A Comparison of Methods Recovering Signals from Non-Uniform Samples

Abstract

Band-limited signals play a vital role in signal acquisition, transmission, processing and storage for decades. However, their recovery from non-uniformly spaced samples is still subject to discussion. There are multiple authors advancing different approaches and the user has to deal with an abundance of literature. Therefore, this paper offers a brief theoretical review of the most promising reconstruction methods. We also consider the importance of regularisation if the signal samples are noisy, which, surprisingly, seems to be neglected by many authors. Subsequently, the suitability of the methods is illustrated using an example of a real-world signal. Assessment of accuracy and speed of the methods is repeated for varying noise levels in signal amplitude, and for increasing degree of non-uniformities in sampling time. Cubic spline methods and sinc function reconstruction offer the best compromise between speed and accuracy for the concrete signal tested in this paper.Band-limited signals play a vital role in signal acquisition, transmission, processing and storage for decades. However, their recovery from non-uniformly spaced samples is still subject to discussion. There are multiple authors advancing different approaches and the user has to deal with an abundance of literature. Therefore, this paper offers a brief theoretical review of the most promising reconstruction methods. We also consider the importance of regularisation if the signal samples are noisy, which, surprisingly, seems to be neglected by many authors. Subsequently, the suitability of the methods is illustrated using an example of a real-world signal. Assessment of accuracy and speed of the methods is repeated for varying noise levels in signal amplitude, and for increasing degree of non-uniformities in sampling time. Cubic spline methods and sinc function reconstruction offer the best compromise between speed and accuracy for the concrete signal tested in this paper.