# Questions tagged [signal-analysis]

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### Proof that two vectors can not have the same power spectrum when one is a permutation (excluding rotations) of the other?

The power spectrum being the absolute value of the DFT of the vector. Has it been proven that two vectors can not have the same power spectrum if one is a permutation of the other? Where, in this ...
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### What is intuitive perception of $T_{\alpha_1} \circ T_{\alpha_2} \circ ... \circ T_{\alpha_M}$ in graph domain?

if $G(V,E,W)$ be a weighted graph and $\vert V \vert =N$. for any vertex $i \in \lbrace 1,2,...,,N \rbrace$ define a generalized translation operator $T_i:\mathbb{R}^N \to \mathbb{R}^N$via ...
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### Optimum frequency estimation over a Rayleigh fading channel

This question comes from the book "Autonomous Software-Defined Radio Receivers for Deep Space Applications"1. The chapter 4.1.3 is "Optimum Frequency Estimation over a Rayleigh Fading Channel". The ...
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### Why do we consider some weakening frames like K-frames, frame sequences, and upper semi-frames?

I have found some applications of the Frame Theory in engineering sciences like signal processing, image processing, data compression, sampling theory, optics, filter-banks, signal detection. As we ...
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### Discrete Wavelet Transform and Gaussian decay

I have a question regarding the possibility of constructing a Discrete Wavelet Transform based on a scaling function having Gaussian decay (and no more decay than that). More specifically, I am ...
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### Problem with state dimensions in IMM algorithm

I'm working on tracking algorithm for radar system. I have 3 motion models with state vector: $x_1=[x,y,v_x,v_y]$, $x_2=[x,y,v_x,v_y,a_x,a_y]$, $x_3=[x,y,v_{abs},\phi,\omega]$. The first two models ...
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Assume that $G$ is a finite vector space over a finite field with order $|G|$. (For example, $G=Z_p^k$). Assume that $\{f_n\}_n$ is a Parseval frame for $l^2(G)$. Can we say that the sequence $\{f_n\}... 1answer 223 views ### Boundary behavior of harmonic function on the square Is there a constant$C$such that if$u:[0,1]^2\to \mathbb{R}$is harmonic with$u\in L^\infty(\partial [0,1]^2)$(if you prefer you can also assume$\|u\|_\infty = 1$on the boundary and$u$smooth ... 3answers 451 views ### Finite realization of irrational transfer functions In the field of digital signal processing, linear time-invariant systems play a distinguished role. These are the systems for which there exists an impulse response, a function$h:\mathbb{Z}\to\...
Is there a characterization of mappings $p : \mathbb R^n \rightarrow \mathbb R^n$ which are proximity operators (in the sense of Moreau) of l.s.c (extended) real-valued functions ? That is, given \$p : ...