Questions tagged [integration]

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z-Transform Methods: Definition vs. Integration Rule

The definition of the z-transform is defined as $z = e^{sT}$ where "s" is complex frequency for continuous-time systems and "T" is the sample period. Why are rules such as the forward rectangular ...
3
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5answers
2k views

Weird behaviour converting velocity to displacement

I'm trying to convert accelerometer data from accelerations to displacement, I assume that the initial velocity is zero and the initial position is also zero. Here's my code, ...
1
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1answer
2k views

Inverse z transform - contour integration

Here is my task: Find inverse z transform of $X(z)=\frac{1}{2-3z}$, if $|z|>\frac{2}{3}$ I need to find it using definition formula, $x(n)=\frac{1}{2\pi j}\oint_{C}^{ } X(z)z^{n-1}dz$. How can I ...
0
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1answer
2k views

Cancel Drift after numerical integration

I am trying to integrate angular acceleration obtained from a set of accelerometers positioned specifically at opposite corners of a cube, based on the paper EcoIMU: A Dual Triaxial-Accelerometer ...
2
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0answers
205 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 ...
-1
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1answer
107 views

Change of discrete summation to definite integral

The Exponential Fourier Series for a signal is written as, $$x(t) = \sum_{n=-\infty}^{\infty} X_n e^{jnw_0t}\tag{1}$$ and, Fourier Coefficient, $X_n$, is written as, $$X_n = \frac{1}{T} \int_{t_0}^{...