Bandpass Sampling for Data Acquisition Systems

A number of modern measurement instruments employed in different application fields consist of an analogue front-end, a data acquisition section, and a processing section. A key role is played by the data acquisition section, which is mandated to the digitization of the input signal, according to a specific sample rate (Corcoran, 1999). The choice of the sample rate is connected to the optimal use of the resources of the data acquisition system (DAS). This is particularly true for modern communication systems, which operate at very high frequencies. The higher the sample rate, in fact, the shorter the observation interval and, consequently, the worse the frequency resolution allowed by the DAS memory buffer. So, the sample rate has to be chosen high enough to avoid aliasing, but at the same time, an unnecessarily high sample rate does not allow for an optimal exploitation of the DAS resources. As well known, the sample rate must be correctly chosen to avoid aliasing, which can seriously affect the accuracy of measurement results. The sampling theorem, in fact, affirms that a band-limited signal can be alias-free sampled at a rate fs greater than twice its highest frequency fmax (Shannon, 1949). As regards bandpass signals, which are characterized by a low ratio of bandwidth to carrier frequency and are peculiar to many digital communication systems, a much less strict condition applies. In particular, bandpass signals can be alias-free sampled at a rate fs greater than twice their bandwidth B (Kohlenberg, 1953). It is worth noting, however, that this is only a necessary condition. It is indeed possible to alias-free sample bandpass signals at a rate fs much lower than 2fmax, but such rate has to be chosen very carefully; it has been shown in (Brown, 1980; Vaughan et al., 1991; De Paula & Pieper, 1992; Tseng, 2002) that aliasing can occur if fs is chosen outside certain ranges. Moreover, particular attention has to be paid, as bandpass sampling can imply a degradation of the signal-to-noise ratio (Vaughan et al., 1991). Some recent papers have also focused on frequency shifting induced by bandpass sampling in more detail (Angrisani et al. 2004; Diez et al., 2005), providing analytical relations for establishing the final central frequency of the discrete-time signal, which digital receivers need to know (Akos et al., 1999) and determining the minimum admissible value of fs that is submultiple of a fixed sample rate (Betta et al., 2009). Sampling a bandpass signal at a rate lower than twice its highest frequency fmax is referred to as bandpass sampling. Bandpass sampling is relevant in several fields of application, such