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IEEE ICASSP is probably still the largest international conference on communications and signal processing. IEEE Transactions on Signal Processing and Communications are well-regarded journals.
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Fourier Transform:
$$X(\omega) = \int_{t=-\infty}^\infty x(t)e^{-j\omega t}dt$$
Replace $\omega$ with $-\omega$:
$$X(-\omega) = \int_{t=-\infty}^\infty x(t)e^{j\omega t}dt$$
Replace $t$ with $-t$:
$$X(-\omega) = \int_{-t=\infty}^{-\infty} x(-t)e^{j\omega (-t)}d(-t)$$
$$ = \int_{t=-\infty}^{\infty} x(-t)e^{-j\omega t}dt$$
To describe this property intuitively,...
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Is it correct that the frequency resolution is dependent on the length of the window?
yes.
and how does the overlap then affects this.
The higher the overlap the more information is "repeated" from frame to frame. Consecutive frames are not independent but become more and more the same as the overlap increases.
Assume I have a very large window ...
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Overlap is and isn't related to time resolution: in sense of the uncertainty principle, only the window width plays a role.
However, any overlap other than maximum (hop_size = len(window) - 1) will alias the STFT and lose analysis information: this loss is for both time and frequency. Depending on hop_size, only a part of STFT is affected, however (see ...
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First a definition: an analytic signal is one who's negative frequency components are zero.
For a real signal $x(t)$, the Hilbert transform computes the imaginary component of the corresponding analytic signal $x_{a}(t)$:
$$x_{a}(t) = x(t) + jH[x(t)]$$
where $j$ is the imaginary unit and $H[]$ indicates the Hilbert transform.
One way of thinking about this ...
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I think you misunderstand what the book is saying. There is nothing like a "unit-energy" that you can compute. There is, however, a "unit-energy [...] pulse", which is a pulse with energy equal to $1$. So if you have some pulse $p(t)$ with energy
$$E_p=\int_{-\infty}^{\infty}|p(t)|^2dt\tag{1}$$
and you want to normalize it such that its ...
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The hilbert function in MATLAB will return an FFT based approximation of the Analytic Signal, and the magnitude of the analytic signal is the "envelope", but this isn't the "complex envelope" the OP refers to.
The analytic signal is given as:
$$x_a(t) = x(t) + j\mathscr{H}\{x(t)\} \tag{1} \label{1}$$
Where $\mathscr{H}\{x(t)\}$ is the ...
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You are right, reducing increasing the overlap you increase the time resolution, and increasing the duration you increase the frequency resolution.
You can increase the resolution as much as you can, by increasing the overlap, what you can't do is to observe fast variations in frequency.
Think of each frequency bin as a moving average, sudden variations of ...
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To align the samples (and realigning with different filter implementations) consider implementing actual timing and carrier recovery loops, or using those discriminators and approaches to manually correcting the offsets as would be done in those acquisition and tracking loops. This will put you on the road toward an actual implementation when the transmitter ...
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