In software defined radio (SDR) I often see sample rate and bandwidth interchanged or maybe I'm misunderstanding... If an sdr can sample a 2 MHz wide slice of rf spectrum does that imply it would be sampling at 2 million samples per second (2M S/s)? And if so what about bandwidth - is the implied bandwidth 2MHz? The particular sdr I am thinking of is the rtl2832u.
I'd like to understand if sample rate and bandwidth are tied together and if not how are they defined in terms of this or other sdr.
They are related, but not directly. The sample rate must be at least 2× the bandwidth in order to satisfy the Niquist criterion with respect to aliasing. However, since "real world" filters are not ideal brick-wall filters, you need to allow a higher margin on the sample rate — or accept a lower usable bandwidth.
Some texts might use "sample rate" as the definition of the individual sample rate of two separate sampling channels (often called I and Q), which could lead you to believe they're equivalent. But the combined sample rate of the two channels together is what makes the system meet the Nyquist criterion.
The rtl2832 does quadrature (IQ) sampling, thus the bandwidth is equal to the sample rate setting (as per its documented command parameters)
Quadrature sampling produces twice as much data (2 8-bit components) per IQ sample, which is partially a rational of why its bandwidth is twice that of a regular single channel Nyquist sampler using the same sample rate oscillator.
