
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Translating SFFT expression to MATLAB code

The Symplectic Finite Fourier Transform (SFFT) of a 2D periodized sequence $x[k,l]$ with periods $(M, N)$ is defined as $$X[n,m] = \sum_{k=0}^{M-1} \sum_{l=0}^{N-1} x[k,l] e^{-j2\pi \left(\frac{mk}{M} ...
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MATLAB: How to copy column vectors from a matrix into a cell array? [closed]

I have some sensor data stored in a 1000 x 5 matrix. I'd like to copy each column into a 5 x 1 cell array such that each cell contains a 1000 x 1 vector. I tried the num2cell(mymatrixname,1) function, ...
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1answer
40 views

Which one can be accompanied by linear filters?

I have a matrix : \begin{bmatrix} 1 & 2 & 3\\ 1 & 4 & 5\\ 2 & 6 & 7 \end{bmatrix} After doing operation 1 , I get \begin{bmatrix} 0 & 0 & 0\\ 1 & 2 & 3\\ 1 &...
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30 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 ...
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36 views

Setting some values in a vector to have specific values after multiplying with such matrix

Assume I have a known matrix $X$ of size, for example, $(16$ x $16)$, and a vector $z$ of size $(1$ x $16)$ where only some equispaced values are known, for example $1:4:16$ or values in locations $(...
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1answer
45 views

Solve equations with conjugates multiplications

If I have a two variables $x_1$, $x_2$ and two equations. In the first equation the first variable $x_1$ is multiplied with the conjugate of same number which is multiplied with $x_2$, and in the ...
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1answer
41 views

Taking inverse Fourier transform in column-wise and solve it in row-wise

$\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT}$Assuming I have a matrix $X$ of size $64\times16$. Taking the $\IFFT$ for it in column-wise, I means that $Y = \IFFT(X)$; Is it ...
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62 views

On the simplification using trigonometric functions

Assume I have a matrix $D$ whose its entries are as below : Where $A$ and $B$ can be written using using the trigonometric functions for (1) as: My question, Is it possible to simplify (1) more? ...
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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,...
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Real time signal processing use cases for eigenvalues of symmetric matrices

I realize that this might be somewhat of an unusual and specific question. I know that the eigenvalues of symmetric matrices are used in a number of ways in scientific computing, such as for finding ...
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315 views

How can I find expansion coefficients of the y vector in a given basis?

Consider the following vectors in $\mathbb R^4$: $$\mathbf{v}^{(0)}=\begin{bmatrix}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2} \end{bmatrix} , \mathbf{v}^{(1)}=\begin{bmatrix}\frac{1}{2}\\\...
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2D FFT Toeplitz Matrix Indexing

I have a convolution sum_j M(x_i-x_j) v(x_j) which I would like to numerically compute using a FFT. x_i and ...
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39 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 $\...
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1answer
66 views

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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1answer
44 views

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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Is sparse dictionary learning just a subset of non-negative matrix factorization?

I saw some people argued that their method should be called sparse dictionary learning or NMF. What are the differences between these two terminologies? If the dictionary is given or fixed, the ...
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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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3answers
409 views

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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185 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 ...
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1answer
34 views

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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63 views

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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2answers
376 views

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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156 views

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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1answer
106 views

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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1answer
46 views

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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2answers
519 views

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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1answer
195 views

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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173 views

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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1answer
105 views

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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1answer
242 views

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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1answer
48 views

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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1answer
48 views

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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69 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 ...
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2answers
403 views

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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761 views

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 another 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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1answer
36 views

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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97 views

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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130 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 ...
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1answer
456 views

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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1answer
1k views

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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268 views

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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76 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 ...
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1answer
444 views

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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1answer
28 views

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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184 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 ...