Measurement and Reconstruction of Impulse Train by Parallel Exponential Filters

Abstract

In many areas of science and technology, the measurement of impulse trains is an important sampling scheme. For example, wireless data transmission has grown enormously due to the recent developments in ultra wide band technology, where the information is represented as impulse trains. In this letter, we present a new approach for sampling of the impulse train using parallel exponential filters (EFs), whose outputs are measured simultaneously. We show that with 2 parallel EFs, it is possible to reconstruct impulses with different amplitudes and appearance times within one sampling period. The reconstruction algorithm is manageable on microprocessor and VLSI circuits. Several applications of the parallel EF network are outlined.

Reconstruction of UWB Impulse Train by Parallel Sampling of Cascaded Identical RC Filters

“…In our previous work [9] we introduced a novel sampling scheme based on parallel RC filters, where the outputs were measured simultaneously. A disadvantage in the practical construction of the parallel RC network comes from the precise adjustment of the time constants of the RC circuits.…”

“…This needs the simultaneous measurement of at least samples from the outputs of the cascaded RC filters. An alternative singular value decomposition (SVD) based null space method is presented in Appendix for the solution of the roots of the pole zero cancellation filter (9).…”

“…Equation (21) forms the basis for the SVD based null space method. By searching very small singular value k 0   , the right singular vector k equals vector in (18) yielding the solution for the roots of the pole cancellation filter (9). In the presence of noise the dimensions of the r h L and matrices should be selected so that there appears only one tiny singular value.…”

“…Our research group has introduced a sampling scheme, where the signal is fed to the parallel RC filters, whose outputs are sampled simultaneously [9,10]. A variant of the parallel sampling scheme is tailored for detection of edges [11,12].…”

Multichannel Sampling of Signals With Finite Rate of Innovation

“…A further extension related to union of shift-invariant subspaces has been recently considered in [9]. The multichannel sampling of FRI signals has been considered in [12], [10] and [14], but in all cases the drift problem was not addressed.…”