All Questions
Tagged with convolution signal-processing
166
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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 ...
1
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33
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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 ...
1
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1
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47
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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:
$$
y_1,y_2,y_3 \text{ are ...
- 515
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25
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Suddenly applied discrete complex exponential inputs and convolution
I am reading the textbook Discrete-Time Signal Processing by Oppenheim & Schafer.
I am confused about how to get $y[n]$.
By discrete-time convolution, we have
$$...
- 8,335
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34
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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,...
- 13
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19
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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
$$h(t) = \...
- 1
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24
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Convolution with a time shifted box function
I have the input:
Delayed box input
Its a box funciton x2(t-0.00225) with L = 0.0005 where it's 1 when 0.002 <= t<= 0.0025 and 0 elsewhere. I want to convolve this with the impulse funciton of a ...
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38
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Convolution of Continuous Signal and Rectangular Function
I have some math problems that require me to convolve a continuous sine function with a rectangular function, which involves Heaviside functions. Here is the math that I've done to solve the problem.
$...
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1
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27
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Computing the 2D greyscale image produced from putting a row and column of zeros between every two rows and two columns in the Fourier transform $F$
I have the 2 dimensional image $f(x,y)$ of dimensions $K\cdot T$, and there is its Fourier transform $F(u,v)$.
Now, I want to compute the image $g(x,y)$ which is of dimensions $(2K)\cdot(2T)$, which ...
- 1,999
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32
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Autocorrelation of a time-limited, wide-sense stationary stochastic process
Problem
Let $\{X_t\}$ be a real-valued, wide-sense stationary, continuous stochastic process and consider the autocorrelation of samples of $\{X_t\}$ taken in time windows of width $T$:
$$R_{X; T}(\...
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52
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Changing variables when $f(x)$ goes to $f(-x)$
I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is, the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
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1
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80
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Equation for Gaussian kernel's effect on a frequency's amplitude
Applying a Gaussian blur/kernel with a sigma of $\sigma_{gau}$ to a sine/cosine wave of frequency $f_{sin}$ will cause what percent reduction in the amplitude $p_{amp}$ (not power) of the sine wave?
...
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1
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51
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Sum of the generalized convolution product of two signals
I am trying to prove this property, which states that the sum of the generalized convolution of two product,
$$\sum_{n=1}^N (f*g)(n)=\sqrt{N}\hat{f}(0)\hat{g}(0)$$
The property is found on the article ...
- 31
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86
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Convex optimization of a convolution problem
I want to optimize a sparse problem using discrete math of the following form:
S [16500x1]: measured data vector
D [1500x2]: a dictionary matrix containing two basis signals of 1500 samples
X [16500x2]...
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34
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Properties of convolution for time discrete signals: Why is signal convolution with "delta" signal true?
I'm trying to explain to myself why this property is true;
signal convolution with "delta" function = signal However, I don't understand why? I know that the Diracs delta function has a ...
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