Questions tagged [derivative]

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Correct way of derivating in frequency domain with FFT

I believe I am very close to the answer and only need a small nudge to get to the answer. What I want: I want to take a signal, use FFT to transform it to the frequency domain (FD), multiply it by $...
2
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0answers
112 views

Helmholtz decomposition implementation

I need to perform the Helmholtz decomposition of a 2D flow. An old and obvious problem is the numerical differentiation (largely amplifying the noise). I do understand the procedure I am just ...
1
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0answers
11 views

Laplacian of Gaussian operator

This might be a silly question. I was reading about the Laplacian of Gaussian (LoG) operator and got confused about the alternative equivelant ways we can make use of it. Let's assume we have a 2D ...
0
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0answers
27 views

2nd derivative using gaussian filter (gnu scientific library) - offset?

I am working on an application where I use gaussian filtering (convolution) to smooth a signal and at the same time get the 1st and 2nd derivative in real time. The signal is an equidistant sampling ...
0
votes
0answers
46 views

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 ...
0
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0answers
20 views

Which frequency bins give the best interpolation for the derivative of a function?

A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\...
0
votes
1answer
42 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 \...
0
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0answers
33 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 ...
0
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0answers
377 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 $y[n]$ ...
-1
votes
2answers
174 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 ...