In D/A conversion, is sample-and-hold necessary?

Vladimir Vassilevsky wrote:
> 
> 
> robert bristow-johnson wrote:
> 
>> On Jul 23, 1:49 pm, Vladimir Vassilevsky <nos...@nowhere.com>
>> wrote:
>> 
>>> There is a DSD audio format which is essentially a pulse density 
>>> modulated signal. There is no sample-hold there.
> 
> Isn't DSD the direct analog to PDM conversion? BTW, I have never seen
> the DSD in the reality. Do you actually use it?
> 
> 

If you have a music recording on SACD, you are using it. How important
it is depends on (a) whether you believe SACD has a long-term (or even
medium-term) future, and (b) which side you are on in the ongoing 
AES-hosted debate over the merits or otherwise of DSD v standard 
over-sampled(etc) PCM encoding. See e.g. refs at the bottom of:
http://en.wikipedia.org/wiki/Direct_Stream_Digital


Richard Dobson

On Jul 24, 3:06=A0am, "m26k9" <maduranga.liyan...@gmail.com> wrote:
> Thank you very much Robert, Steve.

yer welcome, FWIW.

> Actually I do have a impulse train of samples.

really, you actually *physically* have actual dirac delta functions
happening?

this i would like to see.  (perhaps you can get a Nobel prize in
physics for being able to synthesize actual dirac impulses.)

> I am doing the DAC on on an
> IFFT output. So the digital samples are already there.

you have digital samples.  that i can believe.  is that the same as
having attached those digital samples to dirac impulses in the real
(analog) world?

> Does that mean I do
> not need a S/H and do a LPF directly?

in the practical use of DACs, sometimes S/H circuits are used to
deglitch the output (my very first published paper some 2 decades ago
was about that), but the concept of the S/H here in this discussion is
*hypothetical*.  it is to *model* mathematically (and not just any
mathematics, but the mathematics of Linear, Time-Iinvariant systems
and the particular LTI we're referring to is called the Zero-Order
Hold or ZOH) how the output of a D/A looks exactly like the output of
this fictitious ZOH when driven by a fictitious string of dirac
impulses.  that's the whole purpose of this.

> But, even if I do not have a pulse train, I can do sampling on my analog
> signal, get the digital samples, send it through a LPF and it will
> construct an analog signal? would it not?

i presume you mean an LPF in the analog domain.  a filter with a gain
near to dimensionless 1 in the passband and near to 0 in the stopband,
right?

> I am a little confused still as to why I need to do S/H before LPF, as
> oppose to just LPF?
>
> Thank you and I am sorry if I am missing a a trivial point.

the point that you're missing is what is *hypothetical* or
*fictitious* or a *mathematical model* vs. what is real and physical.
you have to get that straight first.

r b-j

On Jul 24, 9:41=A0am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> robert bristow-johnson wrote:
> > On Jul 23, 1:49 pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
>
> >>There is a DSD audio format which is essentially a pulse density
> >>modulated signal. There is no sample-hold there.
>
> Isn't DSD the direct analog to PDM conversion?

i dunno.

> BTW, I have never seen the DSD in the reality.
> Do you actually use it?

no.  i've been sorta a detractor of DSD as using more bits per sample
than good ol' PCM with 32 bit words.  but i tread lightly with that
opinion, especially at AES conventions, lest they hang me up by my
balls.

my only point (besides playfully hoisting you by your own pitard) is
that, even if the oversampling ratio is 64 or 128 (or whatever), so
the sampling rate for this DSD is say 3 or 6 MHz, physically, for
those 160 or 320 nanoseconds, the voltage is still held at a constant
value (i don't think the are spiking it and returning back to zero
between each sample) of either +1 or -1 (pick your units).  that is
still a ZOH, there is still a sinc() function in the frequency
response, even though that sinc() function has little effect below 20
kHz (the zeros of the sinc() function are at integer multiples of Fs,
except for 0).

r b-j

robert bristow-johnson wrote:
> On Jul 24, 9:41 am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:

>>
>>Isn't DSD the direct analog to PDM conversion?
> 
> i dunno.
> 
> 
>>BTW, I have never seen the DSD in the reality.
>>Do you actually use it?
> 
> no.  i've been sorta a detractor of DSD as using more bits per sample
> than good ol' PCM with 32 bit words.  but i tread lightly with that
> opinion, especially at AES conventions, lest they hang me up by my
> balls.

IMO it could make sense to keep the audio in the PWM format with the low 
rate (say, 96kHz). So the PWM specific distortion can be corrected 
offline; the signal could be fed directly into the output stage. The 
volume can be adjusted by changing the supply voltage; the feedbackless 
class D needs the regulated rails anyway.

> my only point (besides playfully hoisting you by your own pitard) is
> that, even if the oversampling ratio is 64 or 128 (or whatever), so
> the sampling rate for this DSD is say 3 or 6 MHz, physically, for
> those 160 or 320 nanoseconds, the voltage is still held at a constant
> value (i don't think the are spiking it and returning back to zero
> between each sample) of either +1 or -1 (pick your units).  that is
> still a ZOH, there is still a sinc() function in the frequency
> response, even though that sinc() function has little effect below 20
> kHz (the zeros of the sinc() function are at integer multiples of Fs,
> except for 0).

With PDM or PWM, although sampled at a fixed rate, math is not so simple 
since the pulse positions could be different within the sampling interval.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Jul 24, 2:42=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> robert bristow-johnson wrote:
...
> >  even if the oversampling ratio is 64 or 128 (or whatever), so
> > the sampling rate for this DSD is say 3 or 6 MHz, physically, for
> > those 160 or 320 nanoseconds, the voltage is still held at a constant
> > value (i don't think the are spiking it and returning back to zero
> > between each sample) of either +1 or -1 (pick your units). =A0that is
> > still a ZOH, there is still a sinc() function in the frequency
> > response, even though that sinc() function has little effect below 20
> > kHz (the zeros of the sinc() function are at integer multiples of Fs,
> > except for 0).
>
> With PDM or PWM, although sampled at a fixed rate, math is not so simple
> since the pulse positions could be different within the sampling interval=
.

AFAIK, the math behind DSD is the same math behind sigma-delta
modulators.  there can be many different PCM to DSD conversion
schemes; they would differ in computational cost and complexity and in
audio quality.  but the demodulation scheme (DSD to PCM) is the same,
no matter how they were created.

   PCM =3D downsample{ LPF{ DSD  }   }

if the bits of DSD are a[n], then the signal that gets LPFed is (-1)^a
[n] (just like with MLS).

r b-j