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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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." ...
user23040
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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:
$$ \mathbf {K} _{k}=\mathbf {P} _{k\mid k-1}\mathbf {H} _{k}^{\text{T}}\mathbf {S} _{k}^...
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involutory transformations - why are they not so much used in signal processing? [closed]
We generally prefer orthogonal transformations/matrices in signal processing as the transpose of the matrix is the inverse and you do not need to find inverse transform separately. But involutory ...
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Calculating covariance matrix for MVDR beamforming
I am trying to calculate the covariance matrix that is required for the calculation of an MVDR beamformer. I am getting confused as to how to calculate it. I have an array of 3 microphones each with a ...
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How is the matrix $\mathbf R_x$ not Toeplitz in case of a signal missing one term?
I am solving a question that says if we have sequence $x(n)$ of a signal missing one term then we have to find autocorrelation matrix $R_x$ as follows:
$$R_x = E\{\mathbf {xx^H}\}$$
Now if I take $...
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Accelerometer - coordinate system transformation
I'm getting some accelerometer readings from an Android phone, but it comes in on the phone's coordinate system. I want to apply a transformation to put the acceleration in the world coordinate system ...
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Why do we assume the matrix of impulse responses to be a Toeplitz matrix during deconvolution
$y(n)$ = output signal
$x(n)$ = input signal
$\mathbf H$ = system response as a toeplitz matrix
$$\mathbf H = \begin{bmatrix}h(0)&&&\\h(1)&h(0)&&\\h(2)&h(1)&h(0)&\\...
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How is the sound converted to matrix in Matlab?
I am using the audioread(filename,y,Fs) function of Matlab and it converts an audio file to a matrix. I want to know how is each value of that matrix generated. Is ...
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Hessian Matrix. Second partial derivative test
I have a question about the hessian matrix / determinant of the hessian matrix. For the Hessian matrix, one is able to determine the local curvature around a point. And with the Second partial ...
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what is happening when i run this code line? [closed]
I have the following MATLAB code:
x=[1 2 3; 4 5 6; 7 8 9;];
u=(0:255)/(255-1).^1.05;
x2=u(x+1)
when I run this code I get the following as a result in ...
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How to make the $\ell_2$ norm of all columns and rows of an $n \times n$ matrix equal to $\sqrt{n}$?
I have an $n \times n$ matrix and I would like its columns and rows to have $\ell_2$ norm equal to $\sqrt{n}$. Is this possible?
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How to calculate the scale, rotation angle and translation between 2 images if we know the homography result matrix?result
I got the result of findHomorgraphy in OpenCv. As below:
Homography transform matrix:
[-1.1534205416542787 0.7834287271121142 527.9064589440736
-0.2415444621693116 0.16412191792642924 ...
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Maximising each element in a matlab array
Is it possible to construct an array A, without looping, where A(i,j) = max(B(i),C(j)) and B ...
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Emulate signal loss of a pixellated detector in Python?
I have a matrix 64x64 where each cell represents the pixel of a pixellated detector.
The spacial response of this detector decreases by going further from its center (that is, coordinates "31,31" or "...
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What does "kernel based" mean?
In my thesis I try to explain what kernel based methods are, especially the meaning for object detection.
I know kernel based methods like Mean- and CamShift and I know how to use them. I understand ...
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Mat and int are incompatible? [closed]
anybody knows what this is?
Mat mat = (Mat_<double>(3, 4) << 0, 0, width, width, 0, height, height, 0, 1, 1, 1, 1);
I dont know what mat would be in ...
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Sensor Data Fusion with Orientation Sensors in 3D Euclidian Space
Preconditions
For measuring the position of a mobile device in 3D space, I utilize two sensors with different characteristics that measure device orientation.
Sensor A (a combined sensor of ...
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Generating Wavelet family matrixes
We have unnormalized Haar matrix which, is for example,
H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1]
After normalizing it, we use for haar transform. I know how to ...
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5.1 Rear To 5.1 Side mixing matrix
I am searching for a matrix definition for converting a audio signal (5.1 with rear) to a audio signal (5.1 with side).
Currently I am using the definitions from: https://msdn.microsoft.com/en-us/...
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Matrix expansion into bases
I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should ...
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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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Distribution of a signal covariance matrix
A common estimation problem in signal processing assumes the following signal model
\begin{equation}
\mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n}
\end{equation}
where $\...
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Are there condition numbers associated with the STFT, DWT?
Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1.
Is it possible to represent the STFT and DWT as ...
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Dominant eigenvectors of an unknown matrix
Do you have any idea about how we can find the principal eigenvectors of an unknown matrix ${H}$?
The elements of $H$ are unknown in general. If you are familiar with channel estimation procedure in ...
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How to get relative rotation matrix from two orientation values in android?
Following http://www.codeproject.com/Articles/729759/Android-Sensor-Fusion-Tutorial , I get two orientation values. Then, I transform those values to rotation matrices R1, R2.
I think the relative ...
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Convert a 1D array into a 'rotated' 2D matrix
simply put, let's say I have this array - [1 2 1]
I want to try and get this output in Matlab
[1 1 1
1 2 1
1 1 1]
It's like my array was 'rotated' into forming ...
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PSNR of two images of different size in matlab
I performed bicubic interpolation on a 256*256 image(img)
dest = interp2(img,'bicubic')
and i got a 511 * 511 image.I want to compute PSNR of a 512 * 512 image(...
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Difference Between Correlation / Convolution and Matrix Multiplication
Can anyone please clarify the difference between correlation/convolution and matrix multiplication? As I thought either convolution or correlation is similar to matrix multiplication. I read this ...
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How to replace Hadamard Product and Column wise addition with new Matrix operation?
Let
$$
A=
\begin{bmatrix}
a_{1,1} & a_{1,2} & a_{1,3}\\
a_{2,1} & a_{2,2} & a_{2,3}\\
a_{3,1} & a_{3,2} & a_{3,3}\\
\end{bmatrix}
$$
and
$$
B=
\begin{...
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What is a covariance matrix?
Suppose you have k samples from each of the N elements of a uniform linear array (ULA) of sensors:
What is the physical meaning of a covariance matrix?
How do you form a covariance matrix with the ...
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Solving an Array Signal Processing Estimation Problem based on the Rayleigh Quotient
The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by
$$
R(\mathbf{C},\mathbf{a}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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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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How to compute regions of matrix
Let's say we have the following matrix:
0 0 0 0 0 0
0 1 0 0 0 0
1 1 0 0 0 0
1 1 0 0 0 0
0 0 0 0 0 0
0 0 0 1 1 1
0 0 0 0 1 1
0 0 0 0 0 0
I want to calculate the ...
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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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How to understand energy function in thin plate splines?
guys! I have carried out some experiments using matlab warp tools from here. But the results are not good, so I decide to read its original paper Principal Warps: Thin-Plate Splines and the ...
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reconstruction of time series in SSA
i am trying to reconstruct time series from SSA ,because according to this link
http://en.wikipedia.org/wiki/Singular_spectrum_analysis
there is procedure
...
user350
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Expectation of product of hermitian matrix
Let $\textbf{h} \in \mathbb{C}^{N\times 1}$, $\textbf{a} \in \mathbb{C}^{N\times 1}$, $\textbf{b} \in \mathbb{C}^{N\times 1}$ and $\textbf{c} \in \mathbb{C}^{N\times 1}$. The variable $h_i$ is defined ...
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Matrix form of STFT
IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? ...
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How to Prevent overflow/saturation in fixed point implementation of Fast Data Projection Algorithm
I am trying to implement an algorithm in real-time on a Fixed point DSP (The Blackfin from Analog Devices). The algorithm does a lot of stuff, but in the middle it performs an algorithm called "Fast ...
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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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Incoherence: Compressed Sensing (CS) vs Matrix Completion (MC)
I am seeking a clarification of the concept of Incoherence within the MC framework.
Specifically,
1) the literature mentions the application of a "strong incoherence" given a set of assumptions. ...
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how to calculate cross correlation of transient signal?
there.
Let me have a noisy speech signal $y(k)$ as below.
$$ y(k) = x(k) + v(k) $$
where, $k$ is the discrete-time index, $x(k)$ is clean speech signal, $v(k)$ is a zero-mean random process, ...
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3 Band Wavelet Transform In MATLAB
I am currently working on an audio watermarking project in MATLAB. I currently have a code I am using to construct a nxn 3 Band Wavelet Transform matrix. However, when I try to construct a matrix that ...
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Digital Image Processing Framework
i'm looking for a free/opensource solution for digital image processing with reasonable performances processing quite large images (e.g. actual smartphones have resolutions of 8-10Mpx) and being ready ...
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Covariance matrix explanation
I am trying to understand and visualize the concept of a covariance matrix. Suppose I have a matrix:
$A = \begin{pmatrix} 2 & 3 & 4\\ 5 & 5 & 6 \end{pmatrix}$
how do I calculate its ...
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Can Cholesky outer product version result in negative square roots?
Say A is symmetric positive definite matrix , which means one necessary condition is diagonal entries of A are positive. If I do cholesky factorisation using outer product form, Can there be any ...
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understanding FFT2 function of Matlab
I am trying to understand what happen when we take FFT2 of a matrix in a matlab.
first have a look at this simple example,
a=ones(8); %8x8 Matrix of Ones
fft2(a)
...
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Reflection Rotation matrix
I'm doing a rigid body between point clouds using SVD.
Sometimes the routine produces an incorrect rotation matrix with a Determinant=-1, ie a reflection matrix.
Any idea why ?
Is there a valid way ...
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Matlab BOC (binary offset carrier)
I am trying to implement a binary offset carrier (BOC) direct sequence spread spectrum scheme in MATLAB. In that scheme, a code $c(t)$ (a binary vector which repeats after a certain number of zeros ...
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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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