Newsgroups: rec.audio.high-end
From: prls!max@uwm.UUCP (Max Hauser)
Subject: MASH, Bitstream, oversampling, etc.
Date: 17 May 91 13:53:09 GMT

In article <12047@uwm.edu>, smithjh@math.orst.edu (Jeremy Smith) inquires:

(1)   what is the MASH 1-bit D/A conversion?

(2)   Is this better than oversampling?

Intelligent questions deserve an intelligent answer.  In fact these and
related questions arise regularly, so I will try a more general response.
I last did so on the "MASH" topic in (I think) summer 1989, on the group
rec.audio.  I will limit myself to the definitions and the technical context
and thus leave the field open to others to comment intelligently on personal
experience and impressions of specific products containing these techniques.

"MASH" is a commercial acronym to describe a class of oversampling data
converters (either A-to-D or D-to-A) introduced and popularized by T. Hayashi
of Nippon Telephone and Telegraph in February 1986 at an integrated-circuits
conference [Note 1].  Thus "MASH" denotes a subset of "oversampling" rather
than a competing technique.  The acronym derives from and means "MultistAge
noise SHaping."  While the technique was popularized by Hayashi, he did not
use the actual acronym "MASH," which came somewhat later, from K. Uchimura
et al. [Note 2].  Also, the underlying idea is much older still [Note 3].

The technique now dubbed "MASH" is a series of small one-bit oversampling
data converters each of which does a partial, and noise-shaped, conversion
and then passes a residue (conversion error) to the next stage.  The
individual outputs of all of the stages are then combined (this is
nontrivial) to form a composite output.  That output is passed to a digital
filter (for an A-to-D function) or an analog filter (for a D-to-A function).
(Yes, that's right -- I've proofread it.) This brutally short explanation
does not do the subject justice and may even leave unfamiliar readers with
the mistaken impression that MASH resembles successive-approximation or
pipelined data conversion (well-defined in the art), which it does not,
differing deeply in philosophy.  However it's an accurate nutshell
description in that it will endure deeper scrutiny.  For further details
you may wish to look in one of my survey papers, such as the AES Journal
January/February 1991.

The technique dubbed "MASH" by NTT is also called, less commercially,
"feedforward" or (less precisely) "cascaded" higher-order noise-shaping
[Note 3].  It is one of several different topologies that can implement the
"noise-shaping modulator" portion of an oversampling data converter.  Other
such topologies include multibit and one-bit pure-feedback modulators.  The
latter (one-bit) class are called delta-sigma in the research literature,
and "Bitstream" by NV Philips in digital-audio products (these techniques
also have many applications outside of audio).  "MASH" data converters are
themselves not truly "one-bit" data converters in a meaningful sense, as I
have explained in more depth in print, although they are made up of one-bit
subsections and this often causes confusion.

Each of these competing modulator topologies has technical strengths and
weaknesses that are very involved and do not lend themselves to reductive
explanation.  The signal fidelity in the "MASH" technique can be very good
but depends on a different set of circuit elements than in the one-bit
schemes.  It is all a matter of "second-order" electrical effects; if the
components are all perfect (as they invariably are assumed to be, in popular
"explanations" of this subject matter), then all the techniques work well.

When Hayashi introduced the "MASH" technique to the international community
in 1986 (I was present), it was suggested from the floor that this method,
although a viable alternative to one-bit oversampling, did introduce certain
additional vulnerabilities to circuit imperfections, and moreover that the
real justification for the method was not clear (Hayashi's actual motivating
statement at the time was dubious).  It has since been suggested, perhaps
insightfully, that the sheer novelty of the "MASH" method might afford a
commercial, rather than a performance, advantage since the other basic
oversampling methods occupy expired patents and are therefore in the public
domain.  (My use of passive verbs in this paragraph is not accidental.)

But I think it even more important, in the context of this newsgroup and the
usual questions, that none of these considerations need correlate at all with
audible differences among finished audio products that employ these data
converters!  Offhand I would suggest that audible quality could easily be
affected far more by such prosaic outboard factors as the choice of output
buffer amplifiers, and the degree of analog-digital isolation in the
conversion-reconstruction circuitry, than by whether the internal modulator
is realized via "MASH," or "Bitstream," or some other topology.  This has
not, of course, prevented legions of advertising copywriters and cult audio
pundits from pontificating about the "revolutionary" aspects of this or that
topology and deploying buzzwords like "noise-shaping" and "one-bit" with
impressive vacuity.  They apparently prefer this to focusing on the
sonically and technically more vital, but less glamorous, issues.

