Is this how oversampling works?

With a 16 bit CD player DAC the analogue output updates every 1/44100 of a second. The output change may be a big step or it may be a small one. By comparison, if you have 256x oversampling, does that mean it uses a 24 bit D/A and every 1/44100 of a second a new data point (that has 16 bit resolution) is specified, and the DAC output then glides up or down to this new point in a 256 step staircase in 1/44100 second instead of just a single chunky jump as before?


It is common to think oversampling means that the laser reads the disc multiple times. It does not, the CD player only gets one shot at reading any part of the disc. Also the number of bits do not play a part in the basic oversampling concept.

Bits are an indication of the amplitude/voltage (or Y axis on an oscope), sampling is an indication of time/frequency (or the X axis on an oscope).

Oversampling is also sometimes called a "digital filter." That is a confusing term. When most people think of a "filter" is something that some how takes away or seperates things. Like a coffee filter. A digital filter (or over sampling) actually adds stuff.

The output of a DAC has little stair steps of voltages. These stair steps equate to high frequency noise that needs to be filtered out. When you oversample you are mathematically and artifically adding more stair steps in between each of the original stair steps. 4x oversampling will give you 3 new steps between each of the original steps. 256x oversampling will give you 255 new steps between each of the original steps.

Why go to the trouble? When you add these extra steps, the frequency you need to filter becomes higher than with no filter. Filters intrude on the frequencies that are closest to them. Also oversampling means that your filter does not have to be as steep. (as indB/octave) The farther away the filter frequency is away from the frequency you wish to keep, ther better off you are.

Oversampling makes desiging a good filter simpler and easier.

That is the basics of oversampling. I hope it helps some.



2002-01-18 11:12 am
Close, but not quite. Oversampling is only the process of making a DAC convert more samples per unit time than are available in the input stream. I.e. a twice oversampled 44.1k system would do 88.2k conversions per second, regardless of the actual value of the 'new' samples.

Now, in digital audio, we (almost) always equate oversampling with digital filtering: in the above example, the over/upsampler prior to the DAC chip contains a digital low-pass filter that cuts with high order at the *original* half sample frequency, i.e. 22kHz.

A result of this filter action is that the output waveform gets smoothed.

There still is a steep-order low-pass in the system, only now, by virtue of oversampling, we implemented it cheaply in the digital domain, as opposed to complex/expensive in the analogue domain.

Hope this helps.

Another advantage of the digital filter, apart from being cheap, is the fact that by using a FIR type filter, it can be made phase linear (i.e. it is only introducing a constant- and frequency-independant delay).
Also the analog output filter, that is still needed with oversampling, can be made with low order and high cutoff-frequency, which can be made cheap as well and does not introduce much phase-distortion either.


Yep, Werner is pretty much spot on. Oversampling is, as the word says, sampling more times than before. So if you oversample by 4, you are squeezing an extra 3 samples in the time interval between every two you already have giving you 176.4 kHz sampling frequency for CD audio.

The advantage is really economic. The speeds available in IC fabrication, particularly CMOS technologies, make large oversampling of audio signals pretty easy to manage. For example 256x oversampling of 44.1 kS/s (kSamples/second) is still only 11.3 MS/s which is well within the limits of most suitable technologies. Whereas to get increased accuracy by increasing the resolution is extremely difficult. The accuracy of a 16 bit converter needs to be greater than 0.25/65536 or 0.00038147% (using the standard spec. of 0.25 lsb). This is not trivial in any technology.

So basically designers trade off accuracy against speed, substituting the latter for the former and ending up with converters that have the same resolution but are easier and cheaper to make. The ultimate example of this is the 1-bit Delta-Sigma converter which will often run at 256x oversampling but with only 1 bit output, ie the output can only be +1 or -1 but there are so many samples that you still get 16-bit or greater resolution out of the system. Sounds weird but it works.



2002-01-18 11:12 am
I wouldn't name 256x oversampling with real 20kHz reconstrunction filtering manageable. The associated FIR filter would be rather excessinve in length, bringing with it a just as excessive number of multiplications to perform per second.

