# Sampling frequency lower than half of sampled signal frequency?

In GNURADIO when RTL-SDR Source block is placed there is a parameter Sample Rate (sps) and Channel frequency.

I can put there for example 32kHz into Sample rate and 107.5MHz into Channel frequency to tune some FM station in my location. FFT block shows a signal of that station in a correct frequency as shown on the picture: But according to Nyquist–Shannon sampling theorem, Sample rate should be at least 2 times higher than signal frequency, so in this situation I should set at least 215MHz into Sample rate parameter.

Why can I set much lower sampling frequency of a signal and it still looks correctly?

If you are interested in the math then if we want to shift a complex signal $X(t)$ by a frequency of $f$ we multiply by $e^{2\pi f i t}$. $i\sin(2\pi f t) = e^{2\pi f i t } - e^{-2\pi f i t}$ where $i = \sqrt{-1}$. So multiplying by $i\sin(2\pi f t)$ gives $X(t)i\sin(2\pi f t) = e^{2\pi f i t}X(t) - e^{-2\pi f i t}X(t)$ which is where the two copies come from. (The multiplication by $i$ in, e.g., $i\sin(2\pi f t)$ ultimately just adds a $90^\circ$ phase shift.)