All Questions
Tagged with fourier-transform probability
10 questions
3
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1
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95
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Characteristic function of transformed random variable
Consider a random variable $X$ and a function $g(\cdot)$. Let $Y:=g(X)$, and let $\phi_X(\cdot), \phi_Y(\cdot)$ be the characteristic function (cf) of $X,Y$, respectively. Suppose that $\phi_X$ is non-...
- 583
3
votes
1
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102
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Product of RVs of Which Distribution Approximates Normal Well?
Suppose that I have $N$ i.i.d. random variables with a distribution $Q$, which has mean around 1. That is $R_1, R_2,\ldots,R_N \sim Q$. I would like $\prod_{i=1}^N R_i$ to approximate a normal random ...
- 4,504
3
votes
1
answer
94
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Name of PDF? - projecting uniform probability distribution on the unit circle to the x-axis
Consider a uniform probability distribution on a circle of radius r, i.e. $\{(x,y) \in \mathbb{R}^2: x^2 + y^2 = r^2 \}$.If we wish to project onto the x-axis, we can consider each point on the circle ...
- 225
0
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Identifying a single dominant number with high probability in a data point array of 4 to 20 numbers
EDIT 3: added below picture of raw readings of oscope from doppler data showing "periods" of sine waves before processed sine signal into square pulses.
EDIT 1: These numbers on the left ...
- 11
2
votes
0
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109
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Uncertainty principle in probability theory
In probability theory, there is the covariance inequality
$$\operatorname{Var}(Y) \geq \frac{\operatorname{Cov}(Y,X)^{2}}{\operatorname {Var} (X)}.$$
In signal processing, there is a similar ...
- 538
3
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1
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3k
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Characteristic function and Fourier transform for a discrete random variable!
Let $\phi_{x}(t)= E [ e^{itx}]$ be the characteristic function
If X is a continuous random variable, then:
$\phi_{x}(t)= E [ e^{itx}] = \int e^{itx} f(x)dx$ (being $f(x)$ the probability density ...
- 31
7
votes
2
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2k
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Fourier transform in Machine Learning
I want to know what are the specific areas in which Fourier methods are used in machine learning. Apart from feature extraction and spectral analysis, I want to know if there are any learning ...
12
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3
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23k
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How to prove that the Fourier Transform of white noise is flat?
If we take $X_n$ a series a random vector with its components each having a probability distribution with zero mean and finite variance, and are statistically independent. How do we prove that the ...
- 325
15
votes
1
answer
9k
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Characteristic function and Fourier transform
I understand the definition of characteristic functions used in
probability theory:
For a random Variable $X$ with probability density function $f_X$ the characteristic function is defined as:
$$\...
- 1,401
3
votes
1
answer
706
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Deconvolution with fourier transform or characteristic function?
Let us consider the following model:
$$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$
Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...
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