[hpsdr] sampling

[Glenn Thomas]

Hi all.

An interesting discussion. My thoughts below.

73 de Glenn wb6w

At 09:32 PM 4/21/2007, Jason A. Beens wrote:
>You would get no information in the case you mentioned, but strictly
>speaking the Nyquist theorem is violated because the sampling frequency
>is equal to 2x, instead of greater than 2x the bandwidth of interest.
>Sampling at exactly 2x would cause an alias to DC.  In this case the DC
>value would be zero because we are sampling on zero crossings.

I agree.

>I think, but am not certain, that the 192 kHz rate is simply being used
>to over sample the audio frequency range (20-20,000 Hz).  I don't think
>the high sample rate is being used to reproduce audio up to 86 kHz,
>because dogs can't even hear that.  :)

Since few if any people can hear above 20 KHz, the 44 KHz CD sampling 
rate (Nyquist plus 10%) will provide all the frequency response 
needed for HiFi audio. The main reasons I can see for a 192 KHz 
sample rate tend to be either marketing (mine is bigger than yours) 
or psychoceramic considerations.

The only other explanation I can think of due to the fact that analog 
audio low pass filters have a significant phase shift, starting at 
about half the cutoff frequency and increasing to 90 degrees or so at 
cutoff. This phase shift is a form of distortion that, when it occurs 
between 10 KHz and 20 KHz, makes the "imaging" beloved by audiophiles 
difficult to achieve. The faster sampling rate allows the use of an 
anti-alias filter with a higher cutoff frequency, thus moving the 
frequencies with significant phase shift out of the audible range.

Some years ago, the CD marketeers were pushing "oversampling" as the 
latest advance in HiFi sound. I went to the Hi-end HiFi show and 
asked most of them "what does over sampling buy me?" I collected no 
more than a large set of dumb looks. What might be going on (though I 
was unable to confirm it) is that the 44 KHz 16 bit samples were 
being interpolated to provide an apparent higher sample rate with 
increased resolution. Of course, the only information they had to 
work with is what is contained in 44KHz/16bit samples, so the output 
is theoretically the same no matter. However, providing interpolated 
samples at a faster rate would allow them to use an anti-aliasing 
filter with a higher cutoff frequency, thus avoiding the phase 
distortion present in a 20 KHz LPF. OTOH, I don't know if they 
actually did this or if the CD oversampling was just marketing bull.

>The over sampling provides extra dynamic range.  If you wanted the
>performance a 192 kHz sample rate gives you but you only wished to
>sample at the CD sample rate of 44 kHz, then you would have to sample
>the audio data with a higher resolution ADC.  There is a limitation on
>the practical bit-width of ADC's, and one solution is to sample with
>less resolution more often.

Here I disagree. The sampling rate has nothing directly to do with 
dynamic range. Dynamic range is determined by the number of bits in 
the sample. In general, the (voltage) dynamic range is the number of 
bits times 6 dB. You can use a faster sample rate with fewer bits to 
improve dynamic range by simply adding N samples and calling the sum 
(with additional bits generated by the carries) the sample, but 
you've then traded sample rate for extra bits at a 1/N sample rate. 
Your sample is then the average over the 1/N sample period, which 
might be different from a single sample taken with a more precise ADC.

>Hopefully someone knows definitively why the 192 kHz rate was chosen,
>and then speak up on the list.  You have me curious now... I will have
>to goo do some research.

I don't know why 192 KHz. The precise frequency really isn't very 
important as long as it is above the Nyquist frequency and it is 
known with some precision by whoever wants to recover the data. Maybe 
it's because 192 is about 10% faster than 44*4=176?

>Jason Beens
>KB0CDN

73 de Glenn wb6w



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