A. Can smoothed noise may be mistaken for an actual signal?

  Here are two examples that show that the answer to this question is yes. The first example is shown on the left. This shows iSignal displaying a computer-generated 4000-point signal consisting of pure random noise, smoothed with a 19-point Gaussian smooth. The upper window shows a tiny slice of this signal that looks like a Gaussian peak with a calculated SNR over 1000. Only by looking at the entire signal (bottom window) do you see the true picture; that "peak" is just part of the noise, smoothed to look nice. Don't fool yourself.

The second example is a simple series of three Matlab commands that uses the 'randn' function to generate a 10000-point data set containing only normally-distributed white noise. Then it uses 'fastmooth' to smooth that noise, resulting in a 'signal' with a standard deviation of about 0.3 and a maximum value around 1.0. That signal is then submitted to iPeak. If the peak detection criteria (e.g. AmpThreshold and SmoothWidth) are set too low, many peaks will be found. But setting the AmpThreshold to 3 times the standard deviation (3 x 0.3 = 0.9) will greatly reduce the incidence of these false peaks.

>> noise=randn(1,10000);
>> signal=fastsmooth(noise,13);
>> ipeak([1:10000;signal],0,0.6,1e-006,17,17)
 
The peak identification function, which identifies peaks based on their exact x-axis peak position and a stored table of identified peak positions, is even less likely to be fooled by random noise, because in addition to the peak detection criteria of the findpeaks algorithm, any detected peak must also match closely to a peak position in the table of known peaks.

This page is part of "A Pragmatic Introduction to Signal Processing", created and maintained by Prof. Tom O'Haver , Department of Chemistry and Biochemistry, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at toh@umd.edu. Updated July, 2022.