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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How to select the location of submatrices to have specific property in the output of multiplication
I want to set the locations of two submatrices W22 and W21 taken from Hadamard matrix, with respect to ...
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Correlation Matrix Problem of Three Decomposition Level of DWT
I'm trying to apply a DWT with 3 composition levels and the following question arose when calculating the composition matrix.
The step I'm trying to follow is:
The DWT coefficientes are obtained from ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 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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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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linear convolution toeplitz matrix vs circular convolution toeplitz matrix
I have an issue in understanding the difference between building the Toeplitz matrix when the convolution is linear and when it's circular. As I know that Toeplitz matrix $H$ can be built as following
...
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Stability of $x(n) = A x(n-1)+b$
I am looking at the following system:
$x(n) = A x(n-1) + b$
where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform?
If ...
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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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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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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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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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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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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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