Randomized continuous frames in time-frequency analysis

Recently, a Monte Carlo approach was proposed for processing highly redundant continuous frames. In this paper, we present and analyze applications of new theory. The computational complexity the method relies on frame being so-called linear volume discretizable (LVD). LVD property means that number samples in coefficient space required by is proportional to resolution discrete signal. We show paper wavelet transform (CWT) localizing time-frequency (LTFT) are LVD. LTFT representation based 3D with richer class atoms than classical transforms like short time Fourier (STFT) CWT. Our analysis proves performing signal has same asymptotic as STFT CWT (based FFT), even though higher dimensional.