Dealiasing Technique for Processing of Sub-Nyquist Sampled Bandpass Analytic Signals

Abstract

Digital processing of signals sampled according to the Nyquist-Shannon sampling theorem in real time in a wide frequency band is based on extremely high-performance requirements of both analog-to-digital converters and processors. With sub-Nyquist sampling, processing occurs at lower sampling rates, but this raises the problem of aliasing. In this paper, the problem of reconstructing complex analytical signals distorted by aliasing of arbitrary degree is solved using multichannel multifrequency sampling. In this case, the signal to be sampled is fed to the N inputs of parallel-working analog-to-digital converters. Deterministic equidistant sampling is provided for each channel, but the sampling rates are different for each channel. The sampling rate on each channel is less than the sampling theorem required for bandpass sampling. In this case, aliasing of the Nth order occurs in the channels, in which at some frequencies there is an overlap of (N+1) periodically repeating aliases of the spectrum. When implementing the proposed approach, the frequency band of the analytical bandpass signal to be processed is divided into sub-bands with the same width. Channel sampling rates are multiples of the sub-band width. For all channels, systems of equations are drawn up that connect the measured aliasing-distorted spectrum values in the sub-bands with the unknown desired spectrum values in the alias sub-bands. However, these equations cannot be solved for analytic bandpass signals. Therefore, a technique is applied based on narrowing the processed frequency band in some channels without changing the sampling rates in them. The paper presents examples of spectrum reconstruction of a bandpass analytic signal for cases of aliasing of the second and third orders.