[hpsdr] sampling

[jeff millar]

FRANCIS CARCIA wrote:
> Say you sample 30 mhz at 60 mhz rate and you just happen to convert on 
> the zero cross at 0 and 180 degrees. What information will you get? I 
> would think you would need to sample at least 4 times to catch real 
> information. Heck we sample audio at 192 khz these days so why ? That is 
> at least 10 samples per highest audio frequency. Frank and other 
> grasshoppers???

Widipedia answers this question well

http://en.wikipedia.org/wiki/Nyquist_sampling#The_sampling_process

   Note that if the original signal contains a frequency component
   exactly equal to one-half the sampling rate, this condition is
   not satisfied, and the resulting reconstructed signal may have
   a component at that frequency but the amplitude and phase of
   that component will not, in general, match the original component.

Generally, real systems sample with two A/Ds 90 degrees out of phase
(I/Q), which captures amplitude information.  If one sample stream
happens to fall on the zeros, the other falls on the peaks.

It really important to get past the idea that you need a lot of
samples to reconstruct the signal.  Because, SDR will often use
input signals above 1/2 of sampling frequency. The theorem states
that
   “Exact reconstruction of a continuous-time baseband signal
    from its samples is possible if the signal is bandlimited
    and the sampling frequency is greater than twice the
    _signal bandwidth_."

This statement allows signals anywhere in the spectrum, including
spreading across the clock frequency or it's harmonics.

Modern A/D's support sampling inputs signals much higher than
their clock frequency.  The designer must bandlimit the input
signal to less than 1/2 the clock frequency.

jeff, wa1hco

 1177253693.0