# Questions tagged [integration]

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### Why is $\int^\infty _{0^-}\delta(t-nT)e^{-st}dt = e^{-nsT}$?

I'm currently in the process of going over the $\mathcal Z$-transform and more specifically its derivation. I understand and I am able to follow it up until the final step whereby involving the ...
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### Evaluating the inverse $\mathcal Z$-transform on the unit circle

I am trying to understand the math. The inverse $\mathcal Z$-transform is given by: $$x[n] = \displaystyle\frac{1}{j2\pi} \int_cX(z)z^{n-1}dz$$ where $\displaystyle \int_c$ is a contour integral. ...
488 views

### Double Integrating Gaussian Noise

My question has to do with integrating gaussian noise. Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. These noise samples are passed ...
113 views

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### Determine spectrum amplitudes for half-wave rectified sine

I am trying to learn how to solve a bunch of digital signal problems and I have trouble understanding the solutions provided by this book I'm using. Basically, this problem asks me to determine ...
505 views

### what are and why are sine and cosine modulated integrals used?

I have found the definition of the following formulas in a paper regarding active vibration control, where they are called sine and cosine modulated integrals. $y$ is measurement signal with a strong ...
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### 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 ...
I am reading some paper, and I am having some trouble with some Fourier transform, Suppose that $F(\omega)$ is the Fourier transform of $f(x)$, i.e. where F(\omega)=\int_{-\infty}^{\infty}f(x)e^{-...