If I had to sum up this application note with a phrase, diagnosis I would re-iterate that the minimum sampling rate to adequately capture a signal depends not only on the frequency content, sildenafil but also the signal bandwidth. To demonstrate, we can look at GSM-based mobile communications which operate at around 1700MHz in the US. Even though the frequency content is high, each GSM channel is only 200kHz wide, so we can use a relatively slow ADC and a bit of good design. The typical trick employed in RF equipment is to set up an oscillator to run at the center frequency (~1700MHz) of the desired GSM channel and multiply it by the incoming RF signal (also ~1700MHz). As with a Fourier transform, the DC component of the result will represent the power at the oscillator frequency and the adjacent frequencies will be shifted to center around DC and will show up as “beats”. This new signal will have a much lower frequency content, on the order of the 200kHz, and will therefore allow slower ADCs to be used with a focus on economics (cheaper handsets) and higher accuracy (better reception).
The application note presents a similar type of trick, except this time, digital undersampling is involved. The idea is that unfiltered frequency content that is outside of the Nyquist band will be aliased into the Nyquist band and still provide meaningful information as long as it has narrow bandwidth and it is the only frequency content coming in. To use the previous example, if we can set up a well-tuned bandpass filter to center around the GSM channel of choice, we can run an ADC at 400kHz and expect the higher-frequency content to be aliased in.
On a final note, I have to apologize for my negligence on keeping up the `Journal Club‘. I have not forgotten about discussing Shannon’s work and plan to write a post about it at the earliest convenient time.