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The two channels exist only inside a transmitter or a receiver; the channels are physically combined in a single signal (or channel) in the physical medium (wire, coax cable, free space, etc). At the transmitter, two signals $s_I(t)$ and $s_Q(t)$ (called the I (or inphase) signal and Q (or quadrature) signal respectively) are combined into a single signal $... 7 What is described in the question is very near the Discrete Wavelet Transform (DWT) with the use of the Haar Wavelet. The DWT decomposes a signal into a sum of dilated and translated orthogonal functions that do not necessarily have to be trigonometric. The DWT does not transform a signal from the time domain to a frequency domain but to a scale space where ... 5 Yeah some of us can do it, you can speed up or slow down without affect the pitch, some guys call this applications of Time Stretch, there different ways to do it, you can do in frequency domain or time domain, you will need choose what is best for you, you will find some advantages and disadvantages of each. Time Domain: In Time Domain you can try some ... 4 It's not shifting, it's sifting. After you find the$m_1$curve, your subtract it from your signal$X$to get$h_1= X(t) - m_1$. You're essentially taking away that signal component and are left with$h_1$, which is your new starting point of your next iteration. I assume you were confused by the terminology. Sifting is a general term in signal processing ... 4 If we stick to the linear version and discrete versions of filter banks and wavelets, filter banks represent the generic tool, and wavelets can be implemented as a specific instance of iterated$2$-band filter banks satisfying some additional properties, namely that low-pass spaces are embedded dyadically. In other words: get a single-level$2$-band ... 3 I found an answer which is good-enough for me. As @Stanley Pawlukiewicz has pointed out in the comments, this is hard to do for a general case when there is little correlation between the images. I, however, want to work with real images of actual things in the real world. This means there will be a lot of low frequency components (that's why jpeg ... 3 I understand that you receive A, B, and C and you want to separate it into A1, A2; B1, B2; C1, C2. From this, you can do the following: Model your expected signal A1 as some pulse shape (here, I assume its a tanh function, which is close to your example). Then, normally you can perform matched filtering on the received signal to find peaks at the position ... 3 The tool/theory you describe is really a large area of research in music technology, broadly called audio time-scale modification. A large component of this field is how you might prevent audible changes to frequency following time stretching. This can be approached with both frequency- and time-domain methods, depending on the constraints or goals of your ... 3 I'd just take a KIS (keep it simple) approach as a first step. Define your (unknown) signal as $$s(t) = k A(t) + m B(t) + n(t)$$ and then just define the error: $$e(\tilde{k}, \tilde{m}) = \sum_{\forall t} \left| s(t) - \tilde{k} A(t) - \tilde{m} B(t) \right|^2$$ and then your estimates$\hat{k}$and$\hat{m}$are just chosen as: $$(\hat{k}, \hat{m}) = \... 3 Let us start with the unsupervised methods... A first approach would be to compute a spectrogram and factorize it with NMF (Non-negative Matrix Factorization). If you are unfamiliar with this technique, it decomposes a spectrogram into a sum of k constant-spectrum sources, each of these having a time-varying amplitude envelope applied to them. This model ... 3 The even part of a 2D image x[n,m] is defined as:$$x_e[n,m] = \frac{x[n,m] + x[-n,-m] }{2} $$and the odd part is$$x_o[n,m] = \frac{x[n,m] - x[-n,-m] }{2} $$. 3 In higher dimensions, provided the definition domain is symmetric, an even multivariate function can be defined (see MathWorld Even Function) by the identity:$$ f(-x_1,-x_2,\ldots,-x_n)= f(x_1,x_2,\ldots,x_n) $$hence one can define the even part:$$ f_e = \frac{f(x_1,x_2,\ldots,x_n)+f(-x_1,-x_2,\ldots,-x_n) }{2}$$and the odd part follows by completion.... 2 Basically, it looks like you need to know some threshold to detect peaks: detect bottom edge (Xbe) calculate the moving average (until the last edge) detect peak itself (current value - average value > threshold) start of peak found: X1=Xbe detect peak end (current value - average value < threshold) detect bottom age (Xbe) end of peak found: X2=Xbe ... 2 To better extend the signal at the border, you can consider a constant extension: [x_0,x_1,x_2] can be extended to the left (and similarly to the right) as [x_0,x_0,x_0,x_1,x_2]. However, this tends to break the slope, as it assumes a zero-derivative (flat signal). A more advanced option resides in anti-symmetric extensions: they are sometimes called ... 2 The idea of being sparse in a certain basis can be extended and one can talk about being sparse in a frame, or even, being sparse in a dictionary. Now we may lose orthogonality, have redundant signals in our dictionary and no longer have unique signal expansions; which is OK if we only care about sparsity. The EMD expansion is sparse in the sense that you ... 2 \Phi is the matrix that represents the way you sample your signal x. Actually, \Phi can be an identity matrix with some rows eliminated, which means you are picking a subset of x. \Psi represents the basis that you choose to expand x:$$x = \Psi c$$A very simple example is that$x$is a cosine function (thus containing only one frequency ... 2 I guess this depends on the digital distance transform that one is approximating on the 3d grid and there are various local connectivities possible. There is an implementation in ImageJ here. It would also be good to verify if you are using a non-flat structuring element or a correct 3d structuring element. Read Matlab reference here. In the place of ... 2 Starting with your original signal$s(t)$, we designate$u(t)$and$l(t)$as the curves for the upper and lower portions of the envelope respectively. You find the upper curve of the envelope,$u(t)$, by picking out the local maximums of$s(t)$and then connect them using splines to get a continuous representation of the curve. You find the lower curve of ... 2 There is absolutely no need for explicit interpolation. The DFT can do that for you. Take you signal frame and apply a windowing function to minimise edge artefacts. Afterwards pad the frame with zeros to determine the number to output bins of the DFT. Then apply your FFT and you have an interpolated spectrum with the frequency step size you desire. 2 How can I count these hit sounds ( I should get six in this clip). In this case you can simply rectify the signal (i.e. run it through an absolute function, then through a simple running average low pass filter and at the output of this add a threshold. Essentially, when the power of the input signal exceeds the threshold you will be receiving a pulse whose ... 2 Below is a link to a simple and valuable tutorial function in C++ (smbPitchShift.cpp) by Stephan M. Bernsee, which can slow-down or speed-up music without changing its pitch. He has released this code under the The Wide Open License (WOL). Within my application, I was able to adapt his function to slow-down music in real-time -- that is while playing a mp3 ... 2 Is it possible to parallelize the Sifting process? No. The "problem" here is not the recursion itself but the fact that the data changes at each recursion step. It is possible to parallelise divide and conquer type of algorithms that imply hierarchy as is the case of the split radix FFT or Quicksort for example. But in that case, the input sequence of ... 1 Best denoising should be related to certain quality measures, often requiring the clean signal reference, which you do not have in general. Or you could rely on some reference-free measures. To the best of my knowledge, many SURE wavelet methods allow to derive risk estimators without a reference, on a given wavelet decomposition (with given levels) in a ... 1 I'd say it depends on the noise properties and of course the image itself. What you can think is that most Denoise Filters can handle only the High Frequencies of the noise. Hence the decomposition process moves Low Frequency of the noise to the High Frequency part for the spectrum. So if your noise is white you need to go down as you can. If it colored ... 1 To avoid mistakes, let us first divide the original sequences by$2$(for the sake of linearity): 0 0 1 2 3 3 3 0 0 0 0$\ldots\$ It can be interpreted as a piecewise linear sequence, so you can expect a solution with about three degrees of freedom with ramps and steps. As these basic primitives are causal, you can use the method of deflation (or successive ...

