Questions tagged [integration]
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114 questions
0 votes
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71 views
Implications of non-minimal realization of an IIR filter
Minimal realization of a system/filter is generally desirable in control design (lower order, efficiency, robustness, ...). What are the implications (pros and cons) of adding an state to the minimal ...
- 91
1 vote
1 answer
89 views
How to evaluate an integral with $\delta(g(t))$ as integrand?
If $y(t)=\delta\big(\sin(\pi t)\big)$, what will be the result of $$\int_{-0.5}^{0.5}y(t)dt\qquad\text{?}$$ This is my solution. it gives the correct answer but i'm not sure my argument is correct: ...
- 33
0 votes
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35 views
How Set Up Integrals For Wavelet Rasterization
Paper 'Wavelet Rasterization' show how calculate coefficient for Haar wavelet and give formula for some function. But I want know how set up integral for any path 2D vector function 2D P(x(t); y(t)). ...
- 101
1 vote
1 answer
50 views
Normalisation of Complex Morlet Wavelet
I am currently writing an essay on Wavelet transforms, and as part of such, I am trying to show that the Morlet wavelet satisfies the standard criteria: $$ \int^\infty_{-\infty} \psi(t) dt = 0 $$ $$ \...
3 votes
3 answers
558 views
Why is sampling a signal equivalent with multiplying with a Dirac comb?
Given a continuous time signal $f(t)$, we can sample the signal by multiplying with a Dirac comb (impulse train) $$\bar{f}(t) = \sum_{n=-\infty}^{\infty} f(nT) \delta(t-nT) \tag{1}$$ where each ...
- 546
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174 views
Does the high-pass filter cause the accelerometer to miscalculate displacement?
I have an accelerometer and I've written a program for it in the ESP32. The program uses a 750sps ADC sampling rate and an accurate 100Hz interrupt for calculations. P.S. The high-pass filter is at 0....
- 1
2 votes
1 answer
215 views
Fourier Transform of $|t|$
I was going through Papoulis' book (The Fourier Integral and its Applications) when I came across the Fourier Transform for $|t|$. To find it he writes $|t|$ as (I am not sure how): $$|t| = -\frac{1}{\...
- 1,728
2 votes
1 answer
327 views
What is the Fourier Transform of $\operatorname{sgn}(t) \cdot \operatorname{sgn}(t)$?
I am wondering what the Fourier Transform of $\operatorname{sgn}(t) \cdot \operatorname{sgn}(t)$ will be, where $\operatorname{sgn}(t)$ indicates the signum function. It would seem obvious that this ...
- 95
0 votes
0 answers
278 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
3 votes
1 answer
102 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: $$ W(...
- 31
1 vote
1 answer
337 views
Complex exponential Fourier series coefficient of periodic convolution
Let the complex exponential Fourier series coefficients of two periodic signals $x_1(t)$ and $x_2(t)$ be $C_{1n}$ and $C_{2n}$, respectively, with $T_0$ being the fundamental time period of both the ...
- 113
1 vote
1 answer
143 views
What filtering I could use to save my displacement data?
I am double integrating my acceleration to obtain the displacement. However, the displacement looks so strange. Basically this is the measured acceleration of a system under a impulse movement. and I ...
- 11
1 vote
2 answers
263 views
Interpretation of the initial value of an integrator
I came across this example the stream processing chapter of a programming book that I'm reading: Streams as signals We began our discussion of streams by describing them as computational analogs of ...
- 113
0 votes
1 answer
1k views
How to compensate phase delay introduced by the digital integrator?
Let's say I have a digital integrator with transfer function in following form $$ \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 ...
- 447
1 vote
1 answer
43 views
Integral Calculation in Matlab for Filter Optimization
I am trying to calculate the area under my FIR filter kernel using trapz but I'm getting weird results. The reason I want to know the area is eventually I would ...
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