An iterative reconstruction algorithm for amplitude sampling

Traditional data acquisition systems rely on sampling of bandlimited signals at uniformly spaced time instants with high-precision amplitude representation. Amplitude sampling, as previously introduced by the authors, is based on uniform amplitude sampling with high precision timing information. This paper presents an iterative algorithm for signal recovery from amplitude samples and compares the results with the use of iterative recovery from the nonuniform time samples implied by the amplitude sampling process. The iterative amplitude sampling reconstruction algorithm (IASR) proposed and evaluated in this paper is based on the interpretation of amplitude sampling as uniform sampling of an associated function obtained from a reversible transformation of the bandlimited input signal. The IASR algorithm exploits uniform sampling and the frequency- and time-domain properties of the amplitude-time function. The IASR algorithm is compared with the use of iterative nonuniform sampling reconstruction as proposed by Voroni. While in numerical simulations the Voronoi algorithm converges to marginally better reconstruction than IASR, the convergence rate of IASR is significantly better.