Questions tagged [derivative]

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55 views

How to find point of inflexion of a digital signal?

Let's say I would like to find a point of inflexion of a digital signal which has been gathered via sampling of a continuous time domain signal with sampling period $100\,\mu s$. The digital signal ...
216 views

Are scipy second-order Gaussian derivatives correct?

For an edge detection algorithm, I need to compute second-order derivatives of an image, and I do this with use of Gaussian derivatives. I assumed that the ...
67 views

How to measure smoothness of a signal

Lets say I have two signals with a different number of data points - a step function and a smooth spline as you can see below. What is mathematical operation I can use to quantify the "smoothness&...
23 views

EMD code question in finding local max/min points

Trying to understand the following part of the EMD code taken from (https://www.mathworks.com/matlabcentral/fileexchange/55448-empirical-mode-decomposition-animation?s_tid=prof_contriblnk) ...
63 views

What phase rotation occurs when you take the derivative of an audio signal?

If you take the derivative of an audio signal, it provides a 6 dB/oct upward sloping filter (increasing high frequencies / cutting low frequencies) all the way across the spectrum. What is the result ...
44 views

Relation between Gaussian derivatives and Gausian-windowed Cosine function

I am doing some research on UWB radars which transmit a pulse given by: $$g(t) = p(t) cos(2\pi f_{c}t) = A e^{(-\frac{t^{2}}{2\tau ^{2}})} cos(2\pi f_{c}t)$$ In some other papers, the transmitted ...
74 views

Bounds of higher order derivative of bandlimited signals

Here is a bandlimited function f(t) with bandwidth Ω: The function f(t) is bounded in [-A,A]. Then the bound of the derivative of f(t) is bounded as: |f'(t)|≤2πΩA. So, what is the bound of its n-th ...
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236 views

Compute the Second Order Derivative of Digital Image with Finite Differences

I was looking for how to compute second order derivative of an image and came across the question kernels to Compute Second Order Derivative of Digital Image. In the top voted answer, it gives an ...
54 views

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 ...
51 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 ...
289 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 ...
24k views

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 ...
468 views

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 ...
53 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 ...
63 views

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 ...
216 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 ...
354 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 ...
59 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 ...
77 views

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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5k 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 $x$, ...
849 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 ...
223 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 $v \sim CN(0,2\sigma^2_v)$ ...
384 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 ...
2k 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 ...
6k 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 ...
120 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 ...
2k 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 ...
67 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 ...
I know there are different ways for partial derivation of an image, among others: Sobel kernel, LoG, Prewitt and so on. But the simplest one is the central difference:  \frac{d}{dx} f(x) \approx ...