Extended Model Variety Analysis for Integrated Processing and Understanding of Signals

In this paper we extend our previous work on model variety analysis of a signal processing algorithm with respect to the class of all input signals that may po tentially arise in a given signal understanding appli cation This analysis has two related objectives The rst objective is to partition the set of all possible sig nals in the application domain into two sets according to whether each signal is correctly or incorrectly pro cessed by the signal processing algorithm under consid eration The second objective of model variety analy sis is to characterize the nature of the distortions in the signal processing output for the cases where the input signal is incorrectly processed The results of model variety analysis are useful for designing signal understanding systems for applications where it is nec essary for the signal processing to be carried out in a situation dependent manner Model variety analysis and its usefulness for the design of signal understand ing systems are illustrated in this paper through exam ples involving the use of STFT processing for a sound understanding application Introduction The analysis of signal processing algorithms has traditionally been motivated by considerations such as computational e ciency nite precision e ects and performance degradation when the signals for which an algorithm is designed are contaminated by noise The need for a new type of analysis of signal process ing algorithms has been pointed out in the context of signal understanding systems that must carry out situation dependent signal processing This type of analysis of a signal processing algorithm has been re ferred to as model variety analysis The basic idea behind such analysis is to determine how a given sig nal processing algorithm performs on a class of signals which includes signals which are not compatible with the assumptions under which the signal processing al gorithm was originally designed The results of such an analysis may be used by a signal understanding system for one of the two following purposes This research was sponsored in part by the Rome Air De velopment Center RADC of the Air Force Systems Command under contract number F C in part by the O ce of Naval Research under a University Research Initiative grant ONR N K and in part by NSF under contract number CDA to decide whether or not to use the given algo rithm in a situation where the input signal is likely to belong to a particular class of signals to decide whether the output from a particular application of the given algorithmmay have been due to an input signal for which the use of that algorithm is inappropriate We have previously reported a relatively sim ple example of model variety analysis of the short time Fourier transform STFT algorithm We have now extended the scope of that example and in the process we have attempted to establish a methodol ogy for carrying out model variety analysis in general The primary purpose of this paper is to present the re sults of our extensions to the model variety analysis of the STFT algorithm and to indicate the generalizable aspects of the methodology used in the example In section we provide some background on why situation dependent signal processing may be required in some signal understanding applications In partic ular we use the example of a sound understanding application for which we have developed an experi mental knowledge based signal understanding system That system performs STFT signal processing and utilizes the results of the model variety analysis presented in this paper to guide the situation depen dent application of STFT algorithms with di erent analysis window lengths t lengths and temporal decimation factors In section we describe our latest results on model variety analysis of the STFT algo rithm