Oversampling DACs or interpolating DACs such as the delta-sigma DAC, use a pulse density conversion technique. The oversampling technique allows for the use of a lower resolution DAC internally. A simple 1-bit DAC is often chosen because the oversampled result is inherently linear. The DAC is driven with a pulse-density modulated signal, created with the use of a low-pass filter, step nonlinearity (the actual 1-bit DAC), and negative feedback loop, in a technique called delta-sigma modulation. This results in an effective high-pass filter acting on the quantization (signal processing) noise, thus steering this noise out of the low frequencies of interest into the megahertz frequencies of little interest, which is called noise shaping. The quantization noise at these high frequencies is removed or greatly attenuated by use of an analog low-pass filter at the output (sometimes a simple RC low-pass circuit is sufficient). Most very high resolution DACs (greater than 16 bits) are of this type due to its high linearity and low cost. Higher oversampling rates can relax the specifications of the output low-pass filter and enable further suppression of quantization noise. Speeds of greater than 100 thousand samples per second (for example, 192 kHz) and resolutions of 24 bits are attainable with delta-sigma DACs. A short comparison with pulse-width modulation shows that a 1-bit DAC with a simple first-order integrator would have to run at 3 THz (which is physically unrealizable) to achieve 24 meaningful bits of resolution, requiring a higher-order low-pass filter in the noise-shaping loop. A single integrator is a low-pass filter with a frequency response inversely proportional to frequency and using one such integrator in the noise-shaping loop is a first order delta-sigma modulator. Multiple higher order topologies (such as MASH) are used to achieve higher degrees of noise-shaping with a stable topology.

Upsampling is a step between the discrete signal and the conversion to a continuous (analog) signal. This is done by the reconstruction filter. This filter might be designed to handle a certain sampling rate as input and thus certain sample rates might need to be upsampled before being fed into it. Other than this I can see no benefit in adding an intermediary upsampling step, since the reconstruction already is a form of extreme upsampling (to a signal with and infinite amount of points).

I don't even know if these exist anymore, but if the DAC lacks a reconstruction filter then upsampling makes sense. The staircase like signal caused by the zero-order hold causes harmonics (above the Nyquist freq) which can be pushed to even higher frequencies by using a higher sampling rate. Not discussing the audibility of harmonics above 22KHz (nyquist of 44.1KHz file) this could alleviate the fear of these harmonics falling into a range where they affect the sound (an instrument's timbre is also defined by its harmonics).
If a simple filter is used that is nothing more than a low-pass filter. This filter might be designed to fit the harmonics of the highest input sampling rate the DAC can handle, anything lower than that will have to be upsampled for it to work.

Quote from: Propheticus on 2013-07-27 18:44:32

Upsampling is a step between the discrete signal and the conversion to a continuous (analog) signal. This is done by the reconstruction filter. This filter might be designed to handle a certain sampling rate as input and thus certain sample rates might need to be upsampled before being fed into it. Other than this I can see no benefit in adding an intermediary upsampling step, since the reconstruction already is a form of extreme upsampling (to a signal with and infinite amount of points).

So this is what I was eluding to above. In this case, you are saying that no matter the incoming sampling rate of the signal, the reconstruction filter works optimally at a set frequency and thus will clock it to whatever it needs (if I feed it 44.1, it will oversample to the reconstruction filter frequency automatically).

Is my understanding of your reply above correct?

Upsampling is a step between the discrete signal and the conversion to a continuous (analog) signal. This is done by the reconstruction filter. [...] Other than this I can see no benefit in adding an intermediary upsampling step, since the reconstruction already is a form of extreme upsampling (to a signal with and infinite amount of points).

For example, a 44.1 kHz D/A converter usually has a brick-wall filter with a transition band that begins at 20 kHz. An upsampling ratio of 22.05/20= 1.1025 will move this brick-wall filter upward to 22.05 kHz. 44.1 kHz x 1.1025 is 48.51 kHz. In other words 44.1 kHz should be upsampled to at least 48.51 kHz. If an upsampling ratio of 1.1025 is sufficient, 48 kHz should be upsampled to at least 52.8 kHz, and 96 kHz should be upsampled to at least 105.6 kHz.

The asynchronous upsampling attenuates jitter and their research showed that ICs (at least the ones they use, but generally most ICs perform worse at 192 kHz) have their peak performance around 96 kHz. The 110 kHz results from their filter design keeping the passband free of aliasing and this reasoning:

Isn't a brick-wall the theoretical ideal, and not something you can actually achieve easily?

Quote from: Propheticus on 2013-07-27 18:44:32

Upsampling is a step between the discrete signal and the conversion to a continuous (analog) signal. This is done by the reconstruction filter. [...] Other than this I can see no benefit in adding an intermediary upsampling step, since the reconstruction already is a form of extreme upsampling (to a signal with and infinite amount of points).

I was always suspecting this.
So I imagine that if the reconstruction filter is "not optimal" for a reason or an other there would be a benefit from upsampling first  from my player (using sox for instance) ? Does hardware handle upsampling as well as software solution like sox in general ?

