# Questions tagged [derivative]

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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 ...
27 views

### 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 ...
27 views

### 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 ...
41 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 ...
72 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 ...
150 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 ...
46 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 ...