Questions tagged [eigendecomposition]

Question 1

Let us consider signals (or finite sequences) that are invariant under the Discrete Fourier Transform (DFT). Suppose we are able to obtain a closed-form (explicit) formula for such invariant signals. ...

Question 2

This question is a follow-up to this Pisarenko Harmonic Decomposition question. In the answer and comments gathered there, it appears that instead of computing the Pisarenko pseudo-spectrum using the (...

Question 3

I'm trying to implement Pisarenko's Harmonic decomposition in Python and can't get a proper pseudo spectrum revealing the three frequencies of the signal I'm analysing. I tried a few things (using <...

Question 4

Consider a real vector time series: $\mathbf{x}_k\in{\mathbb{R}}^{N \times 1}$ where $k$ is the sample index. An associated correlation matrix is updated recursively as: $${\bf R}_k = \alpha {\bf R}_{...

Question 5

Let $F=\frac{1}{\sqrt{n}}(w^{kl})_{k,l=0}^{n-1}$ be the discrete Fourier matrix of size $n$ where $w=\exp^{-\frac{2\pi i}{n}}$. It is a well-known that $F_n^4 = I_n$ where $I_n$ represents the ...

Question 6

After reading a few posts, like this. I know that arbitrary LTI systems always have complex exponential eigenfunctions. And that for specific LTI systems you can also have other types of ...

Question 7

Different sets of eigenvectors for the Discrete Fourier Transform (DFT) are well-established. Are there any potential practical implications associated with deriving explicit formulations for these ...

Question 8

I am seeking clarification on a particular step in the derivation of the MUSIC algorithm as presented in a specific paper. Here, there is an intermediate step I cannot follow and I would appreciate ...

Question 9

Note: this question was initially asked in a different community. Encouraged by the comments, I decided to cross-post here too. Given (z,p,k) my goal is to convert to a state-space representation (A, ...

Question 10

Let $$\dot{x} = Ax+Bu$$ $$y = Cx + Du$$ be a linear ODE with $x(0)=0$. Here, I am assume $A$ is invertible. As you can see, the relation $$H:u(.) \mapsto y(.),$$ where $(u(.),y(.))$ is a solution to ...

Question 11

I am Ph.D in pure mathematics and interested in signal processing. Theoretically, any illustration of the eigendecomposition of the discrete trigonometric transforms (DTTs) is worthwhile. Q. What real ...

Question 12

I am looking for all pairs $(x[n],q)$ where $x[n]$ is a periodic discrete signal with period $N$ and $q$ is a rational number satisfying the following identity: $$\mathcal{F}x[k]=e^{i(q-\frac{\pi k}{...

Question 13

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} = \...

Question 14

While reading the paper "Perturbation analysis for subspace decomposition with applications in subspace-based algorithms" by Zhengyuan Xu, I came across the decomposition technique called ...

Question 15

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 ...

Stack Exchange Network

Questions tagged [eigendecomposition]

On the Utility of DFT-Invariant Signals and Their Closed-Form Representations

Computing modern spectral estimation techniques with FFTs

Mistake in Python implementation of Pisarenko's harmonic decomposition

Fastest way to track dominant eigenvector of recursively updated correlation matrix

The Discrete Fourier Transform (DFT) decomposes any signal into four orthogonal signal components

Are complex exponentials the only eigenfunction for arbitrary LTI systems?

Practical Implications of DFT Eigenvector Formulations

Smallest Eigenvalue in the Derivation of the MUSIC Algorithm

Direct and numerically robust conversion from zero-pole to state-space representation

Why do they say that complex exponentials are eigenfunctions of LTI systems, when there are still transient responses?

The benefit of Eigendecomposition of DCT and DST

When is the Fourier transform of a periodic discrete signal $\mathcal{F}x[k]$ the same as $x[k]$ up to a diagonal matrix

Subspace Methods - Eigenvalues of the Signal Subspace

Subspace decomposition

Why do we need to estimate eigenvalues?

Hot Network Questions