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Optimum receiver (matched filter / correlation)
A response to this thread on comp.dsp.Problem
Detect a pulse, for example five cycles of a sine waveSolution
Convolve the received signal with the reversed pulse shape (FIR filter).This implements a matched filter or correlation receiver, which is the optimum linear receiver.
Matlab script
close all; clear all;
len=50;
% Create a pulse, five cycles, 10 samples per cycle
pulse=cos((0:(len-1))/len*2*pi*5);
% a piece of empty sample
pad=zeros(1, len+3);
% create the received signal from pulses and gaps
s=[pad, 1*pulse, pad, 1*pulse, pad, pad, 0.5*pulse, pad];
% The height of the resulting peaks is the sum of all samples squared
factor=sum (pulse .* conj(pulse));
% FIR filter: Convolve the pulse with the signal
rec=filter(fliplr(pulse), [1], s) / factor;
% Plot
figure(); hold on;
plot(s+1, 'r+-'); plot(rec-1, 'g+-'); legend('receiver input', 'receiver output');
Download  |
The red curve shows the input signal to the matched filter, some delayed pulses.
The green curve is the output from the matched filter (or correlator).
The peaks coincide with the point in time, when the received pulse is fully aligned with the filter.
© Markus Nentwig 2007-2008
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