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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making a laplace s-domain plot from numerical data to decompose signal into decaying sinusoids

I would like to make a 3D laplace s-domain plot from experimental data I have. The examples I have seen for this are when the function is already known and an analytical solution can be obtained (...
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What is the way in which an audio signal is "cleaned"?

I was studying how signals can be "decompose" with the Frequency domain analysis and Fourier transforms; I have also read that through these actions it is possible to clean the signals from ...
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Signal decomposition to even and odd components

I'm trying to decompose some signal to even and odd components, here's the Python code of it: ...
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aperiodic sum of periodic signals

Asumme that a continous signal is a finite sum of sinusoid. If the signal "begins" at $-\infty$ and "ends" at $\infty$, using Fourier transform, one can find the frequency, the ...
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Minimum Phase - All Pass Decomposition For Large Linear Phase Filters

UPDATE: I am looking for a robust approach to decompose linear phase FIR filters with 100s of coefficients into its minimum phase and all pass components. I originally thought determining all the ...
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How to automatically determine if there is NO seasonality from PSD/FFT of time series?

I have around 1000 different time series, and for each one of them I want to automatically determine if there is any seasonality in the time series. Given the assumption that there is seasonality ...
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Subspace decomposition

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 ...
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Why does a wave composed of two waves have an FFT with only one peak?

I am trying to find a value from a given mathematical function whose input is supposed to be derived from FFT components. Essentially, I follow the procedure from [1] which assumes that a given sine ...
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Reflected wave in FFT?

I'm trying to determine the reflective coefficient of sine wave. This one paper suggests a method using Fourier analysis. Here, it suggests Incident Wave = a cos(kx + Constant1), Reflected Wave = a ...
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Decomposition of two equal and overlapping complex signals

I have been wracking my brain over this problem for weeks and I finally have to throw in the towel and ask for help. My background is not formally in signal processing, so I may just lack the ...
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Signal separation

This is probably a blind signal separation problem of sorts, but it seems like it should be easier than I am finding it. Let’s say I have N time series, each of length [M x 1] that are a superposition ...
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Can I decompose a sine signal into its component sine waves?

If I have a sine signal that was composed of the sum of multiple other sine waves, is there any way that i can decompose the sine signal into its component sine waves without knowing any of the ...
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calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources

migrated from math-se... I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and ...
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How to decompose a signal into exponentally decaying sinusoids?

I have a system of coupled oscillators. One is a pendulum acting as a tuned mass damper and the other is a wooden structure. When I loosen the screw that allows the pendulum to oscillate I get a ...
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Testing user's pronunciation of Arabic against correct pronunciation

I'd like to be able to compare two audio streams: one containing the correct pronunciation of Arabic text (from the Quran), and the other containing one from a user learning Arabic. Here is a sample ...
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Separation of many signals all containing 1 common component

I have been struggling with a research question and would appreciate any pointers (or full solutions). I have a data set of many (+/- 50k) observed - correlated - signals. These signals are known to ...
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Compute minimum phase version of a FIR

I am working with HRIR filters, in particular I am trying to interpolate them. One commod method in the literature to perform interpolation of HRIR is to use the minimum-phase decomposition and ...
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Bandpass before EEMD- selecting IMF outside band pass range

I have a vibration signal of 25.6 kHz where I first perform band pass filtering (7000 Hz, 9000 Hz) and then perform Empirical Mode Decomposition (EEMD). I then want to select the IMF where the ...
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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 ...
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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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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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1 answer
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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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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 ...
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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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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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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 ...
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15 votes
2 answers
18k 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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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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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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1 answer
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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 ...
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3 votes
0 answers
280 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 ...
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2 votes
0 answers
120 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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6 votes
2 answers
600 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.
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3 votes
1 answer
405 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 ...
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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 ...
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3 votes
1 answer
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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 ...
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3 answers
3k views

How to get the sum of unit steps and unit ramps from a discrete signal?

I have the discrete-time signal depicted below. This signal can be written as follows $$y[n] = \{0, 0, 2, 4, 6, 6 ,6,0,0,\ldots\}\,,$$ or as the sum of shifted impulses as: $$y[n] = 2 \delta [n-2]...
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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 ...
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10 votes
1 answer
3k 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 ...
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3 answers
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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 ...
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11 votes
3 answers
4k 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 ...
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2 votes
1 answer
287 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 '...
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4 votes
1 answer
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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 ...
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3 votes
1 answer
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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 ...
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1 vote
1 answer
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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 ...
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2 votes
1 answer
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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 ...
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2 answers
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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 ...
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