# 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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### How can we prove using matlab that after each level of decomposition of a signal using DWT the frequency content is halved?

I was trying to decompose an EMG signal, which was sampled at 200 Hz, into 7 levels of decomposition using DWT. And the result is shown in the figure( only up to level 3 is shown here) However, I ...
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### Smooth envelope of an aperiodic signal

I have a signal that looks like this: Red line is the function I'd like to obtain somehow. Everything <= -60 is basically absent data (i.e. not low signal). If I understand correctly, Hilbert ...
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### Video Alpha Matting

I'm looking to composite an opaque object (e.g. 3D art) into video footage of semitransparent fog/clouds before a landscape background so that the object seems immersed in the clouds but occludes the ...
1 vote
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### Narrow bandpass filtering

I want to plot a specific frequency (e.g., 1 kHz or 100 Hz) of an audio file (sampling rate 44.1 kHz). I have done fft and spectrogram analysis on the file, but I am now interested in plotting only ...
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1 vote
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### Amplitude and phase from variational mode decomposition?

If a VMD analysis were fairly successful, in the sense that the spectrum is unimodal and relatively sparse, but still with a bit of bandwidth is it possible to extract a meaningful local amplitude and ...
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1 vote
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### Creating a polyphase filter

I need to design a 3/2 resampling filter using polyphasic filters. On my original filter I have coefficients $$h[n] = [a_0, a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, a_{10}, a_{11}]$$ making it an ...
102 views

### Signal sawtooth decomposition

I'm interested in analyzing a windowed signal in terms of a weighted sum of sawtooth waves. Being a somewhat DSP newbie, is there an obvious approach to this? I realize that sawtooth waves don't form ...
231 views

### A self-supervised learning technique to denoise my specific signal

So I work in this domain of biophysics that has to do with a light-based detection for measuring small movement of molecules (nanometer and piconewton scale) via a Quadrant Photodiode. This signal ...
I was learning the decomposition of a signal into one even signal and one odd signal: $$x(t) = x_{e}(t)+x_{o}(t)$$ with $$x_{e}(t) = \frac{1}{2}\cdot [x(t)+x(-t)]$$ and $$x_{o}(t) = \frac{1}{2}\cdot [... • 227 2 votes 1 answer 194 views ### Why does NMF (Non Negative Matrix Factorization) decompose a spectrogram into time and frequency component? I compute the NMF over a spectrogram (magnitude of STFT of a signal) in this way: W,H = NMF(MyStft,r) # where r=2 is the rank W and H respectively contain the ... • 21 2 votes 2 answers 238 views ### 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 (... • 21 0 votes 1 answer 34 views ### 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 ... 0 votes 1 answer 555 views ### 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: ... • 345 2 votes 3 answers 437 views ### 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 ... • 31 13 votes 4 answers 903 views ### 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 ... • 48.8k 0 votes 1 answer 104 views ### 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 ... • 111 0 votes 1 answer 90 views ### 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 ... • 79 0 votes 1 answer 273 views ### 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 ... 0 votes 0 answers 79 views ### 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 ... 0 votes 2 answers 113 views ### 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 ... 1 vote 0 answers 46 views ### 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 ... • 11 1 vote 2 answers 1k views ### 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 ... • 113 2 votes 0 answers 82 views ### 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 ... • 113 3 votes 2 answers 1k views ### 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 ... 0 votes 0 answers 41 views ### 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 ... • 141 0 votes 0 answers 38 views ### 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 ... 3 votes 1 answer 587 views ### 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 ... 0 votes 0 answers 38 views ### 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 ... • 169 1 vote 1 answer 143 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 ... • 13 0 votes 1 answer 74 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}. $$A and B are unknown. \bar{B} is {B} rotated by 180 degree. For both images, A has higher signal-to-... • 103 1 vote 0 answers 123 views ### Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components? I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components. If it would be a sum of some sinusiod waves, it would be easy to ... • 119 3 votes 2 answers 478 views ### Extract approximation and detail coefficients I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)? 3 votes 2 answers 7k views ### What are the Even and Odd Components of a 2D Signal A signal x can be decomposed into its even, x_e, and odd, x_o, parts. By,$$ 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 ... • 353 2 votes 1 answer 80 views ### 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 ... • 121 1 vote 0 answers 48 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?: ... 1 vote 0 answers 24 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 ... • 31 0 votes 0 answers 29 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) ... • 189 0 votes 1 answer 74 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 ... • 131 15 votes 2 answers 20k 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 ... • 251 0 votes 0 answers 22 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 ... • 189 4 votes 2 answers 1k 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 ... 0 votes 1 answer 104 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 ... 3 votes 0 answers 325 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 ... • 151 2 votes 0 answers 126 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 ... • 151 4 votes 2 answers 698 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. 3 votes 1 answer 495 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 ... • 163 0 votes 1 answer 281 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 ... 3 votes 1 answer 78 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 ... 0 votes 3 answers 4k 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 followsy[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]...
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 ...