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Questions tagged [signal-processing]

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Is the Hadamard Product of two laplacian operators allowed to get some kind of biharmonic operator?

I'm currently working on my masters thesis in computer science and from this point I'm not that into this subject. Right know I try to understand the steps the authors of this paper did to get the ...
dontoronto's user avatar
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Is the Wigner-Ville representation of a non-negative operator a non-negative time-frequency density?

Consider a non-negative operator $K \geq 0$ acting on signals $x$ (say a complex Hilbert space). The associated quadratic form can take the following temporal representation: $$\langle x , K x\rangle =...
Alexandre's user avatar
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Data smoothing with controlled smoothing error

Say I have a data sets $X$ and $T$ of $n$ measurements at $n$ distinct times. The data is slow varying and relatively non-noisy. I want to smooth the data with some curve or a set of piecewise ...
Donatas Šimeliūnas's user avatar
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Concept of signal size for energy saving in optimization

I've been trying to redo this optimization problem from this paper, but on GEKKO Python code instead of MatLAB as they did, which is about finding the maximum Biodiesel concentration at final time: J =...
Luiz Miguel's user avatar
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2 answers
72 views

Finding the optimal offset for periodic signals to minimize concurrent transmissions

I have a system with discrete time, that sends periodic signals with the following periods: [10, 20, 30, 40, 50, 100, 200, 500, 1000, 5000]. The number of signals belonging to each period is as ...
Khashayar's user avatar
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regarding vector of random variables

In my research work I came across the following expression $P = \underbrace{A_1(\textbf{h}_2^T(n)\cdot \Psi \cdot \textbf{h}_1(n)+A_2h_0(n))}_{Part 1}$ + $w(n)$ ---(1) where $\textbf{h}_2(n)$ is a $M \...
Heretolearn's user avatar
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Cross-correlation of a function with itself

I came up with the following question while writing on my thesis. We assume $f:\mathbb{R}\rightarrow\mathbb{R}$ to be a real valued $\mathcal{L}^1$-function. Then the cross-correlation of $f$ with ...
Christoph Richter's user avatar
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Understanding the derivation of the expression

in my research work related to wireless communication, I have the following expression: $$\tag{1} r_1 = \sqrt{P}H_1H_2(\textbf{h}_2^T\Phi \textbf{h}_1)s+\sqrt{P}H_0h_0s+w$$ where, $r_1$ is received ...
Heretolearn's user avatar
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How to prove that sum of infinite complex harmonics makes a continuous time impulse function?

I was trying to substitute complex fourier series coefficients into complex fourier series formula and I came up with this identity in order to get the same function back. How can I prove that this ...
U.AL's user avatar
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Would like to validate whether the AUC equation is correct or not

I found a paper "Chapi, Kamran, et al. "A novel hybrid artificial intelligence approach for flood susceptibility assessment." Environmental modelling & software 95 (2017): 229-245&...
Simon's user avatar
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Inverse-Fourier Recovery of Dirac Delta Coefficients

We have the Fourier transform $F: g\mapsto\hat{g}$ defined as follows: $$\hat g(w) = \int_\mathbb{R} g(x)e^{-2\pi ixw} dx$$ and, using the Dirac delta function $\delta(x)$ and $c_j\in\mathbb{R}$, let $...
WD1's user avatar
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Identifying Waveforms that Satisfy Specific Convolution Constraints

I am attempting to find a set of waveforms, denoted as $y_1$, $y_2$, and $y_3$, that satisfy the following convolution constraints, where $*$ is used to denote a convolution: $$ y_1,y_2,y_3 \text{ are ...
Tiny Tim's user avatar
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1 answer
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(Infinite) sum of products of 'offset' Bessel functions (an application to calculating the RMS power of a harmonic "FM" oscillator)

TLDR version: I'm trying to calculate $\sum_{n=1}^{\infty} J_{n-1}(a) J_{-n-1}(a)$ but can't seem to get it right. For motivation & attempt, read the rest. Consider the harmonic "FM" ...
got trolled too much this week's user avatar
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Why is the autocorrelation of an uncorrelated random noise process the dirac delta distribution?