Those 256x and 384x delta-sigma DACs really just implement a Sinc-like lowpass at 8x oversampling, all other oversampling performed by linear interpolation of even sample-and-holds.

For those who get upset with the apparent time-smear in a FIRs impulse response (you know, the pre- and post-ringing): this is a close(ish) approximation of the ideal Sinc response, the reconstruction method prescribed by uncle Nyquist to retrieve the original signal. All other reconstructors (analogue low-pass, Wadia, Pioneer's Legato, ...) are mathematically wrong. Which of course doesn't say a word about their sound

Werner said:
I wouldn't name 256x oversampling with real 20kHz reconstrunction filtering manageable.

I was specifically referring to the clock speeds as being eminently manageable.

The associated FIR filter would be rather excessive in length, bringing with it a just as excessive number of multiplications to perform per second.

I'm not sure that I would completely agree with you here. You will definitely need to use large FIR filters to get sufficient stopband attenuation and to suppress the passband ripple sufficiently but you can exploit the symmetry of the filters and use multistage and polyphase architectures to make even very large filters manageable. Then there are things like CIC filters which don't use multipliers at all.

Those 256x and 384x delta-sigma DACs really just implement a Sinc-like lowpass at 8x oversampling, all other oversampling performed by linear interpolation of even sample-and-holds.

Again, I'm not sure I completely agree with this. There are plenty of examples of Delta-Sigma DAC's in the literature that use zero padding interpolation and filter the results to remove the images. Sample and hold itself is not necessarily trivial and has it's own issues that need to be dealt with. Many of the D-S filtering systems are using a combination of filtering such as FIR and sinc^k filters. At the end of the day, any of the D-S converters will need good filtering to deal with the large out of band noise, regardless of how you do your filtering.

Hi all

One has to be aware that there are basically two different possibilities for oversampling D/A conversion used within digital audio equipment.

The older one was the approach of using a FIR filter as interpolator/oversampler followed by a DAC whose resolution (bit-wise) is more or less the same as the interpolator's input signal. Some older Philips CD players used 14 bits, my old Philips player is using 4 times oversampling and 16 bit resolution.

The other approach is using the combination of noise-shaping and oversampling. Thats the principle of the delta-sigma DACs (and ADCs as well). The 1-bit DAC for instance is having a resolution of 6 dB only. By the use of noise shaping it's quantisation noise (i.e. the quantisation ERROR) is pushed into the upper range of the frequency spectrum while increasing the resolution at the lower end. Also DSD (the format of the SACD) is using the same approach as well as some switching audio amplifiers (Sharp and Tripath).
The noise shaping is performed with a multiple-feedback loop arrangement using integrators and summers which can be implemented with analog (for instance within a delta-sigma ADC or a switching amp) or digital (within a delta-sigma DAC) circuitry.

I wonder how many audiophiles that are very picky about NFB within their amps, listen to music from their CD player unaware that it is converted using NFB extensively !!!:D :D :D

More recent high-quality sigma-delta DACs are working with more than 1 bit of resolution. Don't forget that there exists no valid mathematical description for the 1-bit converter at all !
Additionally the coefficients of such a feedback arrangement are heavily dependant on the inputsignal applied :eek: .
One of the properties of music is that it's waveform isn't known a priori, at least not for the music I listen to (but I would of course never try to convince anybody not to listen to sinusoids of constant amplitude and frequency for hours).
So all of these noise-shaping loops are compromises in practice.
They are usually designed for a theroretical SNR that is some dozens of dBs higher than they will have in their real-world implementation.


Hi Rodd

I am not sure if I understood your question properly:
Is there any indication in the digital world that the fundamental sampling rate (44.1kHz) will be increased?

Are you asking whether oversampling will provide a means that reproduces a conventional CD as if it was originally recorded with a sampling rate of greater than 44.1 ksamples/s or do you want to know if the FUTURE will bring a format with a sampling rate greater than 44.1 ksamples/second ?

The answer to both is NO.

The first one because there is no additional information available than is actually stored on the CD. Oversampling however allows to get closer to the theoretical maximum performance the 16 bit - 44.1 ksamples/second system would allow.

