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Second (numerical) derivative as estimation of oscillation

I have a discrete signal (vector of numbers) coming from a measurement. This signal has been filtered so that the noise has been removed. Now I am looking for an analytical representation of the ...
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1answer
61 views

What is the form of the spectral derivative in the all-positive-frequency notation in DFT?

The Discrete Fourier Transform (DFT) of a function $u:[0,2\pi] \to \mathbb R$ sampled over $N$ equidistant points $\theta_j = 2\pi j/N,\, j = 0, \dots, N-1,$ is defined by $$ \tilde U_k = \frac1N \...
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1answer
59 views

Time derivative of signal - effect on noise distribution

I have an angular velocity measurement that has a certain amount of ripple that yields an histogram shaped like a gaussian curve. I quantify that ripple using a standard deviation. I am interested in ...
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36 views

derivative filter for computing speed from robot rangefinder

I have a laser rangefinder on my robot and I need to compute the speed of the detected object. I have seen many different filters for that, but all of them apply only to offline data, or introduce ...
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2answers
260 views

Ramp function as derivative in frequency domain?

It is said that to get Laplacian of Gaussian in frequency domain, we may multiply the Fourier transform of Gaussian with two differentiating ramp function (1 ramp gives 1 order of derivative). The ...
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1answer
1k views

Image derivative in the Fourier space

It can be shown that the image derivative in the $x$ direction is given by: $$ \frac{\partial f}{\partial x}=\frac{2\pi i}{N} \mathcal F^{-1}\left(u\cdot \mathcal F(f(x,y)\right) $$ where $N$ is the ...
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381 views

Smoothing the discrete acceleration

In order to know if my signal is increasing or decreasing, I'm using the discrete derivative $y[n] = x[n] - x[n-1]$ or a smoothed version of it (for example Exponential Weight Moving Average of $y[n]$ ...
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1answer
159 views

Digital Derivative

I need to calculate the derivative of a digital signal (sinusoidal). In one of the papers they have mentioned Gilbert transformation is used to calculate the derivative. But I have searched in the net ...
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2answers
178 views

How to find derivative of 2-D elliptical Gaussian function with different standard deviations along $x$ and $y$ directions?

I am trying to find the 2-D derivative of an elongated Gaussian density. The Gaussian has standard deviations $\sigma_x$ and $\sigma_y$. How can I get the scale-normalized 2-D Gaussian derivative in ...

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