System identification based on distribution theory and wavelet transform
Ryuichi Ashino, Takeshi Mandai, Akira Morimoto · Applicable Analysis · 2005
A review of system identification based on distribution theory 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 health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform.