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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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25 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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0answers
9 views

Precoding matrix for MIMO

My question is according to the precoding matrix for open loop and closed loop capacity. For open loop spatial multiplexing transmission, co CSI is available at the transmitter Tx, that is equivalent ...
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0answers
8 views

Two different definitions of coherence parameter

When we have the measurement basis $\varphi_{m \times n}$ and the sparse basis $\psi_{n \times n}$ the coherence parameter is defined as follows, $\mu_1(\varphi , \psi) = \sqrt{n}\max_{j,i}\frac{|\...
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1answer
50 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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2answers
46 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
64 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
86 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
41 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
46 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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0answers
67 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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0answers
24 views

Moving window quadratic form

What is the most efficient way to implement a moving quadratic form in MATLAB? I have a square $n \times n$ matrix $\mathbf{A}$, and I would like to compute $\mathbf{x}^\mathsf{T}\mathbf{A}\mathbf{x}$ ...
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2answers
61 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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2answers
87 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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0answers
37 views

Spatial Correlation Matrix

I have been studying the Minimum Variance Distortionless Response beamformer, and I've come to find I don't understand the spatial correlation matrix as given. For clarity, consider the output of a ...
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0answers
27 views

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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0answers
14 views

Implementing Wavelet family matrices

I want to use CS to reconstruct an image from fewer samples, and I would like to use wavelet coefficients but I don't know how to define them when making a Psi matrix. I have written wavelets ...
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1answer
31 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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2answers
41 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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0answers
42 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
137 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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0answers
30 views

In NMF: How to decide which matrix can be applied group sparsity constraint

In simple setting, my signal has specific pattern peak detected at some minutes like in $V$ matrix. I have prior knowledge that $V$ can be mixed from 6 patterns which is belong to 2 groups but cannot ...
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1answer
267 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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1answer
107 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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0answers
11 views

source separation: the tracking capability of the inverse (unmixing) system in a nonstationary environment?

I'm reading Nonnegative Matrix and Tensor Factorizations (A CICHOCK, p.4). There is a paragraph talking about the inverse system should have the tracking capability. From my understanding, the inverse ...
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16 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 ...
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0answers
35 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
127 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
24 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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0answers
116 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 ...
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1answer
108 views

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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0answers
37 views

Matrix data transmission over fading channel

I have to send a data matrix $A$ over a Rayleigh fading channel $h$. $$y=hA+n$$ where $A$ is data matrix, $h$ is channel vector, and $n$ is receiver noise. The problem is that the data matrix $A$ is ...
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1answer
370 views

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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6answers
273 views

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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0answers
58 views

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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1answer
80 views

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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0answers
120 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 ...
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1answer
613 views

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 ...
2
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1answer
149 views

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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0answers
280 views

Performing circular convolution

I have two 2D matrices and want to perform the circular convolution of them. I can do this quite easily, however my issue is that i essentially want to copy what the 'same' argument does in the conv()/...
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2answers
167 views

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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1answer
220 views

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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1answer
112 views

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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0answers
61 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 ...
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0answers
31 views

SINR Computation for Generalized Frequency Division Multiplexing

I was reading one paper about GFDM. At the receiver part, MMSE (Minimu Mean Square Error) receiver is being used. Here is a quote from the paper The received vector after the removal of CP can be ...
2
votes
1answer
3k views

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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0answers
53 views

MIL given for RLS equations vs the Woodbury derivation [closed]

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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1answer
128 views

Mechanics of a matrix Interleaver

I am having trouble understanding exactly how the matrix interleaver. I have read the following page from MathWorks. In it, it gives the following example where "123456" is interleaved as "142536." ...
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2answers
410 views

Why is this matrix invertible in the Kalman gain?

In the wikipedia article about Kalman filters, the well-known expression of the matrix of Kalman gains is given: $$ \mathbf {K} _{k}=\mathbf {P} _{k\mid k-1}\mathbf {H} _{k}^{\text{T}}\mathbf {S} _{k}^...
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1answer
68 views

involutory transformations - why are they not so much used in signal processing? [closed]

We generally prefer orthogonal transformations/matrices in signal processing as the transpose of the matrix is the inverse and you do not need to find inverse transform separately. But involutory ...
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1answer
802 views

Calculating covariance matrix for MVDR beamforming

I am trying to calculate the covariance matrix that is required for the calculation of an MVDR beamformer. I am getting confused as to how to calculate it. I have an array of 3 microphones each with a ...