[music-dsp] oversampling

[Dan Evans]

>> When I do 2x upsampling, does it make a difference in the spectrum, 
>> whether
>> I insert zeros every second sample, or just use every sample twice?
>
> I acn't remamber the exact justificatiom , but using zeroes is the correct
> method.
>

Inserting zeroes is indeed the correct way to do it. A sampled signal is a 
series of impulses at a given sample rate. Also remember that such a 
signal's spectrum will consist of copies of the original spectrum at each 
multiple of the sampling frequency. When we convert the signal to analogue 
using a low pass filter, these copies are removed. From a time domain 
perspective, we have a form of interpolation between the impulses, that 
reconstructs the signal exactly (providing of course there are no 
frequencies greater than nyquist going into the system).

It's the same thing with oversampling; by adding zeroes we effectively have 
a series of impulses, and therefore we know what's happening to the spectrum 
(the original spectrum is repeated in the frequency domain, as with the 
example above). Using a halfband filter during oversampling gets rid of the 
copies of the spectrum (which will be above nyquist when we downsample 
again, so we have to get rid of it).

I'm not sure exactly what would happen to the spectrum if you simply repeat 
the previous sample, but it's probably not as predictable as inserting 
zeroes.

Dan