Autocorrelation of a noised signal

We are going to calculate the autocorrelation of a signal contaminated by noise. In the case considered, the amplitude of the noise is so high that it makes the signal hardly recognizable

 
-->corrsignalnoise = corr (signalnoise,1000);
 
-->xsetech([0,0,1,1/2])
 
-->plot2d(t(1:500),signalnoise(1:500));
 
-->xsetech([0,1/2,1,1/2])
 
-->plot2d(t(1:500),corrsignalnoise(1:500))

Figure 9.4: Autocorrelation of `signalnoise': the addition of `signal' and `noise' and its autocorrelation. Notice that although a rhythm is not even visible (upper trace) it is detected by autocorrelation (lower trace)

At first sight the signal is not different from the figure in the previous chapter that only contained noise but its autocorrelation extracts the periodicity not visible in the trace. The comparison of this figure and the previous one clearly shows the utility of `autocorrelation' to extract information not evident in the original trace.