I/Q samples

An SDR doesn't store a simple stream of values: each sample is a pair of numbers, I (in-phase) and Q (quadrature). Together they form a complex number I + jQ, which you can picture as a point in a plane: its distance from the origin = the signal's amplitude, its angle = its phase.

        Q ↑
          |      • (I=0.6, Q=0.8)
          |     /
          |    /  amplitude = √(I²+Q²) = 1.0
          |   /   phase     = atan2(Q, I) ≈ 53°
          |  /
   ───────+──────────→ I
          |

Why two numbers instead of one?

With a single real value you cannot tell a frequency above the centre frequency from one below it — both would give exactly the same measurement. With I and Q, the point rotates in the plane: counter-clockwise = frequency above centre, clockwise = below. You recover the negative frequencies, hence the whole window, centred on the tuning frequency.

That's what lets you observe, say, ±10 MHz around 2.44 GHz in one go. The receiver "brings down" the band you care about around zero (the mixing stage, see What is an SDR?), then samples it as I/Q.

The picture that makes it click: the spinning point

Picture the (I, Q) pair as the tip of a clock hand:

The hand stands still → a signal exactly at the centre frequency (zero relative frequency).
It spins 1000 times per second → a signal at +1 kHz from centre.
Its length varies with a voice → amplitude modulation (AM).
Its spin rate varies with music → frequency modulation (FM).
It jumps abruptly in angle → phase modulation (PSK).

Every kind of modulation can be read in this plane. It's also why digital receivers display constellations: for PSK, the points cluster into tight groups (4 groups = QPSK, i.e. 2 bits per symbol); if the clusters smear, the link is noisy.

Concretely, inside the machine

A HackRF's raw stream is a byte sequence I,Q,I,Q,…, each signed 8-bit (−128 to +127); an RTL-SDR does the same unsigned. Practical consequences:

Throughput: at 10 MSps that's 10 million pairs × 2 bytes = 20 MB/s over USB. It's the sample rate, not the listening frequency, that costs.
Max amplitude: a saturated sample "pins" at ±127 — on the spectrum, the whole noise floor rises. You set the gain to stay below that.
The engine reads this complex stream, applies an FFT, and gets the spectrum. Everything else (peaks, SNR, The waterfall (time cascade)) follows from it.

Your turn

A sample reads (I = −0.7; Q = 0). Amplitude? Phase? (0.7; 180°.)
The point completes one full turn every 2 ms, counter-clockwise. What relative frequency is the signal at? (+500 Hz above centre.)
Why does an 8-second I/Q recording at 2.4 MSps weigh ~38 MB? (2.4 M × 2 bytes × 8 s.)