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 ...
Help Appreciated's user avatar
3 votes
3 answers

integration property of fourier series

Please help me sort this issue out. The integration property in Fourier series is as follows: So, for proving the above property, i took this approach: This is where my doubt is. Some books and ...
Nishanth Rao's user avatar
2 votes
0 answers

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 ...
divB's user avatar
  • 473
5 votes
5 answers

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, ...
SamuelNLP's user avatar
4 votes
2 answers

Running Integral of sine and cosine functions

In typical signal processing course we were taught that the integral of signal $x(t)$ is given by $$y(t) = \int_{-\infty}^{t}x(\tau) d\tau$$ How can we use this definition to evaluate the integrals of ...
user5045's user avatar
  • 331
3 votes
2 answers

Help with finishing this integral, to obtain the power spectral density of a pure cosine wave

I am trying to evaluate the power spectral density $S_{xx}(f)$ of a cosine signal $x(t) = A\cos(2\pi f_0t)$, by starting from its definition for deterministic power signals $$S_{xx}(f) = \lim_{T\...
teeeeee's user avatar
  • 681
1 vote
1 answer

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 ...
etf's user avatar
  • 127
1 vote
1 answer

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 ...
Nithin G A's user avatar
0 votes
1 answer

How to compensate phase delay introduced by the digital integrator?

Let's say I have a digital integrator with transfer function in following form $$ \frac{Y(z)}{U(z)} = \frac{T}{2}\cdot\frac{z + 1}{z - 1} $$ I have been looking for a mechanism how to compensate the ...
Steve's user avatar
  • 375
0 votes
1 answer

How to double integrate signal in time domain using FFT (python)

I am looking for a python code to double integrate signals in the time domain using Fast Fourier Transformation (FFT). The idea is to apply FFT to the signal data in the time domain. Then dividing the ...
Yazan Alatoom's user avatar
0 votes
2 answers

Coherent detection in radar and radio signals

Coherent demodulation\detection is usually done via matched filtering in RF signal processing. In radar signals, coherent integration can be done if the phases of the returns are known. In terms of ...
Cindy's user avatar
  • 131
-1 votes
1 answer

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}^{...
a.s.'s user avatar
  • 117