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it seems like the bigger problem is that subsampling the signal would result in aliasing frequencies No, subsampling in frequency domain corresponds to aliasing in time domain. So the idea here is to purposefully alias in time domain so that you get a sub-sampled FFT. That is exactly why 'Claim 3.7' of paper mentions $y_i=\sum_{j=0}^{n/B-1}x_{i+Bj}$. These ...


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after a RF down-conversion using heterodyning principle, will there be an information loss? No, if the original signal was band-limited, and the bandwidth of your IF processing is sufficiently large to capture that. (so, if you've built a sensible heterodyne receiver.) If we translate to a fixed IF frequency, is there is an intuitive way of explain that ...


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The equation looks reasonable to me: The scaling by $\frac{1}{2\pi}$ is to have the result in units of normalized frequency $f$ instead normalized angular frequency $\omega$. What may be confusing is using the index $k$ from the autocorreation instead of $n$ since it would be the time domain variable for $R[k]$ and $w[k]$, while $k$ is often associated with ...


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The OP may have removed DC (the mean of the signal) and that would be clear by zooming in on DC to visibly see the null that does exist there. If the null does not exist, then that would mean the mean signal was not properly removed. The width (effective bandwidth) of the null if done by a simple subtraction of the mean would be approximately $1/T$ in Hz ...


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It is important to understand that the "sub-sampling" mentioned is occurring in the frequency domain, not the time-domain-- so any aliasing that the OP is thinking of would all be time-domain aliasing, not aliasing in the frequency domain. To "sub-sample" the frequency spectrum, the time domain sampling rate is unchanged but the duration in time (number of ...


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You can take a wavelet transform of the given data and obtain a a phase angle time series and then average out the phase angle. The important thing to keep in mind is that this averaging is not the same as averaging a magnitude spectrum. To see an example have a look at the figure below: So if you were to simply average the angle values ($2\pi$ and $-0.1$),...


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Update: After chatting with @oliver this turned out to be more challenging than I anticipated. My approach for comparison against improved alternatives is as follows: Unwrap the phase to create samples of unwrapped phase versus frequency Filter this vector with a moving average filter (directly in the frequency domain) or any other interpolation /...


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Reminder what a permutation is: The exchange of indices in a sequence. That's exactly what they're doing here. Invertible in this context (only read the paragraph so far) means "the multiplication with $\sigma$ under mod $n$ is invertible, i.e. given the result of that multiplication and $\sigma$, you can caclulate the original value in all cases." ...


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Update: as Sundar commented his question is specific to the “incremental Sigma Delta ADC” of which I only have a vague understanding of. To the extent the incremental implementation is a traditional Sigma Delta ADC that is reset periodically I would believe this model still applies as described similar to using a moving average frequency response to model an ...


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For the zero-th cepstral coefficient, the sign is probably always positive since it represents the average energy of the entire spectrum. For higher-order coefficients, seeing that the question was first posted in 2017, does the OP maybe already have an answer? Would be interested to learn.


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I have not seen it in a book but it seems to me that if the STFT definition is:$$X(\tau, \omega)=\int_{-\infty}^{\infty}x(t)w(t-\tau)e^{-i\omega t}dt$$ Then we can define the filter as $$h(t)=w(t)e^{-i\omega t}$$ where $w(t)$ can be interpreted as a low-pass filter and the exponent as frequency shifting method (see Shift Theorem). Next we define $$g(t)=h(-t)...


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Solution in python using Modpoly and Imodpoly algorithm. Python library for baseline correction/removal. It has Modpoly and IModploy algorithm which can return baseline corrected results when you input the original values as a python list or pandas series and specify the polynomial degree. Install the library as pip install BaselineRemoval. Below is an ...


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