I am reading Stochastic Methods by Gardiner and in the beginning of chapter 4 he motivates the rigorous interpretation of a Stochastic Differential equation by describing the properties of a "...
Mashe Burnedead's user avatar
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Average power of an inharmonic "PM" (Phase Modulated) signal

Based on some experiments, I conjecture that the average power of an inharmonic "PM" (in the sense that's used in music, i.e. Phase Modulated) signal tends to be the same as that of the ...
got trolled too much this week's user avatar
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Suddenly applied discrete complex exponential inputs and convolution

I am reading the textbook Discrete-Time Signal Processing by Oppenheim & Schafer. I am confused about how to get $y[n]$. By discrete-time convolution, we have $$...
sleeve chen's user avatar
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finding the finite series $f[n]$ given its length and its DFT

suppose the number $N$ is even and $f[n]$ is a series with length $N$ and a DFT $F[k]=(-1)^k$ how can I find the series $f[n]$. so far I've tried this: since $N$ is even and $F[k]$ is even and real we ...
Elad Elmakias's user avatar
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How can we show that a discrete signal with higher frequency component needs more number of finite samples for approximation?

To realize a finite-impulse response of a digital filter in the context of digital system control, one way is to approximate the input signal by limited number of samples and hence avoid oversized ...
Saeed's user avatar
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4 votes
1 answer
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Intuitive explanation of "Information Filter" formation of Kalman filter

Can someone intuitively explain this "Information Filter" formation quoted from wikipedia ? In particular I struggle to understand why $\mathbf{I}_k = \mathbf{H}_k^\textsf{T} \mathbf{R}_k^{-...
CuriousMind's user avatar
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Fourier transform with and without convolution theorem not equivalent

This is a problem involving Fourier transforming an integral relevant to the computation of Feynman diagrams, which is of the form: $S(r_1,r_2)=\int d^3 r_3 \space v(r_1,r_3)f(r_3,r_2),$ where $v(r_1,...
user2188518's user avatar
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Related to integration transformation from Cartesian plane to Polar coordinates

I am working in area of wireless communication that involves extensive use of probability, random variables and stochastic geometry. My system model is as follows: It consists of a main base station (...
Heretolearn's user avatar
1 vote
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Discrete Fourier transform for time series with small time-shift measurements

I have a time series that can only take positive integer values in the range [0, 100]. This time series shows periodically recurring patterns which can be uncovered by using the discrete Fourier ...
Radu's user avatar
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Laplace Transform of a Second Order Systems Response to Triangular Pulse

I've been trying to derive the time domain response of a second order system to triangular pulse input using Laplace Transformation but even if I seem to be able to derive it Simulink simulations ...
Ahmet Burak's user avatar
1 vote
1 answer
65 views

Inverse Z-Transform of $\frac{1}{(1+z)^2}$ with ROC : |z|<1

I'm trying to Find the inverse Z-Transform of $\frac{1}{(1+z)^2}$ My steps are as such : $\frac{1}{(1+z)^2}$ = $\frac{z^{-2}}{z^{-2}\cdot(1+z)^2}$ = $\frac{z^{-1}\cdot z^{-1}}{(1+z^{-1})^2}$ = $\frac{...
Losh_EE's user avatar
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Applying the Mixed-Product Property of the Kronecker Product to DFT and Identity Matrices of difference sizes

Suppose we have four matrices, $\mathbf{F}_{N_2}, \mathbf{F}_{N_1}, \mathbf{I}_{M_1}, \mathbf{I}_{M_2}$, where $\mathbf{F}_{N_1}$ and $\mathbf{F}_{N_2}$ are a DFT matrix of size $N_1$ and $N_2$, ...
Omid Abasi's user avatar
1 vote
0 answers
72 views

