Spectral resolution and channel width

An SDR digitizes a slice of spectrum as wide as its sample rate. An FFT then splits that slice into equal channels (bins). The width of each one is the sample rate divided by the FFT length. At the hydrogen line, frequency is velocity (about 4.738 kHz per km/s, from the Doppler relation), so every channel width is also a velocity resolution.

Worked example: an RTL-SDR at 2.4 MS/s

• total span: 2.4 MHz, which is about 507 km/s of velocity
• 1024-point FFT: 2,343.75 Hz per channel, about 0.49 km/s
• averaged down to 10 kHz channels: about 2.11 km/s

Galactic hydrogen spans a few hundred km/s at most, so a 2.4 MHz span centred near the line covers it, with room for a baseline on either side. The outer edges of an SDR’s passband roll off, though, so don’t plan on using the last 10% at each end.

Choosing a channel width

Gas in the Galaxy has internal motions of several km/s, so features are rarely narrower than a few km/s. Channels of 1 to 2 km/s resolve everything an amateur antenna can separate. Narrower channels only add noise per channel: by the radiometer equation, halving the channel width doubles the time to reach the same SNR in each channel.

A common practice is to record with fine channels and average adjacent ones afterwards. That keeps the option of narrow resolution if you need it and lets you spot narrowband RFI, which shows up as a spike one or two channels wide that natural hydrogen never produces.

Windowing

An FFT on raw samples leaks power between channels. Applying a window (Hann is a common choice) before the FFT controls the leakage at the cost of slightly widening the effective resolution, by roughly half a channel. For hydrogen-line work that trade is almost always worth it. The processing chain we use is described in LAB-007, and the steps from raw spectrum to velocity plot are in LAB-012.