Re: sample rate

[Bill Fox <billyfox@soundscapes.us>]

Stefan Tiedje wrote:

>> Or, alternatively, as Jon explained,
>> a 22050Hz signal is only captured by 44100Hz sampling if the sampling
>> happens to occur at the peaks and troughs of the signal, and not
>> at the zero crossing points.
>
> Which is only true for exact 22050 Hz at 44100 Hz sampling rate.
> Do you really want to sample exactly a 22050 Hz signal with a 44100 Hz 
> sampling rate? The phase weirdness happens with the analog filters 
> before the converter. 22050 Hz is the theoratical border which cannot 
> be passed, the amplitude and phase you get for this one frequency is 
> arbitrary. But we are talking about real world problems don't we ;-)
>
> Stefan

Right on, Stefan.  The anti-aliasing filter in an audio sampling system 
is designed to remove frequencies above (0.5)Fs (Fs=the sampling 
frequency) that would alias, or fold back into the audio range.  
Remember folks, we're in the real world where there is no such thing as 
a true brick wall filter.  Guard bands are built into sampling systems.  
Does anyone here have a block diagram to scan it for all the 
non-engineers to inspect?  It might shed some light on what's really 
going on.

In the real world, the antialiasing filter removes frequencies above a 
certain point to allow the sampling system to work properly, without 
having to deal with frequencies at or above half the sampling 
frequency.  The signal is then sampled periodically and presented to an 
ADC to make a digital word for storage.

Upon playback, the digital word is fed periodically with the same sample 
frequency to a DAC whose output is fed to the reconstruction (or 
smoothing) filter to smooth out the DAC's output.

Sampling frequency and filter characteristics are carefully chosen so 
that the real word doesn't harm the signal in an audible manner.

In order to have a response up to 20kHz, one does NOT sample at 40kHz.  
That is why CDs use 44.1kHz so that a guard band protects the signal 
where the real world would mess with it.  With Fs = 44.1kHz, one does 
not expect to reproduce a 22.05kHz signal.  In fact, we try to prevent 
such a frequency from ever being sampled in the first place.

Cheers,

Bill