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In Analog-to-Digital Converters(ADC), the signal is first sampled at a rate higher than or equal to the Nyquist, then quantized and encoded. In Analog-to-Informations (AIC), the sampling and compression are combined in one step, mathematically:
$$ y = \Phi \cdot x $$
where $y$ is compressed signal, $\Phi$ is the sensing matrix, and $x$ is the input signal. My questions are: * Simulating the above equation using MATLAB is downsampling, First the input signal is read to obtain a vector of say $N$ samples representing the signal, and then multiplied by the matrix $\Phi$.

Does this mean that we sample the signal to obtain the vector $N$? If so, where is the benefit? How sampling and compression are combined in one step? How can the sampling and compression be combined to perform compressive sensing in a practical way?

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  • $\begingroup$ Since analog to information conversion seems to still be in the research phase perhaps you could cite whatever source you are working from? I'm pretty sure that the benefit is either an enhanced flow of venture capital, or if you actually manage to choose $\Phi$ correctly, a lower sample rate and/or needed resolution on $y$. $\endgroup$ – TimWescott Oct 28 '19 at 19:14
  • $\begingroup$ Reading this: you really should read a basic text on compressive sensing (the wikipedia article has some weaknesses, so a book might help), karem. This is just an application of the very well-known compressive sensing techniques that been around for quite a while. You'd typically have some observer matrix with which you try to estimate your $y$ from an observation shorter than $N$. $\endgroup$ – Marcus Müller Oct 28 '19 at 19:49

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