Questions tagged [integration]

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2answers
196 views

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 ...
1
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1answer
127 views

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. ...
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1answer
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 ...
-1
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1answer
113 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}^{...
2
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2answers
2k views

Integration of square wave

trying to program an integrator. My input is a square wave and my expected output should be a triangle wave. However, whenever I pass it through my low pass filter algorithm (just a 2nd order ...
1
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1answer
504 views

Filter wrap-around to avoid dealing with settling time? Using a Butterworth

I've been using a Butterworth high pass filter to correct the low frequency distortion of an acceleration waveform integrated to a velocity waveform. I throw out a small number of the first data ...
1
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1answer
171 views

Integral of an upsampled signal, without actually resampling it

Given a signal X which is sampled at a certain frequency. The value we currently compute is given as the integral of the upsampled signal. Thus: Y = X but 100 times upsampled, by means of sinc ...
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 ...
2
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0answers
249 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 ...
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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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0answers
313 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 ...
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2answers
1k views

How to compute the Fourier Transform of this ramp-like signal?

I have the following signal: and this as the solution to the problem: $$\begin{align} X(j\omega) &= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \\ &= \int_0^\tau \frac{E}{\tau}t\; e^{-j\...
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1answer
3k views

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 ...
0
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1answer
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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0answers
265 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 ...
0
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1answer
69 views

problem with Fourier transform

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^{-...
1
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1answer
112 views

How does integration of a signal change the spectrum?

It's a very basic question, but I havn't found the question on google or dsp.stackexchange.com: How does integraion of a signal change the spectrum?

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