The theory of bandpass sampling

Potential use of the undersampling technique in the acquisition of nuclear magnetic resonance signals

“…Bandpass signals are characterized by having no frequency components above a frequency f h and below a frequency f l (signal spectral components in the range f l 5 f 5f h ) As shown in different works [12,17], the aliasing produced during the sampling process can be used advantageously when sampling passband signals: a sampling rate smaller than 2f h can be used, according to the bandpass sampling theorem for uniform and instantaneous sampling. This theorem states that a bandpass signal can be reproduced from its sample values if the sampling frequency f s satisfies [12] 2f h n 5f s 5 2f l (n −1)…”

“…As in practical situations this cannot be guaranteed, the sampling frequency must be higher or the signal bandwidth has to be increased with a guard-band [17].…”

“…In a system with a signal with spectral density S, in-band noise power density | i , and out-ofband noise power density | o , the SNR for the sampled signal becomes degraded at least by the noise aliased from the bands between dc and the passband, and can be estimated as [17] SNR :…”

GNSS Signals Acquisition and Tracking in Unfavorable Environment

“…The first variant acquisition and tracking procedure, of our proposed method, consists of acquiring BOCsin/cos(α,β) modulated signals with α ˃ β, and more specifically with α >> β, after undergoing a transformation based on undersampling process. The latter technique relies on sampling one desired signal with a frequency that is lower than twice the highest signal frequency (Shannon frequency) [51], [52], [53], [54]. The main purpose of such processing, which does not meet the Nyquist condition, is to bring closer the main lobes of BOCsin/cos(α,β) signals and provide, thus signals similar to those of BOCsin/cos(α,α).…”

Bandpass Sampling for Data Acquisition Systems

“…By the light of this, the actual value of the sample rate given by the DAS could be different from the ideal one in such a way that alias-free sampling could not be guaranteed anymore. Given the nature of bandpass sampling, simply increasing f s is not advisable (Vaughan et al, 1991), but an appropriate model is rather needed. Taking into account that: (i) the nominal sample rate, f s nom , that the user can set on the DAS, differs from f s of a deterministic quantity ε and (ii) the actual sample rate, f s ' , i.e.…”