How much to decimate?

Question

What I don't understand is the connection between the sample rate, the baud rate, decimation and using convolution or correlation.

I'm sampling at 2048000 Hz but I don't know my baud rate, I estimated it (by looking at the time length of one of the short pulses) to be about 2000 pulses per second.

So these are my steps (roughly):

1. get samples
2. demodulate
3. decimate by about 1000
4. correlate with ones

Here is an example of what my signal looks like after demodulation:

You can see that there are 4 symbols but many many samples. How can I turn those many many sample into just 4 symbols? I think it is related to convolution/correlation, but I'm not sure how.

Answer 1

Here's a general example on how to perform the convolution + decimation for an ASK signal.

amplitudes = [1, 0 0 1 0 1 1 0 1 0];
N = 100; % the symbol length.
pulse = 1.2*ones(N, 1); % the Rx pulse (used for correlation)

% the tx pulse (used to recreate your RX signal);
tx_pulse = pulse + 0.2*sin(2*pi*10/N*(1:N)');

% artificially create a signal
signal = zeros(N*length(amplitudes),1);
for i=1:length(amplitudes)
    signal((i-1)*N+(1:N)) = amplitudes(i) * tx_pulse;
end
signal = signal + 0.01*randn(size(signal));

subplot(3,1,1);
plot(signal);
title('RX signal');

subplot(3,1,2);
after_conv = conv(signal, pulse);
plot(after_conv);
title('After convolution');

subplot(3,1,3);
stem(after_conv(1:N:end));
title('After decimation');