# Questions tagged [integration]

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### How to solve Hilbert Transform with empirical discrete data in frequency domain?, from zero to infinity

I have a filter/LTI system frequency response in form of list of values in the frequency domain. I want to get the phase curve/data from magnitude data. Input data can have either linear spaced points ...
69 views

1 vote
421 views

### How use FIR filter for simulating an integral implemented using the trapezoidal integration?

Suppose I have this equation $$\phi = \frac{60}{T^5} \int_0^T \left( T^2 - 6T \tau + 6\tau^2\right) y(t-\tau) d\tau - \frac{30 \alpha}{T^5} \int(T-\tau)^2\tau^2 u(t-\tau) d\tau$$ and I want to use ...
1 vote
397 views

### Why does my overlap-add integrator in frequency domain result in distorted signals?

With help from the dsp guide and DSP-Related, I tried to implement a leaky integrator in octave/matlab. It seems to work in general, but there are a few problems. So that's what I do: Calculate the ...
1 vote
484 views

### One of the best ways to numerically integrate a signal?

I need to get position $x$ (integration) from velocity $v$. One could use 1st order Euler integration as $x_{t+1} = x_t + \Delta v_t$ However, doing so leads to errors proportional to sampling time ...
1 vote
186 views

### Verlet integration first step

I'm trying to implement color-to-grayscale method from this paper. And they use Verlet's integration as: $$L^*(t+\Delta t)=\frac{F(t)}{m}\Delta t^2+2L^*(t)-L^*(t-\Delta t),$$ for computing new ...
48 views

### Are longer integration times equally good or better than averaging over several shorter timespans?

Consider the signal of e.g. a photodiode or a spectrometer, where a dark measurement has been taken to account for baseline noise. The signal we want to measure is quite weak, so we need a decently ...
45 views

### What filtering I could use to save my displacement data?

I am double integrating my acceleration to obtain the displacement. However, the displacement looks so strange. Basically this is the measured acceleration of a system under a impulse movement. and I ...
31 views

### n-dimentional integral over Multivariate Gaussian

given the prior distribution of $\mathbf{a}=[a_1,\ldots,a_K]^T$ as \begin{equation} p_{\mathbf{a}}(\mathbf{a})= \frac{1}{\pi^K \det{\mathbf{R_{\mathbf{a}}}}} e^{\mathbf{a}^H \mathbf{R}_{\mathbf{a}}^{-...
104 views

### Numerical Integration Drift

I have collected force platform data to which I calculate acceleration and velocity. The velocity data is presenting what I understand as drift from the numerical integration process that I undertook ...
71 views

### Derivation of equation 3.8 in Fundamentals of Wireless Communication by Tse and Vishwanath

In the book “Fundamentals of Wireless communication”by Tse and Vishwanath, Can someone help with the how the integration helps derive equation 3.8 ? The equation is  p_e= \mathbb P\left\{\left\lvert ...
73 views

### How to prove that the integral of Hilbert transform is not equal to the Hilbert transform of the integral?

To prove that $\int_{-\infty} ^\infty \mathcal{H}(g(t))(t)\text{d}t\neq\mathcal{H}(\int_{-\infty} ^\infty g(t) \text{d}t)$, where $\mathcal{H}(\cdot)$ is the Hilbert transform operator My approach to ...
752 views

### Integration of FTIR Absorbance Spectrum in Python

Hello I have a FTIR (fourier transform infrared) absorbance spectrum of a sample, Integrating the single lines is correlated to the quantity of substance present in the sample. The spectrum part I'm ...
I have solved $w(t) = 1dt$ and determined it as power but when $w(t) =\Pi\left(\frac{t}{T_0}\right)$ it is energy.