Bandpass Sampling: How to Digitise a 10.7 MHz IF FM Radio Signal with an ADC of 10 MHz Sampling Frequency?

What You Already Know: Nyquist Sampling

If you have studied Nyquist sampling, your instinct when you see a 10.7 MHz signal is to reach for an ADC running at at least 21.4 MHz. That instinct is correct for baseband signals — but it is wrong for bandpass signals, and understanding why opens up one of the most useful techniques in practical RF and communications engineering.

This article explains bandpass sampling from first principles, derives the conditions that make it work, walks through a concrete example using a 10.7 MHz intermediate frequency (IF) signal sampled by a 10 MHz ADC, and covers where the technique runs out of road.

The Nyquist–Shannon sampling theorem states that to perfectly reconstruct a signal, you must sample it at a rate at least twice its highest frequency component:

For a baseband signal — one that occupies frequencies from DC (0 Hz) up to some maximum frequency fmax — this is the rule you must follow. A 10 MHz audio or sensor signal genuinely requires a 20 MHz or faster ADC.

But here is the key insight that Nyquist is often misquoted as missing: the theorem actually says you need to sample at twice the bandwidth of the signal, not twice its centre frequency. For a baseband signal, bandwidth and maximum frequency are the same thing. For a bandpass signal, they are very different.

But here is the key insight that Nyquist is often misquoted as missing: the theorem actually says you need to sample at twice the bandwidth of the signal, not twice its centre frequency. For a baseband signal, bandwidth and maximum frequency are the same thing. For a bandpass signal, they are very different.

Bandpass Signals Are Different

A bandpass signal does not start at DC. It occupies a band of frequencies centred around some carrier or intermediate frequency. In communications and RF engineering, almost every signal of practical interest is a bandpass signal — AM, FM, Bluetooth, Wi-Fi, IF stages in superheterodyne receivers, and so on.

Bandpass Signal — the signal occupies a narrow band [fL, fH] centred on fc. Because B << fc — the bandwidth is much smaller than the centre frequency — you only need to sample at a rate Fs ≥ 2B, not twice f_c, to capture the signal without loss.

The 10.7 MHz IF signal used in FM radio receivers is a perfect example. After the RF front end mixes the received signal down from its broadcast frequency, it produces a signal centred at 10.7 MHz. This signal has a bandwidth of perhaps 200 kHz (for mono FM) — but its highest frequency component is about 10.8 MHz.

Applying Nyquist naively says you need a 21.6 MHz ADC. Bandpass sampling says you need a 400 kHz ADC — or any ADC running above 400 kHz that satisfies a specific set of conditions. A 10 MHz ADC is more than sufficient, as we will show.

The figure below makes this concrete. It takes exactly the case just described — a bandpass signal whose bandwidth is tiny compared to its centre frequency — and shows what happens when you actually sample it: the 10.7 MHz IF signal, sampled at just 10 MHz, doesn’t get destroyed by aliasing. Instead it reappears, fully intact, at 700 kHz. That’s the practical payoff of the bandwidth-not-centre-frequency rule above. The explanation right after the figure walks through why it lands exactly there, in terms of Nyquist zones and spectral inversion.

Describing the figure

The top row (a) shows the original, continuous IF spectrum before sampling. Because the signal is real-valued, it has mirror-image energy at both +fc and −fc — here centred at 10.7 MHz, with an occupied bandwidth B of 200 kHz. Nothing unusual so far; this is just what a 10.7 MHz bandpass signal looks like on a spectrum analyzer.

The bottom row (b) shows what happens after that signal is sampled at F_s = 10 MHz. Sampling doesn’t just capture the signal — it stamps out a repeated copy of the entire spectrum at every multiple of F_s, spaced exactly F_s apart (shown by the two F_s double-arrows). The two original humps at ±f_c are still visible, but a new pair of images has now appeared much closer to DC, at −0.7 MHz and +0.7 MHz. Those two are the aliases: they exist precisely because 10.7 MHz and its repeated images (10.7 − 10 = 0.7, and −10.7 + 10 = −0.7) land inside the same low-frequency region. That ±700 kHz pair is the “down-shifted” copy of the original 10.7 MHz signal — it carries exactly the same information, just moved to a frequency the ADC’s baseband processing can work with directly.

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Nyquist Zones

A Nyquist zone is just a slice of the frequency axis wide. Each zone is exactly one “Nyquist bandwidth” further out than the last:

• Zone 1:
• Zone 2:
• Zone 3:
• Zone 4:
• Zone k:

Every zone, when sampled, folds down on top of zone 1. Which zone your actual signal happens to sit in — determined by its real frequency and your choice of — decides where in baseband it lands and, just as importantly, whether it lands right-side-up or flipped.

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Spectral inversion in even zones

Here’s the part that trips people up: odd zones (1, 3, 5, …) fold down into baseband with their frequency content in the same order it started in — the low edge of the band stays the low edge, the high edge stays the high edge. Even zones (2, 4, 6, …) fold down mirrored: the low edge of the original band becomes the high edge after folding, and vice versa. This is spectral inversion, and it’s a direct, unavoidable consequence of how aliasing folds the spectrum back and forth like an accordion at each F_s/2 boundary.

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