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Questions tagged [eigendecomposition]

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Eigenvalue based detection threhsold of sub-sampled signal

At the receiver side, I have an observed signal sampled at a rate much lower than the Nyquist rate. I would like to know how many frequency components there are in the signal. I applied the singular ...
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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 ...
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Is there a situation when maximizing SNR doesn't also maximize probability of detection?

The problem I'm working on is signal detection of a radar signal, but I suspect this problem shows up in many different branches of signal processing. Background: From [1], the factor $I_f$, by ...
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1answer
48 views

What are some efficient algorithms for real-time calculation of eigenvalues?

I need to calculate eigenvalues of a square matrix for a real-time implementation using microcontrollers or dSPACE. Obviously, I can find the eigenvalues of a 2by2 matrix analytically. I am wondering ...
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1answer
441 views

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 ...
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Interpretation of Eigen Values of covariance matrix

I am trying to obtain an intuitive understanding of Eigen Values of covariance matrix and have used a few layman terms because I fully do not understand the concept yet. The following is the code ...
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1answer
120 views

Eigenvalues of FIR Convolution Matrix

Are the eigenvalues of the FIR convolution matrix the zeros of the corresponding FIR filter? Suppose I have an FIR filter $H(z) = h_{0} + h_{1}z^{-1} + h_{2}z^{-2}$. I want to implement it using a ...
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1answer
632 views

What are the eigenvalues of the 8 point DFT matrix?

I know that the eigenvalues for 4 point DFT matrix can be found from $F_4^4=I$. Is this also valid for 8, 16 and higher orders? For example with 8 points, will it be $F_8^8=I$ ? If not, how can I ...
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1answer
970 views

Angle of arrival (AOA) estimation using FMCW radar using MUSIC algorithm

I am working with FMCW phased array radar with only upchirps. The range doppler matrix is obtained using the two dimensional fast Fourier transform on multiple chirps. I want to obtain the angular ...
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1answer
250 views

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 ...
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2answers
583 views

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 + \...
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Eigen Value and Eigen Vectors in Image Processing

I have been reading about eigen values and eigen vectors but i haven't be able to find any decent explanation relating their application in image processing/computer Vision for example say face ...
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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 ...