# Questions tagged [derivative]

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### What is a speaker behaviour for out of range frequencies?

I was watching this video. The experiment is to create a square signal and record what is outputted by a speaker. We see two diracs signal (+ and -) that looks like the derivative of the signal. Can ...
72 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 ...
48 views

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### 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 ...
148 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 ...
3k views

### Derivative with respect to complex conjugate

I have a real function $C$ of a complex vector $x$. While taking the gradient of the function $C$ for minimising the same, why do we take the derivatives with respect to the complex conjugate of $x$, ...
172 views

### MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
241 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 ...
774 views

### Why taking derivative amplifies noise

In image processing we may use derivatives to help us detect the edges. While at mean time, this operation would also make the data noisier. But why do we have this effect? My intuition is that if we ...
3k 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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### 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 ...
113 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 ...
1k views

### First derivative analog filter

I'm reading about fault detection via signal processing in time domain. One possibility is to check that first derivative of the signal is in some predefined bounds. The text says that to obtain the ...
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 $x[i]$?
55 views

### How to differentiate the product signal $f(t)\theta(t)$, where $\theta(t)$ is Heaviside's unit step function?

What is the derivative (in the engineer's sense) of the causal function $f(t)\theta(t)$, where $\theta$ is the Heaviside unit step function? I've seen the formula $f'(t)\theta(t)+f(0)\delta(t)$, ...
43 views

### Image Geometry Terms

I getting confused over some basics of image geometry terms due to different definitions, implementations and different outputs in the internet, here is an example. The terms are: Image derivative ...