Convert sine wave signal to square wave signal

Question

I have a signal containing a variation of digital ASK type on-off keyed sine wave among which some stochastic irrelevant harmonic waves occur, like you can see on this figure:

In its current form each pulse duration is the same, but it's not always the case.

I'd like to calculate each pulse duration. To do that, I was thinking of converting this signal to a square wave signal like this:

I'm not sure of the different steps needed for this conversion but I have some leads:

1. Remove the noise => Low pass filter I presume?
2. To have the signal between 0 and the amplitude, I multiply the signal by itself
3. I apply a magic filter to convert the signal to square signal.

So my questions are:

• Do I need a low pass filter to remove the noise?
• What kind of filter do I need to convert the signal to square signal? Is it possible?

For information, I'm using Python and Numpy.

If there is any other method to calculate the duration of each pulse in the sequence, I'm open to all ideas.

Thanks!

Edit: Here's my signal:

   freq = 1000000
   fs = int(2*freq) # sample rate
   x = np.linspace(0, 10, fs)
   noise1 = 0.01*np.sin(2*np.pi * 1*x) + 0.05*np.sin(2*np.pi * 1.5*x) +     0.04*np.sin(2*np.pi * 0.2*x)
   noise2 = 0.1*np.sin(2*np.pi * 0.1*x) + 0.2*np.sin(2*np.pi * 1.8*x) + 0.1*np.sin(2*np.pi * 0.4*x)

  realSignal = 2*np.sin(2*np.pi * freq*x)
  sig =  noise1

  sig = np.append(sig, [realSignal, noise2, realSignal, noise1*noise2])

Answer 1

What you can do is process this signal with a windowed RMS function (I'm writing in matlab code, but it can easily be translated in python) :

windowlength = 5; %you can change that, but keep it odd
hw = (windowlength-1)/2; %hw stands for "half window"
%pre-assigning the output RMS signal
sig_RMS = zeros(1,length(sig)); 
%I'm adding zeros the the signal's left and right for boundary calculation
sig_zero_padded = [zeros(hw,1), sig, zeros(hw,1)];

sig_zero_padded = sig_zero_padded.^2; %squaring the samples
for i=(hw+1):(length(sig_zero_padded)-hw)
   % calculating square-mean inside the window and assigning the result
   %to the appropriate sample in sig_RMS
  sig_RMS(i-hw) = sqrt(mean(sig_zero_padded(i-hw:i+hw)));
end

Then you set a minimum value for which superior values of the RMS signal will be assigned to 1, and the other to zero :

trigger = 0.5; %I chose arbitrarily
square_sig = (sig_RMS > trigger);

And you should get your square signal.

What we are doing here, in simple language, is taking little bits of the signal and calculating the RMS value of each bit. If this calculated value is significant enough to be considered as "not noise", we assign '1' to it.

EDIT : I managed to compute it and it worked. Note that I had to take Fs = 10^5 because my computer does not have enough capacity for Fs = 10^6.

Here is the signal (blue), and the calculated RMS signal (red) for windowlength = 8191 :

Then I set trigger = 0.4 and obtained two crystal clear zones identifying the useful signal :

So in conclusion :

1. Set windowlength to get the RMS signal mean value far enough of the noise while keeping accuracy. In my case it was approximately 1 % of the total number of samples.
2. Set trigger between the RMS crests and the noise

However, I'm having that feeling that I'm reinventing something so feel free to look up for some literature about this method, I'm sure someone did the math to obtain optimal values of windowslength and trigger. ;)

Answer 2

Create the envelope of the signal (analytic signal) using the Hilbert transform and then threshold.

import scipy.signal.signaltools as sigtool

env = numpy.abs(sigtool.hilbert(sig))
threshold = 1
square_sig = (env > threshold)

(I haven't got python installed ATM so I can't test this)