A question about Wiener filter based on Linear Estimation by Kailath

In my linear estimation class based on the textbook Linear Estimation by Kailath, we went through the process of finding LLSE of $\hat{x}(t+\lambda)$ for fixed $\lambda$ given $\{y(\tau)|-\infty<\...
monad's user avatar
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Related to CDF of product of two independent Gamma random variables

I am working on a topic wherein I came across the following expression: $P_1 = Pr(X<\phi)$ ----(1) where $X$ is a random variable And $X = h_0\cdot h_1$, such that $h_0\sim \text{Gamma}(m_0, \frac{\...
Tushar Muratkar's user avatar
3 votes
1 answer
128 views

How does a linear map over $L^{1}$ spaces interact with integration

Lets say we have a linear map $T:L^{1}(\lambda)\rightarrow L^{1}(\lambda)$ where $\lambda$ is some arbitrary measure. Lets say we have some function $F(x):=\int_{-\infty}^{\infty}f(t,x)d\lambda(t)$ ...
Manseej Khatri's user avatar
1 vote
0 answers
27 views

Fourier coefficients for non-periodic signals

Suppose there exists an LTI system h[n]: $$ h\left[n\right]=\:a^{-|n|} $$ Let x[n] represent a discrete signal defined as: $$ x[n] = $$\begin{cases} 1 & 0 < n < N_0 \\ \text{else} & \...
roeihapoel8810's user avatar
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Output of convolution of a shifted box function and an impulse response of low pass filter

I want to convolve this input: Box delayed input function with a low pass filter, with R is resistance in 2000 Ohm and capacitance in F is $1.5*10^{-8}$ And impulse response of the filter is $$h(t) = \...
ferer's user avatar
  • 1
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0 answers
24 views

Convolution with a time shifted box function

I have the input: Delayed box input Its a box funciton x2(t-0.00225) with L = 0.0005 where it's 1 when 0.002 <= t<= 0.0025 and 0 elsewhere. I want to convolve this with the impulse funciton of a ...
ferer's user avatar
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1 vote
0 answers
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Estimate the Power Spectral Dentity of a signal from CWT coefficients

I want to estimate the PSD of a signal from the CWT coefficients. How can I do it? Can you provide me with some algorithms to do this? I have Matlab R$2016$a installed. Thank you so much! I do this ...
Gisela's user avatar
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0 votes
0 answers
16 views

Related to random variable in wireless communication.

I am working on a research paper related to wireless communication, wherein I am facing some doubt while writing expression of SINR (which is a ratio of Signal variance in numerator to Interference ...
Pranu's user avatar
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0 answers
38 views

Convolution of Continuous Signal and Rectangular Function

I have some math problems that require me to convolve a continuous sine function with a rectangular function, which involves Heaviside functions. Here is the math that I've done to solve the problem. $...
Dziban 1996's user avatar
1 vote
0 answers
38 views

Deriving the DCT-II from the DFT

Recently, I was looking into the theory behind the discrete Fourier transform (DFT) when I frequently encountered the discrete cosine transform (DCT-II). Due to the similarities between the DFT and ...
Fynn Zentner's user avatar
1 vote
0 answers
41 views

Approximating the Gaussian White Noise stochastic process for numerical applications

The problem I have at hand is a rather amateurish one. For a modeling task, I have worked out the stochastic differential equation the random process of interest should obey, and the gaussian white ...
Waylander's user avatar
3 votes
1 answer
43 views

Inverse Z Transform of $\frac{1}{(z-a)^2}$

I'm Trying to find the Z-transform of $$\frac{1}{(z-a)^2}$$ in discrete, i.e using $u[n]$. Using the known transformation of: $$n \cdot \alpha^n \cdot u[n] \Longleftrightarrow \frac{\alpha \cdot z^{-...
Losh_EE's user avatar
  • 346
0 votes
0 answers
9 views

Continuity of a quantity in a conical system to determine the velocity field

My research is on radar images and the images are collected in several conical surfaces. These conical surfaces have the same origin, the same maximum length (max flare or max range), but different ...
CfourPiO's user avatar
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1 vote
0 answers
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Help - How to separate 4th order transfer function (Butterworth Approximation) into 2nd order using Python Control Library?

