Questions tagged [derivative]

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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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2answers
3k views

Compute the time derivative of a noisy digital signal?

The issue is that my signal is very noisy. I need extract its time derivative as accurate as possible. P.S. I do not have any prior knowledge on the signal (black box). On forums some suggested ...
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1answer
1k views

Wrong estimation of derivatives with an extended Kalman filter

I am trying to implement an extended Kalman filter (EKF) in MATLAB for the estimation of joint trajectories (angular position, angular velocity and angular acceleration) from noisy motion capture ...
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2answers
4k views

derivative filter transfer function

In many of the papers it is said that the derivative filter transfer function is given by: $$H(z) = \dfrac{1}{8T}\left(-z^{-2} - 2z^{-1} + 2z + z^{2}\right)$$ But no one gave the detailed information ...
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2answers
2k views

Digital signal derivative

I'm new to signal processing and I need your help: I have an array of 128 elements (call it Window) filled with 128 samples taken from a sensor. I was wondering how ...
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1answer
78 views

Derivative Notation as a factor

In the figure below, from the book "Principles of Linear Systems and Signals - Lathi", the author uses the notation D to replace the Leibniz's notation $d/dt$, and after that he rewrites the equation, ...
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1answer
96 views

Derivative of signal with missing samples

I have software that tracks an object moving (in the x-dimension only) across a video shot from a stationary camera. I need to find the velocity and acceleration of the object as functions of time. ...
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2answers
184 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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5answers
8k views

Derivative of noisy signal

My input signal is phase vector. I want to differentiate it to get frequency vector. My input signal is somewhat noisy. Here is the input signal. This is the derivative of the input signal as ...
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2answers
79 views

How do I estimate the derivative of the current position, when I have only values from past to present?

If I have a discrete real-time signal $x[n]$, with its latest value $x[i]$ and all its past values $x[i-t]$, how can I estimate the derivative at $x[i]$?
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2answers
1k views

Ways to compute the n-the derivative of a discrete signal

This is a pretty general question about how to compute derivatives of a digital signal $x[n]$. I would like to know what are the different approaches (from naive to complex) and how are they compared ...

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