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Digital Drive: RE: Theory vs. Real World........ by Werner

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RE: Theory vs. Real World........

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"The non-presence of pre-ringing with a linear-phase filter is impossible...."

Ah, Todd, you still haven't read and understood Shannon's proof, right?

Actually I wanted to waste this evening's time on something else, but OK, here goes ...

This posting contains graphs taken from an audio editor. The dots represent actual sample values in a digital audio stream. **please disregard the continuous lines between the dots as these are generated by the editor's
display routing and are not part of the actual signal stream**.

Let's start with the type of digital, linear phase, FIR filter as typically found in a commercial oversampling / reconstruction filter for CD replay. To keep the graphs manageable it is a 2 x oversampling filter, but as so many commercial silicon implementations it is half-band, i.e. any second coefficient is zero and the attenuation at Fs/2 is 6dB.
This is a particularly popular (because cheap) appromixation of the Sinc
reconstructor prescribed by Shannon and his ilk, and despised by Krieger and his followers (if any). Note the abundant pre- and post-ringing.

--

The second graph is that of an analogue-origin impulse, as it would exist in a 44.1kHz sampled signal space after correct band-limiting (as per Shannon's requirement) and sampling. (This impulse was generated by making a single-sample positive impulse in a digital signal space with an obscenely high sampling rate, followed by very steep minimum-phase low-pass filtering with a very narrow transition band and subsequent decimation to 44.1kHz.)
Notice the absence of pre-ringing and the wide spectrum occupied in the
44.1kHz space.

The relevance of this signal is that this is the fastest analogue-domain
band-limited event without pre-ringing that can be sampled with a 44.1kHz system. If this signal does not trigger pre-ringing upon playback and reconstruction then no signal will.

--
--

The third graph is what one gets when the above band-limited impulse signal is replayed at 44.1kHz but with 2 x oversampling and reconstruction with the initially presented half-band Sinc filter.

Now where has the Sinc's pre-ringing gone?

I did not invent this.



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