An accurate multirate sampling technique and its application to time-scale analysis

An accurate multirate sampling technique is presented, which constructs a sequence x(nsΔt) from a sampled signal x(nΔt) for any positive s, where x(nΔt) is assumed to be sampled with the sampling theorem being satisfied. It is proven that both x(nΔt) and x(nsΔt) can be characterized by a sequence {c_m} which can be calculated from the DFT of x(nΔt). The theory behind the accurate sampling rate conversion is then used to develop a parallel and recursive structure for time-scale analysis. It is indicated that the new approach not only accurately realizes the time-scale analysis, but also possesses a parallel and recursive structure appropriate for efficient hardware implementation