Previously I had the following coefficients in the program. In this program I want to create a transfer function of butterworth approximation (Figital Filter Fesign - Digital Signal Processing). ...
SKevinAR18's user avatar
2 votes
2 answers
112 views

How to confirm if all points lie on sine wave. [closed]

Given at least 3 points $(x_{i}, y_{i})$, how to confirm if all points lie on a sine wave? Or alternatively, how to determine the parameters of a sine wave that best fits the data (I'm guessing ...
Mike Jones's user avatar
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0 answers
13 views

If amplitude and phase of a random signal are independent, then does real and imaginary parts of that signal are mutually exclusive (or) independent?

For a complex random variable If amplitude and phase of a random signal are independent, then does real and imaginary parts of that signal becomes mutually exclusive (or) independent?
Palguna Gopireddy's user avatar
0 votes
1 answer
19 views

Extracting Specific Component Functions from a Composite Numerical Function

I have a function f(x) defined below as, $f(x) = \sum_{n=0}^N c_n(g_n(x + n) + g_n(x - n))$ I have no knowledge of what $c_n$ is, but I do have access to f(x) numerically. Is there a way to apply an ...
JustAnotherGuyOnline's user avatar
0 votes
0 answers
31 views

Any common reference for linear, TIME-VARYING systems?

This isn't exactly a math question (apologies!), but it could prevent many potential misunderstandings I might otherwise encounter in the near future (and also prevent many dumb questions I will post ...
lostintimespace's user avatar
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0 answers
23 views

Fourier series of Fourier series coefficients for discrete time Fourier series

So a buddy of mine and I are sitting in our signals class, and he asks me a question: if the coefficients of a discrete time Fourier series are period, what are their Fourier coefficients? I ...
Spencer Bowles's user avatar
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0 answers
51 views

Theoretical derivation of discrete-time multiresolution decomposition

I started three weeks ago to study wavelets with the intention of later applying them to some deep learning architectures. As a Ph.D. student in mathematics my interest lies mainly in the theoretical ...
Pietro Cestola's user avatar
2 votes
0 answers
42 views

Relate a continuous inner product to a discrete one by expanding a kernel around a Dirac delta function?

I am trying to find the discrepancy between an integral and a discrete approximation. The "ideal" inner product between two signals $f(x)$ and $g(x)$ is an integral, $$ \langle f, g \rangle_\...
Alex's user avatar
  • 161
1 vote
1 answer
44 views

Analyzing an Integral Involving a Complex Function with Symmetry Properties: approximation or simplification

I am exploring the properties of an integral expression involving a complex function f(θ), which is defined over the interval ...
Alireza Ghazavi's user avatar
0 votes
1 answer
183 views

Evaluation of $ \frac{1}{\pi} \int_{0}^{2\pi} \exp\left(-\sum_{k=1}^{K} x_k e^{-ik\pi\sin(\theta)}\right) d\theta$

Background and Motivation I am exploring an integral that emerges within the context of MIMO (Multiple Input Multiple Output) communication engineering, particularly as it relates to computing ...
Alireza Ghazavi's user avatar
0 votes
0 answers
23 views

Distribution of Eigenvalues for a Sum of Kronecker Products in a Randomized Channel Model

I am working on analyzing a communication channel model where the channel matrix is constructed as a sum of Kronecker products of vectors that represent the effect of path delays and angles on the ...
Ivan-SONDER's user avatar
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0 answers
42 views

$ \int_{0}^{2\pi} e^{-(A + \sum_{k=1}^{4} B_k e^{-j k \pi \sin(\theta)})} \, d\theta $

I am trying to evaluate the following integral: $$ \int_{0}^{2\pi} e^{-(A + \sum_{k=1}^{4} B_k e^{-j k \pi \sin(\theta)})} \, d\theta $$ where $A$ and $B_k$ are constants, $k$ is an integer, and the ...
Alireza Ghazavi's user avatar

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