The answer to the second one is no simply because they are ALREADY HERE !:)
DVD audio supports sampling rates as high as 196ksamples/second and a resolution of 24 bit !!!:cool:
SACD is also better than CD in this respect but it is more difficult to define it's upper cutoff frequency properly.




2002-01-19 9:25 am
Hi Charles,

Thanks for the reply.

Sorry for the vagueness. My question is about the high frequency capabilities of CD's. I like the 24 bit resolution.

Is 196kHz the base sampling rate?
If so, what is the Nyquist filter corner frequency for the SACD discs? Will it, for example, store and play back frequencies higher then 21kHz?

Rodd Yamas***a
Hi Rodd

I have to remark that I made a mistake: The highest sampling rate DVD-A uses isn't 196 ksamples/s but 192 ksamples/s giving a Nyqvist frequency of 92 kHz.
The system is quite flexible and will also support 92 ksamples/s, giving a Nyqvist frequency of 46 kHz, and some lower sampling rates as well.
That means that not all audio DVDs will be produced with the highest possible sampling rate and/or the best resolution, it will be left to the taste of the sound engineer(s) and the cost considerations of the producer but the system does at least support them all.

SACD will definitely go higher than 21 kHz of course, but the FR at the upper end will heavily depend on the reconstruction filter used. One (i.e. the developer) has to make a tradeoff between cutoff frequency and how much out-of-band noise he wants to allow.


phase_accurate said:


More recent high-quality sigma-delta DACs are working with more than 1 bit of resolution. Don't forget that there exists no valid mathematical description for the 1-bit converter at all !

I'm not sure I agree with this. There were gaps in the understanding but much work has been done in recent years. There are still issues with mathematical analysis of higher order D-S modulators, particularly in relation to stability criteria. Is this what you mean ? For lower order D-S modulators the maths is not that complex.

Additionally the coefficients of such a feedback arrangement are heavily dependant on the inputsignal applied :eek: .

I don't think I understand what you mean here. Are you refering to the fact that as a feedback system, what is fed back is the error signal and by definition that needs an input signal to define it, or are you refering to the fact that there must be a limiter in the loop to prevent the whole thing from saturating ?

They are usually designed for a theroretical SNR that is some dozens of dBs higher than they will have in their real-world implementation.

I might find myself disagreeing with you here again I'm afraid. In my experience it is possible to pretty accurately model the response you are going to get back from the fab. But then everything in engineering is a compromise. A good engineer just knows what the limits are that they have to work within.
What I really wanted to know...

What made me start thinking about oversampling is very simple; If I stick my ordinary, every day, 16-bit vanilla flavoured CD in my DVD player - an LG DVD-3000P, and just use the 2-channel RCA outputs on the back, will it's internal 24-bit DAC interpolate between 16 bit samples with a 256 step staircase or suchlike? Or in any case should it sound better than the normal low end CD player?

Simplifying a bit, the internal word length of a digital filter fed 16 bit words is 16 plus the word length of the filter coefficients, which typically shall be 16 bit or more. So you internally end up with 32 - meaningful - bits or even more. At the output filters tend to round this off to 20 or 24 bits, properly dithered. This is what feeds all those 20 bit and '24 bit' DACs in players.

Note the quotes.
Oooh, an LG. That's got my chip in it! err, well my company's chip anyway :D

Oversampling creates the missing samples using FIR filters, rather than just a simple linear interpolation or "staircase" like you refer to. FIR filters are better, because they gather information about the frequency content of the signal from many surrounding samples to effectively produce a very accurate "curve fitting" for the new samples it will generate between the original samples. In fact, while it's at it, the FIR filter is going to operate on the original samples too, so everything will end up at, say, 24 bits in the case of a filter which actually outputs 24bit samples (just cuz the DAC is 24 bits doesn't mean it's being fed 24 bit data!). If the DAC itself is doing the oversampling, then chances are very good that if it's a 24 bit DAC, it's filters will deliver 24 bit samples for output.

