# Questions tagged [derivative]

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### How to detect start and finish of temperature control in temperature time series

I have a huge dataset containing temperature data inside a building. I want to extract the time that the building starts and stops controlling the temperature (approximately around the vertical black ...
43 views

### 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 ...
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### 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 ...
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### What is the first derivative of Dirac delta function?

Could you please help me in a simple way, what is the first derivative of a Dirac delta function? I found this answer: The informal answer is a positive Delta function immediately followed by a ...
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### Implementing a finite impulse respone (FIR) filter for computing the derivative of a discrete signal

I am trying to reimplement an algorithm on my own. In the description of the implementation, it's written that they compute the derivate of a series of value using a [-1/2, +1/2] finite impulse ...
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### 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 ...
52 views

### Relation between original points and 1st/2nd derivative points

I have points $\{p_0, p_1, ... p_n\}$, I create a discrete derivative consisting of $\{d_0, d_1, ..., d_{n-1}\}$ like this: $d_k=p_{k+1}-p_k$. I'd like to choose a point in the original signal by ...
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### Validity of differentiation property of Fourier transform

we know the differentiation property of Fourier transform says that, if $$x(t)\longleftrightarrow X(j\omega)$$ then $$\dfrac{d}{dt}x(t)\longleftrightarrow j\omega X(j\omega)$$ We know that we can use ...
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### Why we need Laplacian for edge detection?

I am studying some trivial computer vision processing techniques and I came across edge detection algorithms. IMO sharp changes in the gradient are enough indications to detect the edges in an image ...
117 views

### Frequency response of FM modulation/demodulation chain with phase derivative demodulation

Frequency modulating a carrier by white noise and then demodulating the complex signal using discrete derivative of phase it appears that the discriminator is acting as a low-pass filter. How do I ...
217 views

### Intuition behind image derivative using Fourier Transform for edges detection

This equation can be shown mathematically: $\frac{\partial f}{\partial x}=\frac{2\pi i}{N} \mathcal F^{-1}\left(u\cdot \mathcal F(f(x,y)\right)$ I am struggling to understand the intuition behind it ...
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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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### Numerical higher order derivatives and time axis

I have a rather elementary question. Suppose we wish to study even-derivatives of an instrumental signal say second fourth and sixth derivatives and plot it as a function of time. With each successive ...
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### 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 $x$, ...
625 views

### should I apply low-pass filter when calculating central derivative?

Let us say that we have a discrete signal $I_n$, $n=0, 1, 2, ...$. According to Nyquist theorem the maximum frequency for such discretization is $f_{max} = 0.5$. Now imagine that I want to calculate ...
192 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 $v \sim CN(0,2\sigma^2_v)$ ...
267 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 ...
1k 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 ...
4k views

### Derivative filter in Python

In Alaa Kharbouch, Ali Shoeb, John Guttag, Sydney S. Cash, An algorithm for seizure onset detection using intracranial EEG, Epilepsy & Behavior, Volume 22, Supplement 1, 2011 (section 2.1, 3rd ...
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### 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 ...
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### 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 ...
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### 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 $f'(t)\theta(t)+f(0)\delta(t)$, ...
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### 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 ...
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### Contour sharpening: Optimal direction for derivation

Talking about sharpening a contour in an image. What's the optimal direction for derivation? What's the maximum value of derivative? I think that the optimal direction for derivation is the direction ...
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### What are the implications of resampling the derivative of a signal with a higher frequency than the original signal?

Suppose I have a digital signal measured with sampling time, $T_s=1$ sec. If I take it's derivative, it will, naturally have $T_s=1$ sec. But what are the implications if I re-sample this derivative ...
I need to have causal noise free first order derivation (Derivative). Now I am using a simple finite differences formula: $$\frac{ x \left( n \right) - x \left( n - 1 \right) }{ {T}_{s} }$$ The ...