Questions tagged [parseval]

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1answer
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Is there an equivalent of Parseval's theorem for wavelets?

Parseval's theorem can be interpreted as: ... the total energy of a signal can be calculated by summing power-per-sample across time or spectral power across frequency. For the case of a signal $x(...
3
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1answer
38 views

parseval for a continuos but limited signal

I have a question about the parseval relation written here https://en.wikipedia.org/wiki/Parseval%27s_theorem (In the chapter Notation used in physics). If I have a signal continuous but limited (so ...
2
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1answer
36 views

demonstration using parseval

I have to do a demonstration. If we do the Parseval identity of the signals $x(t)$, $y(t)$ and $z(t)$ that go from $0$ to $T$ and that are real, we have: $\int_{0}^{T} x(t)^2dt=\int_{-\infty}^{\...
1
vote
1answer
40 views

reference parseval theorem limited signal

some days ago I asked here parseval for a continuos but limited signal if the Parseval can be applied for limited signal. Can you recommend me a book or a paper that I can use as reference for this? ...
1
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2answers
100 views

Checking Parseval's Theorem for Gaussian Signal by Using Scipy

I'm trying to check Parseval's theorm for Gaussian signal. It's well known that fourier transform of $\exp(-t^2)$ is $\sqrt{\pi}\exp(-\pi^2 k^2)$. So I implement it by using quad and simps. I think ...
0
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1answer
137 views

Autocorrelation sequence in terms of Fourier transform of the underlying signal

Let $x(n)$ be a sequence of length $N$, which is zero outside the interval $(0,N-1)$. Let $X(k), k=0,1,\cdots,N-1$ be the FFT coefficients of $x(n)$, that is, $X(k)=\sum_{n=0}^{N-1}x(n) \exp\left( -\...
0
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0answers
27 views

Spectral correlation zero modulation frequency $S_x(\alpha, 0)$

I got a simple modulating signal $x(t)=\sin(2\pi\alpha t)\sin(2 \pi \beta t)$ with carrier frequency $\alpha$ and modulation frequency $\beta$. The spectral correlation will obviously have components ...