دانلود رایگان ترجمه مقاله چگونگی استفاده از آلياسينگ در سيگنال های باند محدود (نشریه IEEE 2004) (ترجمه ارزان – نقره ای ⭐️⭐️)

چگونگی استفاده از ناهمواری (آلياسينگ) در سيگنال های باند محدود

How To Take Advantage Of Aliasing In Bandlimited Signals

Abstract

In signal processing systems, aliasing is normally treated as a disturbing signal. That motivates the need for effective analog, optical and digital anti-aliasing filters. However, aliasing also conveys valuable information on the signal above the Nyquist frequency. Hence, an effective processing of the samples, based on a model of the input signal, would virtually allow the sampling frequency to be increased using slower and cheaper converters. We present such an algorithm for bandlimited signals that are sampled below twice the maximum signal frequency. Using a subspace method in the frequency domain, we show that these signals can be reconstructed from multiple sets of samples. The offset between the sets is unknown and can have arbitrary values. This approach can be applied to the creation of super-resolution images from sets of low resolution images. In this application, registration parameters have to be computed from aliased images. We show that parameters and high resolution images can be computed precisely, even when high levels of aliasing are present on the low resolution images.

1 Introduction

In general, we say that a signal can be perfectly reconstructed from its samples if it is bandlimited and the sampling frequency satisfies the Nyquist criterion, i.e. it is larger than twice the maximum signal frequency. If the signal is not bandlimited or the sampling frequency is too low, the sam- pled signal is aliased, and perfect reconstruction is not possible.

Vetterli et al. [1] showed that perfect reconstruction is also possible for signals with finite rate of innovation. Certain types of non-bandlimited signals (like streams of Diracs, piecewise polynomials, etc.) can be reconstructed from a finite set of samples. Vaidyanathan [2] considers some other sampling schemes for non-bandlimited signals, like the use of different sampling kernels. An overview of the current state in sampling is given by Unser [3].

In this paper, we derive some results for bandlimited signals that are sampled below twice the maximum frequency of the signal. We will use multiple sets of regular samples to reconstruct the original signal exactly. A similar problem for discrete-time signals is solved by Marziliano et al. [4] using combinatorial optimization methods.

چگونگی استفاده از ناهمواری (آلياسينگ) در سيگنال های باند محدود

How To Take Advantage Of Aliasing In Bandlimited Signals