What does it mean to downconvert signals within a bandwidth, centered at another bandwidth?

Question

So, conceptually, when a book talks about down-converting signals within a bandwith of say, $25$ MHz, with the bandwidth centered at say, $50$ MHz, down to baseband, what exactly does it mean?

Answer 1

I'll use some different numbers to avoid coincidences between $25$ and $50$. It is also much more common for the band center to be much higher than the bandwidth. If the band center is $900$ MHz and the bandwidth is $50$ MHz, the signal is contained in the region $875-925$ MHz. If you mix it with a fixed sine wave you get the sum and difference frequencies. You can then filter out the high ones and be left with the low ones. Baseband is some low frequency that is convenient. The bandwidth stays the same, only the center frequency is changed. If we wanted, we could mix the above signal with an $800$ MHz carrier and take the difference frequency to get a signal that ranged between $75$ and $125$ MHz for our baseband signal.

Answer 2

That means that the signal is originally between 37.5 MHz and 62.5 MHz. So the bandwidth is 62.5 - 37.5 = 25 MHz, whereas the center is at (37.5 + 62.5) / 2 = 50 MHz.

To down-convert it means to do a "frequency translation" so the signal ends up centered at 0 Hz and still 25 MHz wide, i.e., from -12.5 to 12.5 MHz.

Why might this be common? Often, to transmit a signal through a channel, e.g., over RF, the signal may be up-converted to some carrier/center frequency for multiple reasons, e.g., the transmission needs to be within a certain band (because the system is using licensed spectrum at that band). Then at the receiver, you down-convert to get back the original signal.