There is my terse explanation of the relationship between "MASH," "one-bit,"
"Bitstream," "delta-sigma," and "oversampling" data converters.  Be
skeptical of anyone who asserts glibly that one of these techniques is
"better" than the others.  You might be able to hear differences among
CD players using the competing schemes, but almost certainly not for the
reasons everybody talks about.  Such differences could easily be due to
any of the numerous important factors other than the particular choice of
data-converter topology.

Notes from text:

Note 1:  Hayashi et al., ISSCC 1986.  Printed version in that year's ISSCC
digest, pages 182-183.

Note 2:  Uchimura et al., ICASSP 1986.  Printed version in 1986 ICASSP
Proceedings pp. 1545-1548.  Research papers quite regularly misattribute
the modern origin of these circuits to this ICASSP paper rather than to the
earlier ISSCC paper [Note 1] by co-workers.

Note 3:  The technique has existed in various forms, including a small
paper in "Electronics Letters" in 1969.  Candy and Temes have told me that
they would cite this in their forthcoming broad research overview of
oversampling.  I find it still more intriguing that the technique is also
a data-conversion implementation of Black's multistage linear amplifier
(US patent 1,686,792, issued 1928), a classic invention actually predating
the invention and patent of negative feedback, also by Black.

Max Hauser      {mips,philabs,pyramid}!prls!max      prls!max@mips.com

Copyright (c) 1991 by Max W. Hauser.  All rights reserved.

"A lot of things can be solved by the use of jargon -- for example, the
effort of thinking, or the danger of saying something that someone else
may not like.  You don't have to be clever, and you're always on the side
of whoever has the money or power ..." 
-- Stanislav Andreski, author of "Social Sciences as Sorcery"

Newsgroups: rec.audio
From: exspes@gdr.bath.ac.uk (P E Smee)
Subject: Re: Oversampling for kids
Date: 6 Jun 91 14:06:37 GMT

In article <1991Jun4.174051.594@cs.sfu.ca> rosen@cs.sfu.ca (Wilf Rosen) writes:
>
>Could somebody please explain what oversampling really means with regard
>to CD players. The only information I have been getting is from friends
>who claim to know, or from (ulp) salesmen. No explanation I have  seen yet
>is really believable. (The most common explanation is that e.g. 4x oversampling
>means the disk gets read 4 times. Somehow this seems silly). 

Layman's explanation follows.  I guarantee it to be sufficiently
accurate for your expressed needs, but to keep it simple I'm going to
skip some of the technical complexities at a detail level where they
shouldn't matter.

First, the problem with non-oversampling players:  The mechanics of the
sampling process mean that you also get a spurious signal at half the
sampling frequency (22.05 kHz for CD 44.1 kHz sampling); and that you
also get a sort of 'mirror image' of the real audio signal, reflected
around this 1/2-sampling freq.  E.g. a 20KhZ note will also create an
artifact at 25 kHz.  These artifacts ARE beyond the range of human
hearing, but they can cause follow-on side effects which impinge into
the audible range, so they need to be filtered out.  However, it is
also very difficult (and or expensive) to build a sharp-cutoff filter
which will not do nasty things to the bit of the signal which is passed
through.

So, how do you fix this?  You increase the sampling rate.  However,
there are only 44.1 khZ worth of samples on the disk.  What an
oversampling player does is to take the samples it reads (reading the
disk only once) and by use of various 'curve-fitting' types of
algorithms, works out intermediate values.  Like extrapolation, only
fancier.  A 2x oversampler works out one intermediate value between
each pair of read values.  A 4x works out 3 intermediates.

The effect is to increase the apparent sampling rate, at which (or
reflected around which) the artifacts I first mentioned occur.  Thus,
they can be filtered out by a much less aggressive filter, which will
not mess up the desired part of the signal.  (Some very high x
oversampling players can actually dispense with this filter entirely,
on the grounds that the artifacts have been moved to such a high
frequency that they won't interfere with the final result even if they
are left in.)

If you're going to try to find references, a likely keyword would be
'digital filtering'.

-- 
Paul Smee, Computing Service, University of Bristol, Bristol BS8 1UD, UK
 P.Smee@bristol.ac.uk - ..!uunet!ukc!bsmail!p.smee - Tel +44 272 303132

Newsgroups: rec.audio
From: jpb@calmasd.Prime.COM (Jan Bielawski)
Subject: Re: Oversampling for kids
Date: 7 Jun 91 19:45:48 GMT

In article <1991Jun4.174051.594@cs.sfu.ca> rosen@cs.sfu.ca (Wilf Rosen) writes:
<
<Could somebody please explain what oversampling really means with regard
<to CD players. The only information I have been getting is from friends
<who claim to know, or from (ulp) salesmen. No explanation I have  seen yet
<is really believable. (The most common explanation is that e.g. 4x oversampling
<means the disk gets read 4 times. Somehow this seems silly). I realize this 
<may well be a FAQ, but I haven't seen it discussed for the past 2 months.
<Even a pointer to a good book on the matter would be real swell. Thanks
<for reading up to this point.

