Questions tagged [integration]
The integration tag has no usage guidance.
20
questions with no upvoted or accepted answers
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votes
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answers
201
views
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 ...
- 163
2
votes
1
answer
69
views
Integrating over the translation on a DWT
I'm really a begginer at Wavelet transform and I'm starting to use the pywt module.
I have some difficulties understanding the link between the following integral and the coefficients of the DWT:
$$ W(...
- 21
2
votes
0
answers
953
views
Designing a practical integrator
One way to describe a practical integrator ("leaky integrator") is
$$
H(s) = \frac{g R}{1 + sRC}
$$
I am trying to understand how to choose the values $g$, $R$ and $C$ because in practice, I will ...
- 473
1
vote
0
answers
182
views
Fourier transform of a top-hat function in the Faraday Measurement synthesis context
I'm currently trying to calculate the Fourier transform of a top-hat function in the context of Faraday Measurement Synthesis. This is pretty straightforward, however, I cannot understand why I cannot ...
1
vote
0
answers
415
views
Eliminating drift generated from double integration of acceleration signal using Envelope Method
I'm trying to remove the drift generated upon the double integration of a noisy acceleration signal. But this question discusses only removing the drift upon single integration to generate velocity ...
1
vote
0
answers
172
views
Rocketry : Combine two accelerometers to reduce noise?
I am designing an IMU for an experimental rocket. I'll be using the BN055 9DOF that has sensor fusion - orientation quaternion - and gravity compensation.
My main goal is speed computation, and I was ...
- 11
1
vote
0
answers
34
views
Estimating a discrete summer with constrained input bandwidth
I have a discrete-time system which can be described as:
$$
Y_m = \sum_{r=-N_g}^{R-1+N_g} c_r x[R(m-1) + r]
$$
The unknowns are $c_k$ but I know that they have the following approximate behavior:
$$...
- 473
1
vote
0
answers
421
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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
0
answers
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 ...
- 111
1
vote
0
answers
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 ...
- 111
1
vote
1
answer
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 ...
- 11
0
votes
0
answers
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 ...
- 101
0
votes
1
answer
45
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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 ...
- 1
0
votes
0
answers
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}}^{-...
- 135
0
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104
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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 ...
- 1
0
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71
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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 ...
0
votes
0
answers
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 ...
- 75
0
votes
0
answers
752
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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 ...
0
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0
answers
38
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Energy or power signal for continuous signal
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.
- 1
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0
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49
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Resampling with factor linearly moving from one value to another: calculate expected target length
I am resampling an audio (1D) signal, using a resampling factor that moves linearly from startFactor to endFactor; say the input ...
- 113