Reconstruction of Nonuniformly Sampled Bandlimited Signals by Means of Time-Varying Discrete-Time FIR Filters
- PDF / 1,200,178 Bytes
- 18 Pages / 600.03 x 792 pts Page_size
- 89 Downloads / 200 Views
Reconstruction of Nonuniformly Sampled Bandlimited Signals by Means of Time-Varying Discrete-Time FIR Filters ¨ H˚akan Johansson and Per Lowenborg Electronics Systems of the Department of Electrical Engineering, Link¨oping University, 58183 Link¨oping, Sweden Received 1 September 2004; Revised 20 December 2004; Accepted 6 January 2005 This paper deals with reconstruction of nonuniformly sampled bandlimited continuous-time signals using time-varying discretetime finite-length impulse response (FIR) filters. The main theme of the paper is to show how a slight oversampling should be utilized for designing the reconstruction filters in a proper manner. Based on a time-frequency function, it is shown that the reconstruction problem can be posed as one that resembles an ordinary filter design problem, both for deterministic signals and random processes. From this fact, an analytic least-square design technique is then derived. Furthermore, for an important special case, corresponding to periodic nonuniform sampling, it is shown that the reconstruction problem alternatively can be posed as a filter bank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. This eases the design and offers alternative practical design methods as discussed in the paper. Several design examples are included that illustrate the benefits of the proposed design techniques over previously existing techniques. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
1.
INTRODUCTION
Nonuniform sampling occurs in many practical applications either intentionally or unintentionally [1]. An example of intentional nonuniform sampling is found in analog-to-digital conversion where certain time slots are used for calibration and so forth. This can be viewed as if some samples from a uniform grid are discarded which results in a nonuniform grid. Unintentional uniform sampling occurs in, for example, high-speed time-interleaved analog-to-digital converters (ADCs), where static time-skew errors between the different subconverters give rise to a class of periodic nonuniform sampling [2] as exemplified in Figure 1(c). Regardless whether the continuous-time (CT) signal, say xa (t), has been sampled uniformly (Figure 1(a)), producing the sequence x(n) = xa (nT) or nonuniformly (Figure 1(b)), producing the sequence x1 (n) = xa (tn ), it is often desired to reconstruct xa (t) from the generated sequence of numbers. Thus, in the nonuniform-sampling case, it is desired to recover xa (t) from the sequence x1 (n). This can, in principle, be done in two different ways. The first way is to reconstruct xa (t) directly from x1 (n) through CT reconstruction functions. Although it is known how to do this in principle (see, e.g., [1, 3–7]), problems arise when it comes to practical implementations. In particular, it is very difficult to practically implement CT functions with high precision. It is therefore desired to use the second way which is to perform
the reconstruction in the digital domain, tha
Data Loading...
