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$\DeclareMathOperator{\sgn}{sgn}$ The modulating signal in AM is $$s(t) = C + a(t)\text,$$ where $a(t)$ is the (audio) amplitude, and $C$ is a constant so that $s(t) \ge 0 \;\forall t$. (Otherwise, your audio amplitude would just frequently "switch" the wave's sign, not really modulate the envelope.) That means, $C > - \min_t(s(t))$. Therefore, the ...

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Part of your misunderstanding comes from the fact that there are many ways in which the radar signal processing chain is implemented. Depending on the type of radar, targets of interest, hardware, etc., some methods are more appropriate than others. We will consider pulsed-Doppler radar here. In the chain you describe: In modern pulse-Doppler systems using ...

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When you have the described convolution measurement, you can indeed recover your $X$ using sparse recovery methods. Some examples are, as you suggest, OMP, MP, or for example subspace pursuit (SP), compressive sampling matching pursuit (CoSaMP), iterative hard thresholding (IHT), a plethora of other variants of greedy recovery methods, as well as basis ...

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Maybe normalized autocorrelation and zero crossig rate used together can work nicely... Normalized autocorrelation can be defined as: $$NAC(k) = \frac{\sum^{N-1}_{m=k}S[m-k]{\cdot}S[m]}{\sqrt{\sum^{N-1}_{m=k}S^2[m-k]\cdot\sum^{N-1}_{m=k}S^2[m]}}$$ The great advantage of using a NAC function is that we are normalizing Autocorrelation values, so these ...

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Pitch estimation is not a trivial problem. As a basic approach you can use the autocorrelation and/or cepstrum methods. The results can even be combined to obtain optimal results. For pre-processing you can do low-pass filtering and define the fundamental frequency ranges.

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SWIPE is a pitch estimator that worked well for me in the past. You can find dissertation & code in MATLAB here. It might give you some ideas.

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Without disagreement to Dilip's valid comments, this is to show the corner case as to when you can detect the presence of DSSS. This is not demodulating the data but detecting the presence of a repeating DSSS signal that is buried well below the noise. Specifically this would occur when the sequence repeats such as done with the GPS C/A code signals (the PRN ...

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