Questions tagged [parseval]

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1answer
61 views

Understanding Parseval's Theorem with Discrete Wavelet Transform

I have difficulty to understand the results I get with implementing Parseval's Theorem in Python to DWT. I have the good results getting the Energy with Fourier transform and the time series in python:...
1
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1answer
39 views

Getting the power of a signal from its Fourier transform?

I have a non-periodic signal that contains the sinc function in the time domain and so it is a bit difficult to calculate its power (because of the integral) through: $$ {P_x} = \lim_{T \to \infty} \...
2
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1answer
75 views

FFT one-sided and Parseval theorem

I'm trying to get Parseval theorem working on a one-sided FFT. So far I have this code (matlab): ...
1
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3answers
295 views

Help with obtaining the power spectral density of a simple continuous cosine (using both forms of the definition for PSD)

I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice and would be very grateful if someone could check my ...
0
votes
1answer
37 views

Refinement equation and orthogonal wavelets basis

I have a wavelet function space defined by, $ \phi(x) = \sqrt(2) \sum_n h_{\phi}(n) \phi(2x-n) $ . given the Fourier transform of the function is: $\hat{\phi}(\omega) = \frac{1}{\sqrt(2)} \hat{h}...
0
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0answers
30 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 ...
1
vote
1answer
46 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? ...
2
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1answer
38 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}^{\...
3
votes
1answer
39 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 ...
4
votes
1answer
305 views

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(...
4
votes
2answers
192 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
votes
1answer
238 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( -\...