Intermediate Frequency Spectral Placement of Bandpass Sampled Signals

摘要

Systems and methods for bandpass sampling of a continuous analog signal according to several embodiments can use a linear relationship between sampling frequency and intermediate frequency; $$ f_{\mathrm{IF}}={\left(-1\right)}^{n+1}\left(-\lfloor \frac{n}{2}\rfloor F_{S}+f_C\right)$$ ;where f_IF is the intermediate frequency and F_s is the sampling frequency of the bandpass sampling, f_c is the carrier frequency, B is a bandwidth and f_U is an upper frequency for the signal, and n is an integer such that; $$ 1\le n\le \lfloor \frac{f_U}{B}\rfloor .$$ ;The sampling frequency F_s can be chosen first and the IF can be calculated without iteration using the relationship above. Or, when f_IF is the most important design parameter, f_IF can be selected first, and sample frequencies which will not cause aliasing can be solved by calculating F_s given IF using the equation above, for all values of n so that; $$ 1\le n\le \lfloor \frac{f_U}{B}\rfloor ,$$ ;and then selecting a particular F_s. f_IF can be chosen to be F_s/4.