Quote from: extrabigmehdi on 2013-07-27 21:05:26

Quote from: Propheticus on 2013-07-27 18:44:32

Upsampling is a step between the discrete signal and the conversion to a continuous (analog) signal. This is done by the reconstruction filter. [...] Other than this I can see no benefit in adding an intermediary upsampling step, since the reconstruction already is a form of extreme upsampling (to a signal with and infinite amount of points).

I was always suspecting this.
So I imagine that if the reconstruction filter is "not optimal" for a reason or an other there would be a benefit from upsampling first  from my player (using sox for instance) ? Does hardware handle upsampling as well as software solution like sox in general ?

The upsampling in this case is just zero stuffing+lowpass filter.  So 128x means take one sample of the input signal, then 127 samples that just zero.  Then 1 more sample of input, and so.  Then a DSP filter low passes at just below Nyquist and passes it though to the DAC itself. 

If theres something wrong with the DAC's filter, doing it yourself might help a little, but generally these things are so simple there is little room for error.

When you are talking about upsampling here, you are referring to the oversampling down by the recon filter, not during playback, correct?

Btw. for the record, I am also under the belief that there is a lot of value in oversampling during ADC to make aliasing less of an issue during reconstruction via DAC (I have got more samples in the recorded signal which means less aliasing products, correct?).

Quote from: pisymbol on 2013-07-27 22:44:50

When you are talking about upsampling here, you are referring to the oversampling down by the recon filter, not during playback, correct?

Correct.

Quote from: pisymbol on 2013-07-27 22:44:50

Btw. for the record, I am also under the belief that there is a lot of value in oversampling during ADC to make aliasing less of an issue during reconstruction via DAC (I have got more samples in the recorded signal which means less aliasing products, correct?).

I don't think it really matters what you believe here.  Virtually all devices are oversampling and have been for a very long time.  Regardless of what you like you'll probably end up with oversampling.

You are talking about during sample-and-hold of the ADC I believe.

Quote from: pisymbol on 2013-07-27 23:03:21

You are talking about during sample-and-hold of the ADC I believe.

Sample-and-hold is something that is used with successive approximation (SAR) ADCs. Sigma delta ADCs don't need or use it.

I don't even know if these exist anymore, but if the DAC lacks a reconstruction filter then upsampling makes sense.

The upsampling in this case is just zero stuffing+lowpass filter.  So 128x means take one sample of the input signal, then 127 samples that just zero.  Then 1 more sample of input, and so.  Then a DSP filter low passes at just below Nyquist and passes it though to the DAC itself.

Quote from: saratoga on 2013-07-27 22:16:05

The upsampling in this case is just zero stuffing+lowpass filter.  So 128x means take one sample of the input signal, then 127 samples that just zero.  Then 1 more sample of input, and so.  Then a DSP filter low passes at just below Nyquist and passes it though to the DAC itself.

I've been thinking that it would more logical to repeat values rather than zero stuffing.

Also I thought why  sox or else would not use some interpolation method like lanczos , just like it's done for pics.

So I guess my question is, are they any added *TECHNICAL* (not necessarily audible) benefits for software or hardware to upsample a signal today during playback with respect to filtering requirements and/or less overall jitter impact on the signal?

Quote from: pisymbol on 2013-07-27 17:24:58

So I guess my question is, are they any added *TECHNICAL* (not necessarily audible) benefits for software or hardware to upsample a signal today during playback with respect to filtering requirements and/or less overall jitter impact on the signal?

It's possible to use a technically better upsampling filter in software than you'll find in the DAC itself, so of course the answer is yes.

It is not that difficult to get so close a perfect brick wall filter that the result is indistinguishable from a perfect brick wall filter, if that is what you want to do. No DAC is going to bother to do this.

It is pointless since it'll sound the same as something that isn't as close to a brick wall filter. Also, where the different filters are audible (generally a lot lower than 20kHz) something gentler than a brick wall filter is to be preferred (less ringing). This can and has been verified in the real world using lower sample rates where the differences are easily audible.

With brick wall filters especially, the phase is important...
http://www.hydrogenaudio.org/forums/index....showtopic=68524
...though there are only two positive ABX results for it being audible at 20kHz (i.e. when upsampling CD quality audio) in that thread. It's easily audible when the transition band is within the normal range of human hearing (i.e. well below 20kHz) but that's never true when oversampling decent quality audio.

Quote from: extrabigmehdi on 2013-07-29 01:16:53

've been thinking that it would more logical to repeat values rather than zero stuffing.

You can, but zeros work better.

The fact that practical digital-to-analog converters (DAC) do not output a sequence of dirac impulses, xs(t) (that, if ideally low-pass filtered, would result in the unique underlying bandlimited signal before sampling), but instead output a sequence of rectangular pulses, xZOH(t) (a piecewise constant function), means that there is an inherent effect of the ZOH on the effective frequency response of the DAC, resulting in a mild roll-off of gain at the higher frequencies (a 3.9224 dB loss at the Nyquist frequency, corresponding to a gain of sinc(1/2) = 2/?). This droop is a consequence of the hold property of a conventional DAC, and is not due to the sample and hold that might precede a conventional analog-to-digital converter (ADC).

Isn't a brick-wall the theoretical ideal, and not something you can actually achieve easily?