Bandpass Sampling Algorithm with Normal and Inverse Placements for Multiple RF Signals

Abstract

Bandpass sampling algorithm is effectively adopted to obtain the digital signal with significantly reduced sampling rate for a single radio frequency(RF) signal. In order to apply the concept to multiple RF signals, we propose bandpass sampling algorithms with the normal and the inverse placements since we are interested in uniform order of the spectrum in digital domain after bandpass sampling. In addition, we verify the propose algorithms with generalized equation forms for the multiple RF signals.

An efficient algorithm for bandpass sampling of multiple RF signals

“…In [3], they have described schemes to determine valid bandpass sampling frequencies for two distinct RF signals. A generalized solution for downconversion of multiple RF signals has recently been proposed in [4]. It is, however, noted in [4] that a constraint in finding the sampling ranges is suggested such that each replica of the RF signal is placed at each segment of the sampled bandwidth divided proportional to the size of the signal's bandwidth, which may lead to a failure in finding all possible sampling ranges.…”

“…A generalized solution for downconversion of multiple RF signals has recently been proposed in [4]. It is, however, noted in [4] that a constraint in finding the sampling ranges is suggested such that each replica of the RF signal is placed at each segment of the sampled bandwidth divided proportional to the size of the signal's bandwidth, which may lead to a failure in finding all possible sampling ranges. Furthermore, most of the previous works have not taken into consideration a guard-band or marginal spacing between downconverted signals when finding the sampling frequency for downconverting the multiple RF signals.…”

“…We thus limit our interest to one particular case, a signal permutation of normal placement and no change in the ordering of the given RF signals, namely, , , as assumed in [4]. Fig.…”

“…Taking account of the minimum guard-band in the sampling range, we can obtain the following equations by the boundary constraint: (2) and (3) where is defined by for as a frequency shift coefficient with the guard-band, which is similar to in [4]. Here, denotes a floor function.…”

“…Here, denotes a floor function. Combining (2) and (3), we can find an intersection range as (4) The range of each now becomes (5) Note that the range of except can be considerably reduced as explained below. The range of can be found as (6) Here let us define .…”