I'm wondering if there's a simple way to decode this pulse signal as I'm reading it in. I'm thinking the simplest way to decode this is if i can shift the whole signal down so that it's centered around 0. Then if my pulse goes above 0, I know it's a 1 and it'f it's below zero, i know it's a zero. Figures below to see what i'm trying to do. Please note that my sampling frequnecy $Fs = 8Hz$, my pulse width is between 1-2 seconds, and come in pairs of 2. these pairs are spaced about 20 seconds apart. There is also a 3 pulse header which denotes the start of the message, with the first pulse being wider than the other pulses.

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if I know the peak value of the pulses, then this is obviously just taking my signal and subtracting half of the peak, $d(t) = r(t) - peak/2$. The problem is this peak amplitude is going to vary, as is the noise level. If i try to just subtract a running average, then the noise part of my signal will be centered around 0 as well, which then my decision won't be a simple above/below zero decision. I've plotted subtracting the mean in figure 3 below. My signal is $d(t) = r(t) - runAvg(past 4 samples)$enter image description here

It seems like there should be an easy way to filter this, either in the time or frequency domain, I'm just not thinking of it. Thanks for your time!

  • $\begingroup$ Look up "integrate and dump filter". $\endgroup$ – MBaz Mar 25 '16 at 19:25
  • $\begingroup$ I used the matlab function intdump(r(16 samples), 16) and plotted the output of this, which looks like it filters the noise a good amount, but the signal is still in the same position (not centered around zero). As @vaz mentioned, I really just need to define a threshold, i was just trying to define that threshold as 0. Is there a good algorithm for determining this threshold if the amplitude of the pulse and noise vary? $\endgroup$ – gerrgheiser Mar 25 '16 at 21:48
  • $\begingroup$ If the amplitudes vary you can high-pass the signal to remove DC and use 0 as the threshold (you still use I&D to maximize the SNR), or you can use an automatic gain control algorithm to keep the gain roughly constant. $\endgroup$ – MBaz Mar 25 '16 at 23:30

You don't need to remove the DC part of your signal (i.e. "to center" it). In terms of decoding performance, there is no gain. Your signal looks like a typical ASK. Applying a simple integrator and sampling at $t=T$, where $T$ is the pulse duration, would do the job.

You only need to define a threshold, which usually corresponds to $AT/2$, where $A$ is the expected pulse amplitude.

Edit: forgot to mention the fact that you need to determine when to sample the output of the integrator. A symbol-level synchroniser is required for that.

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  • $\begingroup$ The threshold is my problem though. My received signal amplitude can vary, and my noise amplitude can also vary. I if i can look at the signal and tell that there are distinct pulse shapes, then i should be able to always decode the signal. Also, my synchronizer is supposed to be done on the 3 pulses at the beginning of the signal. So I guess my real question is is there a good, simple way to come up with the threshold, to where the threshold would always be close to the mid point of my pulse? $\endgroup$ – gerrgheiser Mar 25 '16 at 21:33
  • $\begingroup$ If your signal amplitude varies with time, but stays roughly constant between the transmission of two consecutive pilots, then you can use the pilot pulses to estimate the channel gain. $\endgroup$ – vaz Mar 25 '16 at 22:02

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