Great question — this is a very common confusion when first applying the Nyquist theorem to radio astronomy.

You do not need a 2.8 GHz sample rate to observe the 1420.405 MHz hydrogen line.

Here’s why:

1. Nyquist applies to the bandwidth, not the RF centre frequency

Nyquist’s theorem says:

sample_rate >= 2 × (signal bandwidth)

It does not say anything about the absolute RF frequency (1420 MHz).
We almost never sample the RF carrier directly.

Instead, radios use mixers to shift the band of interest down to a much lower intermediate frequency (IF) or even baseband.

So the relevant quantity is:

How many MHz of spectrum around the H-line do you want to capture?

Typical hydrogen line bandwidths for amateur work:

10 kHz

50 kHz

100 kHz

2 MHz (wideband total-power)

To sample 100 kHz of bandwidth you only need:

sample_rate >= 200 kHz

That’s why your SDR can sample the hydrogen line with rates like 2 MHz, 5 MHz, or even 250 kHz.

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2. The radio does the frequency conversion for you

A typical SDR (RTL-SDR, SDRplay RSPduo, AirSpy, etc.) does:

RF (1420 MHz)  -->  Mixer  -->  IF/baseband (e.g., 0–2 MHz)  -->  ADC

After mixing, the 1420.405 MHz line turns into something like:

+405 kHz

or

-300 kHz

etc.

depending on the SDR’s LO.

The ADC only needs to sample that low-frequency signal.

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3. Hydrogen line is extremely narrow

Natural linewidth of the H I transition is tiny:

~1 Hz for the quantum transition

~kHz from galactic Doppler broadening

~tens of kHz from galaxy rotation

~tens of kHz from receiver filtering

So the actual radio signal of interest occupies maybe:

5 kHz – 200 kHz

Nyquist rate for this:

10 kHz – 400 kHz

Much lower than GHz.

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4. You only need a high LO, not a high ADC rate

To tune to 1420 MHz, the radio uses a high-frequency local oscillator (LO), but LO frequency ≠ sampling rate.

The LO can operate at 1–2 GHz, but the ADC still sees only a narrow IF band.

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5. Oversampling is optional, not required

Many hydrogen-line observers use:

2 MS/s

or

8 MS/s

or

250 kS/s

depending on the SDR and desired spectrum resolution.

Your spectral resolution is determined by the FFT size and integration time, not the raw sample rate.

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Summary (ASCII)

You do NOT sample 1420 MHz directly.

You sample a narrow "slice" of spectrum after mixing.

Nyquist applies to the width of the slice:

      Bandwidth of interest = tens of kHz

      Nyquist sample rate   = a few × 100 kHz

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