[sdiy] Digital audio demo on Youtube

[ASSI]

On Tuesday 18 February 2014, 21:47:10, Ingo Debus wrote:
> You guys are talking about distortion. What's your definition of
> distortion here?

Distortion in the sense of how many dB is the error signal (actual minus 
ideal signal) below the ideal signal.  For a synthesized signal we usually 
have an exact representation of what the ideal signal looks like, so this 
isn't hard to calculate.

> Look at it this way: transforming the ideal sampled signal (infinitely
> short nonzero values at the sample points and zero in between) to the
> real-world stair-step signal is nothing else but convoluting the ideal
> signal with a single rectangle with the length of the sampling period.
> Convolution in the time domain means multiplication in the frequency
> domain; and a single rectangle in the time domain corresponds to a
> sin(x)/x in the frequency domain.

Right.  Except that the stair-step signal never exists in the real-world 
since it still requires infinite bandwidth and therefore energy.

> So, going from time-discrete, infinitely short samples to a stair-stepped
> waveform means low pass filtering the signal, albeit that's a crude
> low-pass. But it makes the analogue reconstruction filtering easier, not
> more complicated.

The more important point is that it's not sufficiently band-limited and the 
passband isn't flat.  At which point you'll start to use more than a single 
sample and a windowing function that has some tradeoff between smoothness 
and delay (due to need to make the filter causal for implementation).  As 
said before, this problem is easily solved if you have some spare bandwidth 
around that enables oversampling.  As it turns out, this has become the 
preferred way of doing digital audio, improving the quality way past the 
limit of human hearing and in a lot of cases way past the ability of the 
rest of the system to keep up.  This doesn't mean it's the only way to do 
it, but if you look at the alternatives you gain an appreciation for why it 
has become that way.

> Am I completely off?

No.


Regards,
Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+

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