	Let me try, see how much I don't know.  A digital oversampling
filter is a piece of software that accepts digital data (representing
the 44.1 kHz samples from the CD), does some number crunching on them
and outputs recalculated digital data that represent identical
musical information as the original but because of certain reformatting 
the new data is easier to transform into analog ("easier" meaning mostly
"using less expensive electronics" although it's probably true that
this oversampling approach is inherently better).  The algorithm
does look like sticking in extra samples between the existing ones.
One even hears of sticking in *zeros* in between but this seems to have
come from the fact that the oversampling program initializes the variables 
representing the extra samples to zero before processing -- something
any decent program does (well, usually...).

	The algorithm is described, for example, in John Watkinson's 
"Art of Digital Audio".  A bit drier and theoretical discussion is in 
Teukolsky's et al. "Numerical Recipes".

	Jan Bielawski
	Computervision, San Diego
	jpb@calmasd.prime.com

Newsgroups: rec.audio.high-end
From: cs.utexas.edu!wotan!prls!max@uwm.UUCP (Max Hauser)
Subject: Oversampling for the curious, the furious, and the damned
Date: 24 Jun 91 12:47:18 GMT

You may wish to save this article either for interested friends or for
future reposting as necessary since my readership of these newsgroups is
irregular.

Introduction:

This is a broad and not-very-technical online summary of CD oversampling,
antidotal to the lies and nonsense served up in consumer-audio retailing
and an alternative to the well-intentioned but misleading or fractional
explanations often seen in the popular audio press (including the so-called
serious or high-end publications).  This synopsis is less detailed but much
broader than my earlier "technical summary," written for engineers and posted
to rec.audio in 1987 and occasionally since.

If you want more depth of information on these topics, my colleague Prasanna
Shah recently published a dense technical overview of audio oversampling in
the popular magazine Audio in January.  I published a long technical tutorial
(not specific to CD or DAT products) in the Journal of the Audio Engineering
Society, January/February 1991 (vol. 39 no. 1/2 pp. 3-26).  A lighter and
shorter overview of mine is also available as Preprint #2973 from the Audio
Engineering Society, 60 East 42nd Street, New York, New York 10165 USA,
Telephone 212-661-8528, FAX 212-682-0477.  This preprint was recently
recommended by the popular magazine Stereophile.  AES charges $5 for such
preprints ($4 for members), $3 for journal-article copies and $10 for back
issues, and is pretty efficient about getting them into your hands if you
FAX them a request with V. or MC. credit-card information (I did so recently
and the copies arrived in the mail in about three days).  These papers
contain many further references.  Some of these sources emphasize the A/D
rather than D/A path but the core principles are identical (the circuit
implementation of each section interchanges between analog and digital).

Do not be alarmed if the following summary takes an approach different from
what you read elsewhere.  There are details here not usually mentioned in
popular summaries (or even in the research literature).

A. Thumbnail Sketch of Oversampling

Signals such as audio, stored digitally, entail a finite *sampling rate*
(44.1 kilosamples/sec for the 12-cm CD) whereas in their natural (analog)
form they are continuous-time waveforms (you can think of this usefully as
an "infinite" sampling rate).  The circuitry that regenerates the
continuous-time analog output in a CD player has two major tasks:  
translating a stream of digital numbers into analog values ("conversion")
and also bridging between the finite sampling rate of the digital sequence
and the "infinite" sampling rate of the outside world (that is, restoring
a correct continuous waveform from discrete samples) -- "reconstruction."

Non-oversampling conversion-reconstruction (C-R) systems make the transition
from finite to "infinite" sampling rate in one step, while oversampling
systems do it through one or more intermediate sampling rates (higher than
the original, but still finite).  Although the details may not be obvious at
this point, producing these intermediate signals with elevated sampling
rates is a purely digital process and can thus be performed predictably and 
repeatably (although it does require that you have technologies where
digital logic is very cheap, and therefore it was unattractive until recent
years, although the basic techniques have been known since the 1950s and in
embryonic forms since the time of the second world war).

