# Questions tagged [signal-processing]

Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

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### Can a quadruple integral be simplified through 2D autocorrelation definition?

I am trying to calculate this integral $$P(l) = \int \int \int \int \langle\Psi^*(x',y',z)\Psi(x,y)\rangle \phi^*(x,y,z)\phi(x',y',z) dx' dy' dx dy, \qquad (1)$$ which corresponds to the detection ...
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### Bspline problem

I have some confusions about Bspline interpolation. In wiki and some websites, e.g. Bspline1. It is using something like repeated interpolation. But in some literature, e.g.Bspline2. It is using ...
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### Should we apply filtering on points sampled from a distribution

Let us assume that there is a stationary random process defined as $\mathbf{X}_{k+1} = f\left(\mathbf{X}_k, \eta_k\right)$ , where $\eta_k$ is a Gaussian white noise and $f(.)$ is a linear/nonlinear ...
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### How to find the period of this sinusoid?

I'm stuck trying to find the period of this sinusoid and would really like some pointers to different ways to approach this problem. $$x(t) = \cos(\frac{4\pi t}{5})\sin^2(\frac{8\pi t}{3})$$ I would ...
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### setting the value of a variable in such equation to have a specific output

Assume I have, for example, $x = 0.7 + 0.7i$ and the equation as below: $$\tag{1} (0.5+0.5i)y + (0.5 - 0.5i)x = 0$$ in that case $y$ has the same magnitude of $x$. At the same time, if we swap $x$ ...
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### Is there a way to get an approximation of $\det( \sigma_s^2A+B)^{1/N}$ in the GLRT?

Both $A_{N \times N}$ and $B_{N \times N}$ are symmetric Toeplitz matrix, $\sigma_s^2$ is a constant. In detection theory, the computation of $\det(\sigma_s^2A+B)^{1/N}$ arises in the computation of ...
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### What does $U(e^{j \lambda})$ mean?

I am reading āSignal processing for communicationsā by Paolo Prandoni and Martin Vetterli. In the section 4.4 The DTFT (Discrete-Time Fourier Transform) (p. 72 of 2008 ed.) they write: The somewhat ...
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### Find the output $y(t)$ given the input and system response using Fourier Transform

I need to find the output $y(t)$ given the input $x(t)=\cos(t)$, and impulse response $h(t)=u(t)$ using the Fourier Transform. I know that convolution in time domain is multiplication in the frequency ...
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### Autocorrelation of two functions multiplied and raised to arbitrary powers

Given a signal $A$ and a signal $B$ with autocorrelation times of $\tau_A$ and $\tau_B$, respectively, where $\tau_A > \tau_B$, is there any general statement that can be made about the ...
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### Pulse train rect function

Why $X_\delta (f) = \frac{4A}{3} ( 1 - \frac{1}{2} rect \frac{f}{B} )$ is equal to The $X_\delta (f)$ signal I wrote here ? my book obtained the same equation I wrote on the paper but , before ...
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### Is the optimizaion function convex?

I'm not sure how to approach this exercise. One idea is to derive it w.r.t z, show that there is a min-extremum at $z=f_k$ and then show that for each value from the right and the left of the loss ...
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### sampling using L1 optimization

As much as I understand the F should be the interval medians (correct me if I wrong), according to the next slide, where is also the Loss function defined: What I don't understand is the next note in ...
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### How to find average and power of signal expressed by fourier series

I need to find the average and the power of this signal: $$x(n)=\sum_{k=1}^{\infty}2^{-k}e^{j2{\pi}kn}$$ The problem is that the summation starts at 1 and not at 0, and a part of that how can I find ...
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### Multidimensional signal synchronization

I am trying to find ways of synchronizing multidimensional waves gotten from the brain. For one dimensional signals, I used Cross correlation and was able to synchronise, but for multi dimensional ...
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### Given a signal I(m,n) = a + b*m + c*n and a non linear filter e.g. median filter, find the response.

I stumbled upon this question and I can't seem to solve it correctly "Given a signal $x(n,m) = a +b{\cdot}m + c{\cdot}n$ and a filter, find the processing system response defined in a finite ...
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### Computing a least-squares least-norm solution to image deconvolution

I want to deconvolve an image $h$ by a kernel $f$. More precisely, let $$G = \operatorname*{argmin}_g \|f \ast g - h\|_2$$ be the set of least-squares solutions. I want to find the least-norm solution ...
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### If you have three trigonometric functions that are defined for all real numbers, are they linearly independent as long as they have different periods?

Say, for instance, that I have trigonometric functions $f$, $g$, and $h$, where $f(x) = \cos(\pi x /2)$, $g(x) = \cos(\pi x/4)$ and $h(x) = \cos 4(\pi x)$ Since each function has a different period, ...
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### Discrete Time convolution calculation error

i'm trying to find the convolution among this three signals : $$h1= \delta(n)-\delta(n-4)$$ $$h2= u(n)$$ $$X= ({1}/{2})^n * u(n)$$ If i try to do $$x*h2$$ i get : $$2-2^{-n}*u(n)$$ ...