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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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9 views

### Physical meaning of a signal with 4 IMF?

If a signal is composed of four implicit mode functions, where the last one is a constant residue, does the instantaneous frequecy of the signal have physical meaning?
14 views

### How to get NMF sparse component factors

In the NMF framework, whenever I want to get a sparse component, I set the rank to 1 (lowest possible) and get the W and H matrices of the low-rank component by doing a multiplication of the resulting ...
29 views

### Difference between “Discrete Wavelet Transform” and “Discrete Wavelet Decomposition”

I have a rough overview on Discrete Wavelet Transform (DWT). However, I am confused about Discrete Wavelet Decomposition and did not find a good reference yet which explains this well. What is it ...
57 views

### 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-...
47 views

### 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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### 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 ...
171 views

### 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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### 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 ...
1k views

### What are the Even and Odd Components of a 2D Signal

A signal $x$ can be decomposed into its even, $x_e$, and odd, $x_o$, parts. By, $$x_e(t) = \frac{1}{2} [x(t) + x(-t)]$$ $$x_o(t) = \frac{1}{2} [x(t) - x(-t)]$$ What would be the equivalent for ...
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### Ways to parallelize Sifting in EMD (Empirical Mode Decomposition)

Sifting process, which is recursive in nature, is used in EMD (Empirical Mode Decomposition) to decompose the signal (x(t)) into Intrinsic Mode Functions (IMFs) and residue, which is a monotonic ...
44 views

### 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?: ...
22 views

### 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 ...
20 views

### 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) ...
61 views

### Is there any special when all Fourier components have the same angle?

When a square wave doesn't jump, its oscillators aren't aligned: But if they are in sync, the wave will jump to its extrema: However this is just an example of square waves. The tool Understanding ...
12k 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 ...
18 views

### 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 ...
596 views

### 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 ...
60 views

### How to express one image in terms of another one

I have two (black and white) images of identical size - let's say 128x128 pixels. I'm interested in expressing Im2 in terms of ...
195 views

### 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 ...
101 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 ...
455 views

### Optimal Level of Wavelet Decomposition for Denoising

If a certain mother wavelet is defined and the optimal threshold shall be defined via Donoho, how can I define the optimal decomposition level to achieve the best denoising results.
302 views

### Difference(relation?) between filter banks and wavelet decomposition

I'm implementing multirate system and met concepts of filter banks and polyphase decomposition of filters. While trying to understand them, I've found that they look very similar to wavelet ...
41 views

### How many times does a certain sound appear in an audio clip?

I have an audio clip which can be found here or here. If you hear the audio clip you will notice that there are six times a kind of hit sound in the clip. My questions are: How can I count these ...
71 views

### Advice needed for separating 3-channel signals

I'm working on a personal project, where I'm trying to make a touch screen that uses force sensors as the basis of the technology. The rig I've made has have three transducers underneath a square ...
2k views

1k views

### How can I decompose a signal into square waves?

I am dealing with signals that are a superposition of different square waves with different amplitudes and phases. Normally, one would decompose a signal into sine waves with help of the Fourier ...
633 views

### Trying to decompose a signal into sine waves whose wavelengths aren't restricted to 1/N times sample range?

I am trying to essentially do a Fourier transform - I want to fit some data with sine/cosine functions. At first I was trying to do this using FFT, but my problem is that the FFT algorithm doesn't ...
2k views

### Slow Down Music Playing While Maintaining Frequency

Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...
220 views

### Algorithm for Discrete Signal Decomposition

I am building a sensor and I am trying to understand how to process the signal that it generates. The sensor has a library of reference signals. When 'event a' occurs, it produces signal A, when '...
369 views

### Decomposition of a signal to slow and fast components

I am currently recording biological responses which are triggered by different events. The figure below shows the original signal (black) and the occurrence of input events (colored dots). There is ...
108 views

### Extracting original signal from overlapping area

Considering this image, where I have a spectral decomposition of a light bulb. Due to the non point shaped light source, the spectral decomposition using a diffraction grating in front of my camera ...
207 views

### What is the right algorithm to detect segmentations of a line chart?

To be concrete, given 2D numerical data as is shown as line plots below. There are peaks on a background average movement (with small vibrations). We want to find the values of pairs (x1, x2) if those ...
64 views

### Decompose an image into better compressible components

Our team develops an application that, in some feature, connects to a scanner (via TWAIN or WIA) and scans a document, and makes a PDF file out of it. The application is mostly used to process mail or ...
138 views

### Why is successive decomposition of a signal performed only on low pass component?

The question says it all. In typical (wavelet-like) decomposition of a signal, why is only the low pass component chosen for successive decomposition ?
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### 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 ...
210 views

### Q and I part in QAM

I have one confusion in QAM about in-phase I and quadrature Q part, i.e. do they transmit identical data or not? For e.g. if i have 11001001 as a byte to be transferred, so will 4-QAM separate it like?...
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### Suitable metrics for summarizing or visualizing the spatial activation of components after temporal Independent Component Analysis (ICA)

I will first describe the Independent Component Analysis (ICA) steps, so that the question becomes clearer, and more relevant to similar questions. Assume we have $N$ sensors distributed in space. ...