Anyway, oversampling is widely recognized as delivering superior sonic performance over non-oversampling DACs (though there are some people who would disagree). So, yes, you should get better sonic performance out of your 24bit oversampled DAC than some low-end solution.
D/A's Sound Different

Panasonic use their MASH oversampling arrangement.
Sony has their own 1 bit oversampling.
IME these oversampling arrangements can sound quite different.
In my understanding these feedback type digital filter stages allow tone control (noise shaping) of the error noise and this low level error noise characteristic adds a sonic flavour/character.
I have serviced and lived with Mash sound and I don't like it.
The Sony sound is easier on my ear, as are others.

Q - Can the filter algorithms be arranged to compensate for the characteristics of recording industry standard A/D convertors ?
I.E. - multiple programme presets to allow compensation of A/D convertors from differing eras and recording labels, and/or allow user control of the noise tonal characteristics, and subsequent audio influence ?.
Or is this a job for DSP ?

Regards, Eric.
Hi DocP

To avoid any confusion: The points where our opinions diverge a bit is the properties of the S-D MODULATOR.

About the mathematical description of the 1-bit converter: Could you determine the quantization step size or the gain of a 1 bit quantizer ?? It wouldn’t be a problem for a 4 bit qantizer for instance, would it ?
As far as I understand, it is this uncertainty plus the fact, that a 1-bit quantizer can be regarded as permanently overdriven, that leads to the stability problems for noise-shaping loops of order three or greater.

With the second point I am actually refering to the fact that a given loop design doesn’t have the same behaviour for any possible input signal level. The achievablemaximum input or output level is not even the same one for different input signal frequencies.

About the SNR issue: Why do they state a SNR of 120 dB at 100 kHz for SACD for instance, when a 7th or-der S-D loop with a sampling rate of 2.8224 MHz would allow a dynamic range of 172 dB approx @ 100 kHz ?

The latter one was calculated with this formula:

SNR [dB] = ( looporder * 6 + 3) * ld (0.5 * samplingfrequency / signalfrequency)

To be honest: I have never worked in the development of AD or DA converters but did some simulations with 1-bit switching amplifiers in mind. These behaved worse than old-fashioned PWM amplifiers in the simulations, but might probably perform better than the latter ones in a real world situation, because they could be less susceptible to transient ringing.


Hi Charles,

I think we are in danger of hijacking this thread and also disagreeing about nothing here. There is a bit of the "how many angels fit on the head of a pin" about this discussion.

As with all complex engineering systems, the modeling of it must make assumptions and as one of my old lecturers used to say, "Assumption is the mother of all ****-up's". In this case the biggest assumption is the modeling of the very non-linear quantiser as additive white noise. In most design work, the sort of formula you have quoted are really just a starting point for the design. It's the much more complex "real world" model that will give you a true idea of what you're going to get at the end of the day. All IC design is done this way, with simulation forming the basis of the design, rather than relying on mathematical rules of thumb.

On a final pedantic point, you say that the 1-bit converters can be considered to be perminanatly overdriven. I would have to disagree with this. The formula you quote (which is not quite the same as the one I am used to seeing but I'm sure it's just a variation on it) will be based on the assumption that it's not overdriven. If you do overdrive a modulator you get a lot of harmonic distortion generated, which is definitely not what you want.
A few months has passed since I started this thread, and just now I lifted the lid on my newer dvd player (not the LG)and took some measurements aroound the D/A while it was playing a cd. The D/A chip is a Cirrus Logic CS4334K
Pin 1 = serial data = 2,116,837 Hz = 44100 x 2 x 24.
Pin 2 = serial clock = same as pin 1
Pin 3 = left/right clock = 44100
Pin 4 = Mclk = 11,289,600 = =44100x256 (actual = 11,289,796)
Pins 5&6 = left & right out, you can see some 1,058,400 = 44100 x 24 sampling ripple.

Sooo... given that info, is the D/A working it's best to make good sound from the 16 bit source? It's sounds just fine, but it would sound *so* much better if I knew it was smoothing the 16 bit lumps with 24 bit polish. :)