Bandpass Sampling & Nyquist Zones
A bandpass signal can be digitized directly at a sample rate far below its carrier — undersampling — as long as the whole band lands inside a single Nyquist zone. This tool finds the zone the signal falls in, the aliased IF it appears at after sampling, whether the spectrum is inverted, whether folding corrupts the band, and the theoretical minimum sample rate.
Equations & Parameters ▸
\(\text{zone } n = \left\lfloor \dfrac{f_c}{f_s/2}\right\rfloor + 1 \qquad f_{\text{IF}} = \left|\,f_c - f_s\cdot\text{round}(f_c/f_s)\,\right|\)
\(f_{s,\min} = 2B \qquad \text{no folding if } \left\lfloor\dfrac{f_L}{f_s/2}\right\rfloor = \left\lfloor\dfrac{f_H}{f_s/2}\right\rfloor\)
\(f_{s,\min} = 2B \qquad \text{no folding if } \left\lfloor\dfrac{f_L}{f_s/2}\right\rfloor = \left\lfloor\dfrac{f_H}{f_s/2}\right\rfloor\)
| fc | Signal centre frequency (MHz). |
| B | Signal bandwidth (MHz). The band spans fc ± B/2. |
| fs | Sample rate (MHz). |
| fIF | Frequency the signal aliases to in the first Nyquist zone (0 … fs/2). |
| inversion | Even Nyquist zones fold the spectrum, reversing the frequency axis. |
References: R. G. Vaughan, N. L. Scott & D. R. White, "The theory of bandpass sampling," IEEE Trans. Signal Process., 1991. · Analog Devices, MT-002, What the Nyquist Criterion Means to Your Sampled Data System.
Inputs
MHz
CarrierMHz
Signal BWMHz
ADC clockResults
Sampled result
Nyquist zone—
Aliased IF—
Spectral inversion—
Validity
Folding-free?—
Min. sample rate—
Diagram