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Dave,
the fundamental limit on the bandwidth that GQRX can display is
set by the sample rate of the RF hardware. As others have pointed
out, an RTL2838 has an absolute maximum sample rate of 3.2MHz, for
a received bandwidth of ±1.6MHz from the centre, for a maximum
bandwidth of 3.2MHz. Dongles such as the Funcube Dongle Pro have a
much lower limit of 192kHz. Other hardware will allow a wider
bandwidth, generally costing more! [Technical reasons will
generally limit the useful bandwidth to 80%-90% of the Nyquist
limit, which is the limit quoted above.]
There's a much longer version of this reply. Not knowing where you start this conversation from, I'd recommend your favourite search engine, looking for SDR (software defined radio) and DSP (digital signal processing). The wikipedia article on SDR doesn't explain how SDR works, but might be a good place to start.
HTH,
Robin, G8DQX