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It appears the OP is missing a critical point about the effects of sampling a continuous time signal, so I provide some slides I have below that may be helpful demonstrating the periodic frequency spectrum that results due to sampling. The spectrum is only unique from $-f_s/2$ to $+f_s/2$ where $f_s$ is the sampling rate and for real waveforms that spectrum ...

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Sampling any signal including a signal of a given power spectral density will create a unique spectrum over the range of the sampling rate (so any $n(f: f + F_s)$ for n integer will be unique in the sampled spectrum where $F_s$ is the sampling rate and the signal is assumed to be complex. Typically we use ranges of $0:F_s$ or $-F_s/2: F_s/2$ and refer to ...

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Reconstruction is possible so long as NOLA is obeyed - which is an easier criterion (on synthesis information) to meet than what you seek (analysis information). To discriminate temporal variations finer than $T$, the window's temporal width must be $\leq T$. You can use ssqueezepy's window_resolution with appropriate unit conversion (mult by $f_s$) to ...

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First hit on Google seems to be a reasonable start: https://github.com/gpeyre/matlab-toolboxes/blob/master/toolbox_sparsity/toolbox/l1eq_pd.m

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A method that I use very often to approximate the CDF is based on the observation that given a set of $N$ samples, the CDF at the point x the fraction of the points that are smaller than $x$. So if have a vector of sorted samples $S$ you could approximate the CDF as $cdf(x) = i/N$ if $S_{i-1} < x < S_i$. A simple way to plot the CDF would be plot(sort(...

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So I took a look at the slides and it seems to be giving a cursory overview of how to measure Doppler with multiple pulses, so it's very generic. Hopefully this is a pretty straight forward thing to discuss given that your questions are suspicious of their statements, that's good! First Question: why is the Nyquist theorem applied to the doppler frequency $... 1 The baseband information-bearing signal$s(t)$is a train of time-shifted orthogonal pulses: $$s(t) = \sum_k a_k p(t-kT),$$ where$a_k$is the sequence of symbols and$T$is the symbol rate. The problem is, how to generate this signal in Matlab (or any other discrete-time numerical language)? To start, note that the$j$-th pulse$a_j p(t-jT)$can be written ... 1 Sinc interpolation can exactly reconstruct an above-Nyquist-sampled strictly bandlimited signal from noiseless samples. See the Whittaker-Kotelnikov-Shannon reconstruction or resampling theorem: https://en.wikipedia.org/wiki/Whittaker–Shannon_interpolation_formula and https://ccrma.stanford.edu/~jos/resample/Theory_Ideal_Bandlimited_Interpolation.html For ... 1 To implement a digital-to-analog converter, all you need is an ideal low-pass filter to filter out the periodic frequency response that$\varOmega \geq \varOmega_s/2\$. H(j\varOmega) =\left\{ \begin{aligned} T,\ \ \ \ |\varOmega|<\varOmega_s/2 \\ 0,\ \ \ \ |\varOmega|\geq\varOmega_s/2 \end{aligned} \right. The impulse response of an ideal low-pass ...

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Unlike the Gardner Loop, the M&M synchronizer should be performed after the RRC filter in the receiver for best performance. With cases of high RRC alpha, the M&M won't work as expected without the complete Raised-Cosine filtering (RRC in transmitter followed by RRC in receiver) as the slope of the error term will reverse, with high self-noise, as I ...

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Q1: is this a correct setup? I'm guessing "no" but that really depends on your application and goal. The process will produce numbers but if these numbers are useful or not depends on what you want to do with them. Q2: is there a minimum requirement for the buffer (FFT window?). Mathematically speaking : no. You can run a FFT on a single sample ...

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