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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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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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22 views

Ensemble Empirical Mode Decomposition and significant or relevant components

Regarding EEMD analysis, my query is how do we go about choosing the IMFs and residual for aggregation step? I know it depends on signal components having highest powers (more significant components)....
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20 views

orthogonality of intrinsic mode functions after empirical mode decomposition

I am wondering what are 'acceptable' values of orthogonality (as defined in this python library), namely how this relates to the reliability of the EMD analysis. I was also thinking to propose a ...
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36 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?: ...
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17 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 ...
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18 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) ...
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1answer
45 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 ...
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24 views

Stress analysis via Voice Signals (EMD, Hilbert Transform etc.)

I have several questions about our graduation project's voice signal processing part: 1) Is it necessary to use Hilbert Transform to get IMF's after the execution of EMD with input of WAV. file? 2) ...
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1k 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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36 views

Delay compensation in wavelet decomposition

I am working on wavelet based ECG delineation and I'm trying to implement the algorithm developed by J.P Martinez. I'm applying a quadratic spline wavelet and using the atrous algorithm(using the swt ...
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9 views

source separation: the tracking capability of the inverse (unmixing) system in a nonstationary environment?

I'm reading Nonnegative Matrix and Tensor Factorizations (A CICHOCK, p.4). There is a paragraph talking about the inverse system should have the tracking capability. From my understanding, the inverse ...
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16 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 ...
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44 views

What are some simple ways to corporate phase information into spectrogram factorization

In time-frequency representation, if I have prior information that each frequency should be presented in specific time range, are there any simple ways to corporate this information into spectrogram ...
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302 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 ...
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1answer
53 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 ...
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0answers
980 views

Difficulties with Empirical Mode Decomposition (EMD) Codes

I've been writing some code in Matlab to generate an EMD from time series data and I'm wanting to verify my outputs somewhat. I've tried a range of codes I've found on the internet and I've found ...
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36 views

speech transient separation techniques?

I am trying to separate a noisy speech mixture. I did several tests, for example, try to filter the speech with random broadband noise, harmonic noise, reverb, etc, but I can't seem to tackle the ...
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92 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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29 views

Multilateration using Fourier Transform versus Cross Correlation

Hey so I want to find the source of a stationary pinger using three microphones. Which is a better technique to find the TDOA, Fourier Transform or cross correlation? thanks
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80 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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2answers
273 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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183 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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1answer
36 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 ...
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1answer
68 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 ...
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3answers
819 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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23 views

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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809 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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3answers
298 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 ...
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3answers
884 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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1answer
176 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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1answer
255 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 ...
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1answer
96 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 ...
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1answer
197 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 ...
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1answer
53 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 ...
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88 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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53 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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1answer
158 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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1answer
45 views

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. ...
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128 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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165 views

How would I represent an image using a basis $A$, given a sparse or compressible image?

Looking for a Basis representation: Given a sparse or compressible image M, how would one represent this image using a basis A? If I let m = vec(M) m = Ax where A is my "representation" basis and ...
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1answer
452 views

Calculating an incoherence property from sub-optimal sampling patterns

EDIT (after comments and subject matter review) CS is based on a choice of a sensing basis $\Phi$ relative to a representation basis $\Psi$. Using an "Incoherence Property" $\mu$ that measures the ...
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1answer
621 views

Decomposition of **3D** structuring elements for morphological operations

I am struggling to implement a mathematical morphology toolset in an image processing package. I base my implementation on what I saw in MATLAB, and on several papers on the subject. There seems to ...
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2answers
997 views

How do I perform the sifting process in empirical mode decomposition?

I am programming a voice activity detection algorithm and I found a paper that recommends the use of HHT. I have been trying to program it and understand how to calculate $m1(x)$, but the shifting ...
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1answer
287 views

wavelet transform boundary

I am doing 1D wavelet decomposition and I am particularly interested in parts at the border of the signal. These parts are affected by boundary effects. I know that some of the methods to extend the ...
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0answers
143 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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1answer
7k views

I and Q Channels

My understanding of I and Q channels is as follows (please correct me if I am wrong): I = In-phase, or real component Q = ...
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1answer
638 views

Time-frequency analysis of non-sinusoidal periodic signals

Given the history of the sum of a time-varying mixture of periodic signals, say square waves, how would you efficiently estimate the number and frequencies of components active at a particular time? ...
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1answer
298 views

Empirical Mode Decomposition and Sparsity

In what sense does empirical mode decomposition (EMD) bring out the sparsity in a signal? For instance, if I had a signal $f$ and I broke it down into $n$ intrinsic mode functions (IMF), what should ...
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1answer
637 views

Mathematics / Signal theory behind billiard ball 'wave pendulum' effect

This YouTube video shows a very interesting effect. What is the underlying science? I have recently started studying Fourier theory and DSP, and and trying to understand what is going on in terms of ...