The paper describes the processing of non-stationary signals, which takes the advantages offered by the use of signaldependent techniques in sampling and analysis procedures. The level-crossing approach is exploited for signal sampling, whereby the local sampling density provides information about the local maximum spectral frequency of the signal. The frequency is used to build signal-dependent reconstruction functions required for signal recovery by solving a least squares problem. The results of simulation are presented using speech as an example. The approach developed can be implemented using asynchronous design techniques and could be aimed at application in speech transmission over wireless networks