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Questions tagged [decomposition]

The concept of signal decomposition relates to the need to separate one component from the others in a signal; this can be achieved through a filtering operation which require a filter design stage.

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Separation of overlapping frequencies

I have a signal with multiple frequencies, and two of them, one of which is my main frequency, overlap. Are there any techniques that could separate two frequencies that almost overlap? I can ...
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7k views

Discrete Wavelet Transform - Visualizing Relation between Decomposed Detail Coefficients and Signal

I'm trying to directly visualize the relation between discrete wavelet transform (DWT) detail coefficients and the original signal/its reconstruction. The goal is to show their relation in an ...
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Blind source separation with one source rotated

I have two images: $$ I_1 = w_{11}A + w_{12}B, \\ I_2 = w_{21}A + w_{22} \bar{B}. $$ $A$ and $B$ are unknown. $\bar{B}$ is ${B}$ rotated by 180 degree. For both images, $A$ has higher signal-to-...
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Extract approximation and detail coefficients

I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
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Intuitions on Kumaresan-Tufts algorithm for exponential fit

I am analyzing a transient signal presumably consisting of superposed exponentials. Such a case is indicated for the Prony analysis, but my data aren't noiseless enough, so I have turned to the ...
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90 views

Helmholtz decomposition implementation

I need to perform the Helmholtz decomposition of a 2D flow. An old and obvious problem is the numerical differentiation (largely amplifying the noise). I do understand the procedure I am just ...
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167 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 ...
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40 views

Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components?

I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components. If it would be a sum of some sinusiod waves, it would be easy to ...
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About filtering and composing signals

I have got three signals, acc_x, acc_y, acc_z. I need to compose them in order to compute the magnitude of the acc. I would like to ask the following question: what is better opt1 or opt2? or opt3?: ...
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why is my inbuilt function is not matching with the db5 CA and CD coefficients generated by my code

I am working on wavelet decomposition.As read by the theory i have implemented wavelet decomposition in MATLAB. CA and CD for wavelet decomposition of db1 matches with the inbuilt function but not ...
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65 views

What is the difference between Time-Frequency Represenation and TF Decomposition

I'm asking as I'm looking at Wavelet transforms, and I see that it is possible to have a TF decomposition or a representation of the signal. Looking for example at the code here we can see that the ...
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137 views

Optimal filter bank from SVD/PCA

Given a million data points in say 100d, is there a way to generate an optimal filter bank of say 20 filters from an SVD of the data ? Call the 100d space $F$ (as in Frequency), with coordinates $[f_1,...
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What's the difference between Wavelet transform coherency and Singular Spectrum Analysis

I know that Wavelet transform Coherence is the most common method to find the linkage between two time series, in field of finance. Can we use Singular Spectrum Analysis to find out the linkage of ...
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How to reproduce a signal from its decomposed components?

Given a dataset of a signal which has been decomposed into its IMfs (with EMD (Hilbert-Huang transform)), how can synthetic replicas of that signal be reproduced from the decomposed signal? There are ...
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Find which groups of ants are coexisted in the location from their signal profiles using NMF

I try to solve biological problem to tell which groups of ants are co-existed at this location by their sounds in specific time frame. My chosen framework is Non-negative Matrix Factorisation (NMF) ...
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Join 2 NMF models where dictionaries has hierarchical structure

I have two NMF models $A = W_1A_{dict}$ and $B = W_2B_{dict}$ (where the $W$ represents weight coefficient matrix). What is a good way to join two NMFs if I know each column of $B_{dict}$ is summed up ...
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Method to Decompose Modulation Series

Given a signal $$\sin\left(\frac{2\pi}{\sin(2\pi/Tx)x}\right)+n$$ (where n is noise) is there a way to isolate and decompose the number, frequency, and causal (carrier-modulator) order of the ...