A review of [Ashino, Mandai, and Morimoto, Applications of wavelet transform to system identification, Advances in Pseudo-Differential Operators, Birkhauser, Basel, 2004, 203-218] and [Ashino, Mandai, and Morimoto, System identification based on distribution theory and wavelet transform, Applicable Analysis, 84(2005), 165-195] is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time-frequency information of kernel distributions are deduced. A new wavelet based system identification method for time-invariant linear systems and its discretized formula using stationary wavelet transform are proposed. As an application to health monitoring systems, a changing point of system parameters of a linear system of ARX models is detected.

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