# Questions tagged [derivative]

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### Why is a first/second derivative useful in spectroscopy?

I'm currently working on Raman spectroscopy and while reading some literature I came across the first and second derivative of a spectrum. It's not clear to me why they are useful to look at since ...
33 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 ...
338 views

### Bilinear Transform (Tustin's Method) applied to the Derivative

I hope that I have not misunderstood something terribly wrong, but the continuous derivative $D=d/dt$ can be considered a transfer function in Laplace space $D(s) = s$, right? So when I try to ...
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### What exactly is Savitzky-Golay differentiation filter?

I could understand Savitzky-Golay filter as being smoothing filter, but then there also seems to be Savitzky-Golay differentiation filter, though for some reason, details do not seem to be clear. So ...
135 views

### Bounds of the difference of a bounded band-limited function

For a continuous signal (function), we have Bernstein inequality : $$|{df(t)}/dt| \le 2AB\pi$$ where $A=\sup|f(t)|$ and $B$ is the bandwidth of $f(t)$. The question is: is there a relationship ...
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### 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 ...
67 views

### Estimating a Signal Given a Noisy Measurement of the Signal and Its Derivative (Denoising)

I have a signal and its derivative simultaneously measured, both including additive noise. The measurement is completed before the analysis, so it can be looked ahead. Now I want to reconstruct a less ...
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### 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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### How do derivative masks work for finding edges in image?

As I know, masks like follow are derivative mask, but I don't get it why they can detect edges and which one of them can find vertical edges and which one can find harizontal edges?
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### Why level of noise can be magnified twice through each numerical differentiation?

I was reading a paper and saw this is mentioned there, but I cannot figure out how this can analytically be proven?
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### Differentiation of sine in Fourier domain

The derivative of $\sin(\omega_o t)$ is $\cos(\omega_o t)$. The Fourier transform of $\sin(\omega_o t)$ is $\frac{\pi}{j}[\delta(\omega-\omega_o) - \delta(\omega+\omega_o)]$. Differentiation in the ...
874 views

### discrete-time (slew) rate limiting algorithm

Consider uniformly-spaced samples of smooth, bandlimited signal observed in noise and subject to some artifacts (small jumps). Physical restrictions impose a constraint on the maximum magnitude of ...
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### 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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### 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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### 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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### 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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### 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 ...
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 $x[i]$?
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 ...