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See the Wikipedia page on CRC computation for general information. Some software (byte-oriented) computations of CRC checksums use the method described in the paper "Computation of Cyclic Redundancy Checks via Table Look-Up". Communications of the ACM. 31 (8): 1008–1013 but there are lots of details that can be different in various implementations (...

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What is the best practice (and code solution) for detecting the onset of an impulse? ... The waveforms for these pulses do not necessarily go to zero between impulses, in fact, they rarely do. The signal goes close to zero, but not precisely. (I expect this has something to do with ambient noise around the signal, but am not certain . . .) Both of these ...

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If the constellation at the tarsmitter is symmetric about 0 on the real line then you can simply threshold the output between -1 and +1 with 0 as the threshold. So anything above zero is a logical 1 and everything below zero is a logical 0. This detection is rule is optimal when the noise is additive.

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Hint: (1) $sinc(\frac{t}{T})$ is the inverse fourier transform of a $rect$ function in frequency domain with $f=[-\frac{1}{2T}, \ \frac{1}{2T}]$. Time-shift will only result in a phase term in Fourier transform which does not impact the bandwidth. (2) $z(t)$ is product of two $sinc(\frac{t}{T})$ in time-domain. Hence, its frequency domain representation will ...

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CRC is a "definite" indicator of the channel impacting the bits and error in received symbol. So deploying a CRC check would definitely help. Length of CRC would depend on the overall system and data packets.

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Pitch is a human psychoacoustic perception phenomena, so an absolute ground truth might not be well defined enough to “solve”, except in some statistical sense, especially for a string bass, whose waveforms can evolve over time in both frequency and inharmonic as well as harmonic spectral composition. A pure perfect periodicity for many natural sounds does ...

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Try this: Apply a moving-average-window to the output signal. A window with a length close or equal to your matched-filter template signal. This window is supposed to add all the samples within its range. When this window applies to the location of first and second waves, the result's sign would be different to that of third and forth. You can also try a ...

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You are referring here to sparse signal sampling and Reconstruction. You do not require the sampling matrix to be sparse. Infact we require the sampling matrix to follow the restrictive isometry property. And sparse matrices do not follow this property. Random matrices do. So no point having a sparse sampling matrix

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