Multiple scale correlation of signals by shift-invariant discrete wavelet transform

Correlation of signals at multiple scales of observation is useful for multiresolution interpretation of image, data and target signature analysis. Multiresolution analysis is inherent in the discrete wavelet transform (DWT), but shift-variance of the coefficients of the transform in dyadic orthogonal and biorthogonal basis spaces is the problem associated with it. Shift-variance of the transform and absence of direct transform domain relationship make correlation of signals inconvenient at multiple scales by the DWT. In this paper, the circulant shift property of the DWT coefficients is used in a novel way to produce correlation of signals at multiple scales with the critically sampled DWT only. The algorithm is derived in both discrete time and z-domain for signal vectors of finite duration. The algorithm is independent of signal waveform and wavelet kernel and is applied particularly for multiple scale correlation of radar signals, namely linear frequency modulated (LFM) chirp signals.