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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24 views

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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19 views

Large scale consecutive matrix multiplication applications

I am running some experiments with matrix multiplication and I am looking for applications (preferably signal processing applications) where multiple input matrices A(i), [i=0,1.....] are multiplied ...
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44 views

How I can optimize the DFT become the FFT?

As title, I am trying to understand fast Fourier transform, but I have a little trouble, that is: The DFT said that we must multiply the matrix 2n x 2n with ...
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1answer
34 views

Is there a way to perform 2-D 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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0answers
51 views

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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17 views

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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1answer
98 views

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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1answer
113 views

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' ...
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1answer
216 views

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 ...
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1answer
126 views

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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127 views

how to compute the power spectral density matrix of the signal

I am implementing in Matlab a paper (*) which used the power spectral density matrix of the signal in the initial step. I will sum-up below. Suppose there are M channel measurements, and dividing ...
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26 views

Do eigenvalues shift with change in SNR

Let $H = \frac{1}{\sqrt{2}}M + \eta$ where $M= \frac{2}{\sqrt{15}}\left( \begin{array}{cccc} 3 & 2 & 1 & 3 \\ 1 & 2 & 3 & 1 \\ 1 & 2 & 1 & 1 \end{array} \right)$ ...
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48 views

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= ...
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1answer
105 views

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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0answers
40 views

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}) := ...
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89 views

Least Angle without matrix inversion?

Sorry if this is too damned long. I did what I could to abbreviate it. I'm new to numerical work with matrices. I believe I have a way to compute Least Angle without explicit matrix inversion. I'm ...
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3answers
77 views

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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37 views

Matching 2 undirected weighted graph in matlab

Consider 2 undirected weighted graph as shown in figure.Consider first graph as G1 and second graph as G2.Graph G1 consist of vertices V={F1,F2,F3,F4,F5} and Graph G2 consist of vertices ...
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71 views

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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1answer
474 views

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 ...
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0answers
31 views

How to calculate the freedom of projection matrix?

I learned projection matrix from textbook. It says that the 9th is redundant, so it has 8 freedom. But I can not know the reason clearly. Following the equations. I can not understand why i does ...
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1answer
39 views

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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1answer
38 views

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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116 views

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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1answer
101 views

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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1answer
104 views

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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0answers
329 views

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 ...
2
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1answer
108 views

A good Digital Image Processing environment

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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2answers
303 views

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 ...
2
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0answers
66 views

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 ...
2
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1answer
4k views

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, ...
2
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1answer
105 views

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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2answers
453 views

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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1answer
342 views

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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2answers
983 views

Shortest geometric distance from surface in 3d dataset?

I have a three-dimensional binary image of a collection of discrete, individual voxels ("seeds") contained in a connected 3-dimensional surface ("skin"). (Like a small fruit, with a surface delineated ...
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2answers
657 views

Why do we deal with the eigenvectors of the autocorrelation instead of the data itself?

How intuitively to understand why eigenvectors of the autocorrelation matrix are used, but eigenvectors of the matrix constructed from temporal samples have no sense and aren't used? For example, in ...
8
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1answer
3k views

Analytical expression for the eigenvectors of a 3x3 real, symmetric matrix?

I am writing an algorithm that process 3D images based on the local moment of inertia. I have a 3x3 real symmetric matrix, from which I need to find the eigenvalues. I have found a variety of ...