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.

Filter by
Sorted by
Tagged with
0
votes
0answers
38 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 $\...
0
votes
1answer
56 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 (...
0
votes
1answer
34 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 $CP$ ...
0
votes
0answers
11 views

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 ...
1
vote
0answers
19 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. ...
0
votes
3answers
167 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 ...
1
vote
0answers
107 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 ...
0
votes
1answer
23 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 ...
2
votes
0answers
25 views

A good reference for matrix completion [closed]

Does anyone know a complete reference or book on matrix completion?
0
votes
1answer
51 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?
1
vote
2answers
312 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 ...
0
votes
1answer
128 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 ...
0
votes
0answers
49 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, ...
0
votes
1answer
77 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'= -\...
0
votes
1answer
44 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}\...
1
vote
2answers
377 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 ...
0
votes
1answer
155 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 ...
-2
votes
2answers
152 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?
3
votes
1answer
88 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 $l_1$-...
2
votes
1answer
193 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, ...
0
votes
1answer
47 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 ...
0
votes
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 $NN=0$....
4
votes
0answers
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 ...
3
votes
2answers
325 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 ...
0
votes
2answers
677 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), ...
1
vote
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....
1
vote
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} \...
0
votes
2answers
83 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 ...
1
vote
0answers
121 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 ...
0
votes
1answer
397 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 ...
0
votes
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). ...
-1
votes
2answers
250 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 ...
0
votes
0answers
18 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 ...
1
vote
0answers
56 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 ...
0
votes
1answer
378 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 ...
0
votes
1answer
25 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 ...
2
votes
0answers
170 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 ...
1
vote
1answer
181 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 ...
2
votes
1answer
728 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 ...
6
votes
6answers
424 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 $X_1$, $X_2$, $X_3$ ...
1
vote
0answers
63 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 ...
0
votes
1answer
170 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 ...
1
vote
0answers
172 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 ...
2
votes
1answer
1k 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
votes
1answer
251 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 ...
1
vote
2answers
357 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 ...
0
votes
1answer
336 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^{-...
1
vote
1answer
220 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 ...
2
votes
0answers
86 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 ...
2
votes
1answer
6k views

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)...