Hg. Schulze et al., SIGNAL-DETECTION FOR DATA SETS WITH A SIGNAL-TO-NOISE RATIO OF 1 OR LESS WITH THE USE OF A MOVING PRODUCT FILTER, Applied spectroscopy, 52(4), 1998, pp. 621-625
We report on a method to reduce background noise and amplify signals i
n data sets with low signal-to-noise ratios (SNRs). This method consis
ts of taking a data set with mean 0 and normalized with respect to abs
olute value, adding 1 to all values to adjust the mean to 1, and then
applying a moving product (MP) to the transformed data set (similar to
the application of a moving average or 0-order Savitzky-Golay filteri
ng). A data point in the presence of a signal raises the probability o
f that data point having a value >1, while the absence of a signal inc
reases the probability of that data point having a value <1, If the au
tocorrelation lag of the signal is larger than the autocorrelation lag
of the associated noise, the use of an MP with window comparable to t
hat of the signal width (i.e., 2-3 times the signal standard deviation
) will tend to reduce the values of data points where no signal is pre
sent and similarly amplify data points where signal is present. Signal
amplification, often to a considerable degree, is gained at the cost
of signal distortion. We have used this method on simulated data sets
with SNRs of 1, 0.5, and 0.33, and obtained signal-to-background noise
ratio (SBNR) enhancements in excess of 100 times. We have also applie
d this procedure to low SNR measured Raman spectra, and we discuss our
findings and their implications. This method is expected to be useful
in the detection of weak signals buried in strong background noise.