Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [eigendecomposition]

27 questions
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Are complex exponentials the only eigenfunctions of LTI systems?

Is there an example of an eigenfunction of a linear time invariant (LTI) system that is not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but I am not able to find one.
Vinod
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Eigenvalues and Eigenvectors of a 3D Image Laplacian

I need to compute the eigenvalues and eigenvectors of a 3D image Laplacian. I'm trying to evaluate the heat kernel on the 3D uniform grid (the uniform structure generated by the voxelized image) at different time values, to implement a Volumetric…
Federico
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What Is the Difference Between PCA and Karhunen Loeve (KL Transform)?

I have been reading about Karhunen-Loeve or also known as KL transform and I see that when it is used to reduce dimension the procedure is identical to PCA, that is, for both methods the covariance matrix of the data is constructed and then the…
Roger Figueroa Quintero
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Eigen Values and Eigen Vectors in Image Processing

I have been reading about eigen values and eigen vectors but I haven't been able to find any decent explanation relating their application in Image Processing / Computer Vision. For example, How can those be used for face detection and eye…
silver surfer
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Subspace Methods - Eigenvalues of the Signal Subspace

Subspace frequency estimation methods like MUSIC or ESPRIT decompose the signal correlation matrix into a signal and a noise subspace. Assume the signal model is given by $$\boldsymbol{s} = \boldsymbol{H}(\boldsymbol{f})\boldsymbol{a} +…
Lukas
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MUSIC algorithm terminology

Looking for clarification on the notation described in the MUSIC algorithm in Ralph Schmidt's IEEE paper$^{[1]}$. The data model is: $$X = AF + W$$ Schmidt defines the following: X = received signal for each array element A = steering vector F =…
BigBrownBear00
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MUSIC algorithm derivation

Setup Suppose we have a complex $L\times 1$ signal $\mathbf{x}$ with two tones at (unknown) frequencies and phases defined as: $$ x_n = A_1 e^{j \omega_1n + \varphi_1} + A_2 e^{j \omega_2n + \varphi_2} $$ for $0 \leq n \leq L-1$. We observe…
Atul Ingle
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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 eigenvalues (this might be a silly question in your…
陈绍伍
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Proving that a product of matrices invertible

Given $R_x$ a Positive Definite (PD) covariance matrix of size $M\times M$ and $C$ a full rank $M \times N$ matrix, I want to prove that $C^* R_x^{-1} C$ is invertible to derive the Linearly Constrained Minimum Variance Beamforming. My ideas so…
Oriol B
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Are all exponential functions eigensignals of LTI systems?

I know that complex exponential functions are eigensignals to LTI systems. Do these include real exponential functions? E.g. $2^t, e^t, ...$ Thanks for the help!
Phobos
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Intuitive explanation of subspace

There are many techniques in signal processing that use eigen analysis (MUSIC, SVD, eigen decomposition, etc) that result in signal and noise subspaces.The mathematical definitions for signal subspaces are abundant, but what is the intuitive,…
BigBrownBear00
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Problem with Covariance matrix using diagonal loading involved in calculation of eigenvalues

I have the following problem : I'm calculating the sample covariance matrix in the frequency domain ( $y_{k}$ is the FFT of a time domain $k_{th}$ symbol vector signal , basically a simulated received signal) as…
Ricardo García
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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? In linear algebra, a matrix is basically a linear…
Sagnik
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SVD vs matched filter

Reading about singular value decomposition (SVD) in the context of signal processing applications, one can separate the signal from the noise into orthogonal subspaces. On the surface this sounds like using the decomposed output of the SVD is more…
BigBrownBear00
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How to estimate noise by eigendecomposition of the variance covariance matrix?

I'm new here so I will try to be as clear as possible. I am trying to apply some techniques from signal processing framework to denoise financial time series. I would like to know if what I am trying to do makes sense or if I am committing some…
Chaos
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