Comparison between adjustable window technique and wavelet method in processing backscattering lidar signal

The "lidarist" frequently wishes to process his experimental data to obtain as accurate and clean a representation of water vapor as is consistent with his measurement accuracies. In measurements contaminated by high-frequency noise this usually means smoothing the experimental data by some method (which is equivalent to smoothing with a low-pass filter) to eliminate or greatly reduce the amount of high frequency noise without distorting the desired signal. For data which are continuous in time (analog data) this is commonly accomplished using low-pass RC filters. However, with the increasing use of computer-controlled data acquisition systems which record data in digital form, there has developed a need for techniques which perform the same filtering process on the digitized data. Filtering or smoothing process should be as simple and efficient as is consistent with experimental situation. Poissonian averaging has been using for filtering lidar signal data. In previous work we showed the opportunity of using digital filtering in order to overcome problems created by poissonian averaging. To introduce further improvement in filtering we have used binomial filters; some scientists also use differentiating smoothing in an attempt to compensate for the fact that differentiation reduces the signal-to-noise ratio. This can easily be performed with the binomial filter by convolving either the filter coefficients or the data by sequences [1,0,-1]/2. This may be repeated any number of times to obtain the second-third-, and higher-order derivatives, after which the data are low-pass filtered in usual manner. The advantages of the above adjustable windows compared to the fixed windows are their optimality and flexibility. A wavelet analyis is used to increase signal retrieval. Wavelet analysis represents the next logical step: a windowing technique with variable-sized regions. Wavelet analysis allows the use of long time intervals where we want more precise low-frequency information, and shorter regions where we want high-frequency information.