Not only the reconstruction process but also separately the conversion
process (bits into volts) benefits from the use of an intermediate sampling
rate on the way to continuous time.  Designers can orchestrate eloquent
mathematical tricks to trade a higher deliberate sampling rate for lower
required resolution in internal digital-to-analog converter (DAC) circuitry.
This in turn tends to render the analog part of the C-R chain simpler and
more tolerant of component fluctuations.  But moreover, in practice
oversampling C-R systems blend the two tasks of conversion and
reconstruction so that they overlap in actual hardware, unlike a classical,
non-oversampling system.  The subjects of this paragraph are extremely
complex and seductively counterintuitive even to well-trained engineers,
and they habitually garner the most imaginative misinterpretations in
popular-press writing.

An oversampling conversion-reconstruction (C-R) system in practice normally
contains a series of four major blocks.  The first is a sampling-rate-
increasing digital filter, the second a digital quantization-management
subsystem or "noise-shaping modulator," the third a DAC circuit _per se_
and the fourth an analog lowpass filter.  A classical, or non-oversampling,
system lacks the first two blocks, but is far more demanding of the last
two blocks, which are analog circuits that largely determine the
performance and subtler behaviors of the signal path.  (That's the whole
reason for oversampling, in a nutshell.)

By the way, these four blocks reflect a combination of traditionally
separate specialties in electrical engineering, each with a different
intuition and set of assumptions about what is technically difficult or
important.  This is why you will find many different explanations of
oversampling (some of them seemingly in conflict) even from competent
specialists.  The first of the four blocks is generically a digital
filter, the second a quantizer (or quantized feedback system), the third
a precision analog circuit and the fourth an analog filter, and most or
all are realized in integrated circuitry.  Thus, for example, someone
familiar with digital filtering will usually focus on the first of the four
blocks, and when asked for more information will instinctively steer you
to the general digital-filter literature (which unfortunately is extremely
dilute on this subject).  In reality an oversampling C-R chain entails
intimate concert between all four blocks and between multiple technical
specialties -- none alone is sufficient to explain what is going on.

B. Interpolator

The first block, the sampling-rate-increasing digital filter, in an
oversampling C-R system is commonly nicknamed an "interpolator."  This
jargon is triply unfortunate.  First, almost everybody unfamiliar with
multirate digital filtering assumes from the name, incorrectly, that this
block performs "interpolation" in the common mathematical sense (such as
linear or polynomial interpolation between data points).  Actually the name
is a specialized digital-filtering coinage subtly but crucially different.
Second and third, as if that weren't trouble enough, the term
"interpolative" is sometimes applied in two further ways to oversampling
C-R systems (one of these usages is a subset of the other).  More details
about this and other glorious terminological pitfalls are in my recent AES
Journal paper.

Here is the briefest sketch of how the rate-increasing filter works.  The
objective is to convert a signal at a sampling rate like 44.1 ks/s to a
signal at a higher sampling rate *without* changing the information content.
Mathematically this is a well-defined and tractable problem.  If you just
take the original sequence of samples and insert after each of them, for
example, three new samples (with value zero, or holding the last old-sample
value, or almost anything else intelligent) then you will obtain a new
sequence at four times the original rate.  In frequency spectrum this new
sequence will however include new high-frequency replicas (images) of the
original signal's spectrum.  A digital lowpass filter will remove these
images and leave a signal spectrally identical to the original.  In the time
domain, you will now see a higher-rate sequence that will look like the
original but with the "right" new samples smoothly inserted between old.
(In actual practice the "insertion" of new samples is NOT a separate
step as above, but is incorporated into the digital-filter arithmetic.)

C. Multibit vs. single-bit vs. MASH etc.

All four of the major blocks of an oversampling C-R system, outlined in
Section A, admit endless variations, opportunities for design cleverness,
and high/low quality choices, and account for practical performance and
manufacturing-cost differences among CD players.  (All of which players,
incidentally, appear more or less indistinguishable in the rudimentary
and unrevealing standard specifications -- peak SNR, frequency response,
step response -- commonly published.)  A lot of fuss and advertising copy
are however devoted to one particular design difference, the organization
of the noise-shaping modulator (and consequently the format of the
internal DAC circuit(s)).  The common organizations are:

-- Multibit feedback noise shaping.  The modulator properly predistorts
(noise-shapes) the oversampled digital signal sent to a lower-resolution
multibit DAC so that when properly analog-postfiltered its output will
yield the full 16-bit resolution stored on the CD.  This is the oldest
scheme common in consumer products, widely popularized by the NV Philips
SAA 7030 / TDA 1540 chip set (1983) with a 14-bit internal DAC and 4:1
oversampling yielding 16-bit final resolution.  (For more details on how
4:1 relates to two additional bits, see either of my AES papers above.)

