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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Matrix form of Overlap-add
We know overlap-add of a en-framed signal can be done easily by following code
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To find the unitary matrix which is the null of the results of multiplication with another matrix
I have a matrix $F ∈ \mathbb{C}^{(m × N)}$, where $m < N$, and $F \times F^H$ is a unitary $m × m$ matrix.
I need to find a unitary matrix $G$ with a dimension of $N × N$ such as results of $F\...
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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-...
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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 $\rightarrow$ ...
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Deconvolution using Toeplitz matrices [duplicate]
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 look like a gaussian).
I tried ...
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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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Matching 2 Undirected Weighted Graph in MATLAB
Consider 2 undirected weighted graph as shown in figure. Consider first graph as $G_1$ and second graph as $G_2$. Graph $G_1$ consist of vertices $V=\{F_1,F_2,F_3,F_4,F_5\}$ and graph $G_2$ consist of ...
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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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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?
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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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How are LTI systems related to Toeplitz matrices?
I am having trouble understanding why the system matrix of an LTI system is Toeplitz. I am following an Edx online course by Professor Richard Baraniuk of Rice University, named discrete-time signals ...
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Relationship between discrete deconvolution and Toeplitz matrices
I have 2 vectors, $a$ & $c$, both of length $M$. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b = \mbox{deconv} (c,a)$. I am only interested in the first $M$ elements ...
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Inverting $6 \times 6$ complex matrix on the ARM Cortex M4F processor
I want to invert a $6 \times 6$ complex matrix on the ARM Cortex M4F processor. I have the C code to invert a real matrix using the CMSIS library. Has anyone written a similar C code for complex ...
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Understanding y=Hx+n equation in detail?
Consider a wireless communication system having $t$ transmitting antennas and $r$ receiving antennas. Then, the received signal is given by
$y = \mathbb{H}x+n \tag{1}$
where $\mathbb{H}$ is a $r \...
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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 ...
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What is the complexity of big-$O$ $O(N \times \mathrm{log}_2(N))$ vs real operations
I usually see books/references writing the complexity of such operations as $O(N \times \mathrm{log}_2(N))$; For example, the complexity of FFT/IFFT operation is $O(N \times \mathrm{log}_2(N))$. ...
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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$ ...
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Expressing mathematically the number of real addition operation for a vector after dividing it
I assume I have the length of such vector $y$ is $N$. In the first time I divide that vector into two columns and then sum them point-wise summation. The second time, I divide the same vector $y$ ...
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What is the complexity of multiplication a real matrix with real vector
I have a real matrix $Z$ which is following the form as following:
$Z = \begin{bmatrix}
x_1& 0& 0& 0& 0& 0& 0& 0\\
0& x_2& 0& 0& 0 & 0&...
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How can I express the flipped output of multiplication in function of original inputs?
I have the vector $y = Dx$ where $D$ is a complex matrix with dimension $N \times N$, and $x$ is a complex vector of dimension $N \times 1$.
If the vector $y_2 = [y'_N, y'_{N-1}, y'_{N-2},.... , y'_{...
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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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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 ...
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How can I find expansion coefficients of the a vector in a given basis?
How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors?
Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$
What are the expansion ...
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What is the relation between eigenvalues and state-space response in control systems?
I understand the mathematics behind it but I want to know what happens physically in a real-life system. How do the eigenvalues come into the picture from a non-mathematical (physical) point of view? ...
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Least Angle Regression (LARS) without Matrix Inversion
Sorry if this is too damned long. I did what I could to abbreviate it.
The question is about Least Angle Regression (LARS).
I'm new to numerical work with matrices.
I believe I have a way to ...
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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, .... ...
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Can we recover a vector from one element of resulted vector after multiplication?
I have a matrix $X = \begin{bmatrix}
0.5000 + 0.5000i & 0.5000 - 0.5000i\\
0.5000 - 0.5000i & 0.5000 + 0.5000i
\end{bmatrix}$ multiplied with a column containing a complex number and its ...
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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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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)...
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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 ...
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how do you know if your matrix is sparse after sparsifying transform?
To successfully compress the data using Compressive Sensing method, I need to have sparse vector, theoretically a vector is sparse if the entries of the vector has many zero or nearly zero. My ...
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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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Proving that the uncertainty can not increase during the update step of a Kalman filter - positive semidefiniteness
I am trying to prove mathematically that the update step in a Kalman filter can not result in a increase in uncertainty. I found the following proof which is based on the inversion lemma and the ...
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Is it possible to detect the sparse vector based on a non-invertible matrix
Given a non-invertible matrix $X \in \mathbb{R}$, let's say that matrix is, e.g. :
$X = \begin{bmatrix}
0.7500& -0.2500 &-0.2500 & -0.2500 \\
-0.2500& 0.7500& -0.2500 & -0....
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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 ...
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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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Apply Low Pass (Smoothing) Filter on a Set of Matrices and Reject Outliers
Given a set of a $ 3 $ by $ 3 $ matrices $ {H}_{i} $.
Each matrix is an Homography matrix.
They are used to stabilize Video Stream.
Yet some of them are outliers which creates "Jumps" in the "...
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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 ...
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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 ...
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Optimization of square matrix multiplied with another matrix to have the final result a unitary matrix
I have a square matrix $D$ whose size is $m \times m$ multiplied with another $m \times m$ square matrix $C$, I need to optimize the matrix $C$ to have a unitary matrix $DC$. I mean optimize the ...
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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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Wave Digital Filter Bridge-T Resonator implementation, gives expected cutoff frequency but incorrect gain and roll-off
Trying to implement the WDF in Fig 5(a) of this publication. The response of the ideal op-amp implementation is given by the black curve in Fig 7:
Here is the plot I get when trying to implement the ...
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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/...
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Why do we need to estimate eigenvalues?
I am not working in signal processing field, but recently I happen to read a paper which estimates source numbers using Gerschgorin radii, and I feel kind of confused about why we need to estimate ...
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Matrices of complex numbers multiplication
I'm trying to implement the multiplication of two matrices something like this picture in c langage.
I want to read the numbers from a text file of x and store it later in an array the code that i ...
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Is There a Way to Perform a 2D Image Rotation by Matrix Multiplication?
In my understanding, unlike shifting and scaling, image rotation actually rotates the coordinates whereby interpolating the pixels at discrete positions. It is like a projection that discrete values ...
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Property of the trace and expectation
I'm reading the paper Model-Driven Deep Learning for Joint MIMO Channel Estimation and Signal Detection by Hengtao He, Chao-Kai Wen, Shi Jin, and Geoffrey Ye Li on Orthogonal Approximate Message ...
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why use svd() to invert a matrix?
In MATLAB, i compared elapsed time to invert a Hermitian matrix using inverse(), svd(), and chol(). svd() took the longest. So is there any reason to prefer svd() to the other two methods?
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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 $...
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Relation between the matrix trace and the amplitude of each element
Assume a diagonal matrix $\mathbf X$ whose size $N\times N$ and its diagonal elements are $0.5 + 0.5i$, and the vector $\mathbf p$ of size $N\times 1$ whose elements have similar amplitude.
I have ...
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