A Flexible AnalysisSynthesis Method for Transients.pdfVIP

A Flexible Analysis-Synthesis Method for Transients Harvey Thornburg, Fabien Gouyon CCRMA, Stanford University harv23@ccrma.stanford.edu Abstract We propose a new transient model which naturally extends the sinusoidal model to nonstation- ary phenomena. An integrated online-offline segmentation approach is developed, followed by an explicitly time-variant sinusoidal model. 1 Introduction tegrated solution, we summarize features of optimal detection and estimation algorithms: The sinusoidal model is a convenient sound- Detection: Online algorithms operate sequen- representation in analysis-synthesis frameworks. The tially to detect a single change in model parameters. signal is modeled as a sum of sinusoids, with time- By the stopping time of the test, an “operating char- variant amplitudes and frequencies, plus a residual acteristic” (OC) tradeoff is optimized between miss r (n), or unmodeled part: and false alarm probabilities (PM , PF A) and detec- tion delay (∆T ). 2p y (n) = Ak,n cos(mn ωk,m + φk,n) + rn With small ∆T , the stopping time gives also a (biased) estimate of the segment point. To detect k=1 multiple changes we restart the test. When a group of Such a parametric, time-frequency representation is changes lies between