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In the process of trying to learn dialup, I've managed to learn/figure out everything except how to convert a demodulated/filtered signal back into the original data.

Here I have a random two-bit signal (red) sampled at 16000Hz at 2400 symbols/s (gray lines separate symbols), as well as the filtered signal (blue). The filter is a raised-cosine filter with α=1200Hz, β=0.5, and a length of 27 samples.

original signal vs filtered

Given the filtered signal, it's clear that a simple A/D converter is insufficient; for example, at about 7 symbols in (about a third from the left), the original signal crosses zero four times, whereas the filtered signal only crosses twice. I imagine this is due to higher frequencies being attenuated more than lower frequencies.

I realize that because the signal is being filtered at half the symbol rate, there shouldn't be any loss of information. How do I go about reconstructing the original signal from the filtered version?

In case it helps any: because the dialup training signal consists of known, pseudo-random data, should I use that to construct an adaptive filter/equalizer? Is it as "simple" as "un-attenuating" the higher frequencies?

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1 Answer 1

up vote 3 down vote accepted

Your low-pass filter's pass band is smaller than your signal's bandwidth, so it is destroying a significant portion of your signal. Given that, you cannot reliably reproduce the original signal without using sophisticated techniques like error correction codes.

I would try increasing $\alpha$ to 2400 Hz. Then the rolloff point will be 2400 * .5 = 1200. The resulting signal should look much better. If that filter bandwidth is too large you can find your sweet spot somewhere between 1200 and 2400 Hz.

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Oh wow! For whatever reason I thought α was supposed to be half the symbol rate. This works wonders! –  Drew McGowen Aug 12 at 17:33
    
Actually, it turns out it was a bug in my code; now, even when α=1200Hz, it still looks fine (this is what I suspected since 1200Hz is the Nyquist frequency of 2400baud). –  Drew McGowen Aug 12 at 18:25

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