-- One-bit feedback noise shaping (called "Bitstream" by Philips and
"delta-sigma" by the research community [Note 1]).  Same as the previous
but taken to an extreme: the internal DAC has only one bit of resolution
and the 16-bit net D-to-A resolution is accomplished by the oversampling,
noise-shaping and postfiltering process.  This approach requires a higher
oversampling factor, such as 128 or 256, other things being equal.

-- Feedforward or multistage noise shaping (abbreviated "MASH" [Note 2] by
Nippon Telephone and Telegraph).  A series of small one-bit feedback noise
shapers, each of which operates on a quantization-error (residue) output
from the previous stage, while simultaneously the quantized outputs are
combined properly to form the main output.  "MASH" data converters are
definitely not "one-bit" data converters in a meaningful sense, as I've
explained in more depth in print, although they are commonly made up of
one-bit subsections and this sometimes causes confusion.

Each of these competing modulator topologies has technical strengths and
weaknesses that are very involved and do not lend themselves to summary.
The signal fidelity in each of them can be excellent but depends on
different sets of circuit elements.  It is all a matter of "second-order"
electrical effects; if the components are all perfect (as they invariably
are assumed to be, in popular explanations of this subject matter), then
all the techniques work equally well.  Very broadly, however, I would say
that the one-bit designs have the fewest subtle distortion vulnerabilities.

D. What does it mean for sound

The electrical specifications of an oversampling C-R system depend on
innumerable component values and design choices and are in no way simply
predictable from whether the internal modulator uses, for example, MASH or
Bitstream or some other topology.  Still less predictable are perceptual
fidelity measures, which of course are the ultimate figures of merit in
audio and other human-interface electronics (a point taken for granted not
only by musicians but also, of course, by competent engineering researchers
and by the graduate communication-theory texts, such as Jayant and Noll).

This does not, of course, prevent glib advertising copywriters and cult
audio pundits from directly linking this or that audible property to the
glamorous _au courant_ labels like MASH and delta-sigma (just as it is
thought very fashionable to talk about Fast Fourier Transforms, no matter
how ignorantly or irrelevantly, in stock-price analysis, or about chaos
theory in management -- I could go on and on, and I do).  Such writers
might even be right, but they almost certainly don't know it -- the audible
differences are much more likely due to the oblique dependence of the C-R
topology on other design choices in the player, or to the quality of
analog-digital ground isolation, or to the choice of output-filter op amps.

Notes from the text:

Note 1:  "Delta-sigma" modulation and data conversion (the inventors' term)
was unintentionally rechristened "sigma-delta" at the Bell Telephone
Laboratories in 1963 and this reversal has propagated through many paper
titles, so you will see both names in use.  No difference is intended.
I have made efforts to redress this reversal and the principals are now in
accord.  My recent JAES paper mentions this and I have further details if
anyone professionally interested sends a mailing address.

Note 2:  Some people dislike the acronym MASH for MultistAge noise SHaping,
though there certainly are endless well-known precedents (UNIted nations
ChildrEn's Fund; GEheime STAatsPOlizei).  When its coiners introduced "MASH"
in the US in 1986 a colleague remarked to me that MUSH was better on acronym
style.  I think however that MUSH would have less audio-marketing cachet.

The technique now dubbed "MASH" by NTT has existed in various forms since
long before its recent popularization by Toshio Hiyashi et al. in February
1986 (this origin itself is usually misattributed to a later paper by
Uchimura et al.).  I have antecedents going back at least to 1969. 
Multibit feedback noise shaping is even older, due to Cutler in 1954.

Max W. Hauser     {mips,philabs,pyramid}!prls!max     prls!max@mips.com

Copyright (c) 1991 by Max W. Hauser.  All rights reserved.

"In graduate school, books are called `Introduction to ...' while in high
school, they are called `All About ...'   This seminar is `All About'
high-speed vertical-amplifier design."     -- Einar Traa, Tektronix, 1978

(PS:  Experience with the Usenet compels the following cautions.  This 
summary is a terse sketch of a complicated and counterintuitive subject.
Abundant clarification and amplification of details is available to anyone
who will take the trouble to obtain and study the references cited at the
beginning, and if necessary take the further trouble to acquire, or else
discuss them with someone having, the technical background on which the
entire subject is built.  If you cannot be bothered to take these steps
then please do not ask me to do them for you.  Also, I regret that I cannot
offer audio-equipment recommendations.)