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If you signal is stable long enough, one method is to gather more data over a longer time period, and then use a longer FFT. If the sine/cosine functions of interest are far enough apart in frequency, and the noise and interference levels are low enough, you can use your current FFT results and interpolate between the FFT result bins (the ones that are Fs/N ...

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I'd calculate the horizontal point spread function for each color channel separately and use the spectral sensitivity ratios of the channels for frequency calibration; the resulting sensitivity-weighted spectra should obey the same ratios. Deconvolution can be implemented as frequency domain division of each diffracted row by the corresponding direct ...

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Assuming that the image is gray level (not color) Use Otsu's thresholding method to detect whether the image has bi-modal histogram. If Otsu tells you with high confidence that the image is bi-modal, use the threshold that it gave you in order to binarize the image. That is your binary mask that can be effectively packed into bits. Find the gray values of ...

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A filter bank is just one specific implementation of the wavelet transform. Typically wavelets are motivated and defined differently, namely as a family of (orthogonal) basis functions that are generated from a mother wavelet by translation and time scaling. It turns out that such a family can only be an orthogonal basis if the time-frequency plane is ...

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Wavelets decomposition separates out the details/fluctuations/high-pass information from the image or signal. At each step details are separated out from the remaining of the signal. The processing is therefore only applied on the coarse part not the part that already has the details.

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