Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

Abstract

Abstract-This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, which is referred to as the Interpolation Identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time. The Interpolation Identity also leads to new sampling strategies including an extension of Papoulis' generalized sampling expansion.

Time-Frequency Localization and Sampling of Multiband Signals

“…also [4] for more recent work). Two notable related approaches that rely on iterated filterbanks are due to Herley and Wong [13] and to Eldar and Oppenheim [12]. These approaches and others conceptually lie somewhere between those of Venkataramani and Bresler and of Behmard and Faridani.…”

“…Among them, works of Venkataramani and Bresler and of Behmard and Faridani establish formulas or algorithms for interpolating multiband signals from samples and their methods will be reviewed in Section 7. Filterbank based approaches due to Herley and Wong [13] and Eldar and Oppenheim [12] will not be discussed. The common goal of these methods is to reproduce signals from samples taken at an average rate inversely proportional to the measure of the frequency support.…”

A Versatile Iterative Framework for the Reconstruction of Bandlimited Signals from Their Nonuniform Samples

“…When it is applied to the timing mismatch correction in TI ADCs, more savings in hardware costs can be achieved over conventional filter bank methods [3][4][5][6][7][8], as the implementation complexity of the overall iterative procedure is independent of the number of channels. Compared to multivariate polynomial FIR filters in [6][7][8], the VDF has much lower dimensionality and hence implementation complexity since it is just a bivariate polynomial FIR filter.…”

“…For the special case of M-periodic nonuniform sampling, the uniform DT signal reconstruction is particularly important for the timing mismatch correction in time-interleaved (TI) analog-to-digital converters (ADCs) [2]. Conventionally, this problem is usually analyzed and represented using the concept of perfect reconstruction filter bank because of the periodic nonuniform sampling pattern [3][4][5]. However, when the sampling pattern changes during operation, say due to component variations, the synthesis filter bank has to be redesigned to compensate for the new pattern.…”

Nonuniform Interpolation of Noisy Signals Using Support Vector Machines

“…Alternatively, a number of iterative methods have been proposed, including alternating mapping, projections onto convex sets, and conjugate gradient [7], [13]- [15]. Other authors have used noniterative methods, such as filter banks, either to reconstruct the continuous time signal, or to interpolate to uniformly spaced samples [16], [17], [3], but none of these methods is optimal in a LS sense, and thus many approximate forms of the Yen's interpolator have been developed [18], [19]. The previously mentioned methods have addressed the reconstruction of bandlimited signals, but the question of whether a signal that is not strictly bandlimited can be recovered from its samples has emerged.…”