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From: shauns@vice.UUCP (Shaun Simpkins)
Newsgroups: net.audio
Subject: Re: Carver CD Player & Technology
Message-ID: <91@vice.UUCP>
Date: Wed, 20-Mar-85 00:19:05 EST
Article-I.D.: vice.91
Posted: Wed Mar 20 00:19:05 1985
Date-Received: Sat, 23-Mar-85 00:30:27 EST
References: <14700008@hpfcms.UUCP> <5000001@hplsle.UUCP>
Organization: Tektronix, Beaverton OR
Lines: 87

> 
> (Re: why do 4x oversampling?)
> 
> > ... DAC sharing (i.e.,
> > channel after the DAC) effectively doubles the data rate.  Solution? Go to
> > 14 bit DACs that settle faster if you want to use only one, or make do with
> > 2x oversampling if you still want 16 bit conversion.  This is what Yamaha did.
> > I suspect that Philips made a silk purse out of a sow's ear with their 14bit
> > 4x scheme \- at the time that chip set came out cheap 5us 16bit DACs weren't
> > even on the drawing board but 14 bits was within the reach of existing IC
> > processes.  ...
> > 
> 
> The real reason to do 4x oversampling is not to accomodate the lack of
> technology in DACs, but rather, to ease the design requirements on the
> analog filter that follows the DAC.
>
^^^^Undoubtedly.  But my point was: given that you wish to oversample, how can
    it be done the cheapest?  There are certain technology limitations.
    Quote Philips:

	"The conversion of the 16 bit words into a analog signal is
	 performed ... by a 14 bit digital-to-analog converter
	 available as an integrated circuit and capable of operating
	 at the high sampling rate of 176.4 kHz."
> 
> 4x oversampling is accomplished by padding the one real sample with 3 zero
> samples (BTW - done in the digital filter) and producing a sample stream at
> the output of the digital filter at a rate of 176.4 KHz.  This sampled data
> only needs to be converted with 14 bit precision because the 'extra' bits
> come from the oversampled samples.  (It's a difficult concept to write
> about but can be shown graphically very easily)  The resultant output still
> has 96 dB dynamic range even though the DAC is a 14 bit one.
> 
> Using 4x oversampling and 16 bit DACs is overkill since there is no
> information available in the LSB's (unless one wants to manufacture it as
> noise somewhere in the system).
> 
> Bob Kunz
>
Continuing the quote from Philips:
	"Partly because of
	 the fourfold oversampling and partly because of the feedback
	 of the rounding-off errors in antiphase, rounding off to 14
	 bits does not result in a higher noise contribution in the
	 audio band.  This remains at the magnitude corresponding to
	 a 16 bit quantization ... so that even though there is a
	 14 bit digital-to-analog converter it is still possible to
	 think in terms of a 16 bit conversion system."

Strike me dead if I'm wrong here, but the resolution of the Philips system
is NOT the same as the 16bit systems - it's 14bits.  It's just the S/N that's
the same.
Let's follow a signal through the Philips system.  At the beginning, the 2 LSBs
are truncated and applied to the digital filter.  The filter interpolates 3
new data points between samples, `recovering' the lost 2 bits if 16 were used
at the output, which they are not.  Thus the base S/N of the Philips system is
84dB.  Since the final bandwidth of the system is 1/4 the effective bandwidth
of the filter output(i.e., the maximum bandwidth of an input signal sampled at
the filter clock frequency) we gain 6dB in S/N.  The roundoff feedback further
averages the quantization error to return to a 96dB S/N. 
But what if we kept the 2 bits that we threw away at the filter output and
ran them into a sixteen bit DAC?  Assuming a noise free input 
(< 1 input LSB), we'd get an 17-bit S/N ratio from the action of the
reconstruction filter! But-if we put in a slow staircase signal, the output
would only move in 16 bit increments, just very stable 16 bit increments -
with a touch of rounding at the edges.
Similarly, the Philips system moves in 14bit increments, just very stable 14 bit
increments.

I would say that there's information in those last 2 bits - as long as the
input noise is less than an LSB - even at 4x oversampling.
Indeed, if we were able to find an 18-bit DAC that could run at 176 kHz
(and a 16-bit ADC with a S/N of more than 108dB) we could use a 16-bit
input digital filter and get an output S/N of 19+ bits! 114dB!

Anyone care to clear up this matter?

The wandering squash,


-- 
				Shaun Simpkins

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