The king of all upsampling/oversampling questions...

[annex666]

I have been researching the use of upsampling/oversampling (not to state that they are the same, but are very similar) and I have come across a very interesting question.

I understand the theory behind the system - interpolate between real samples to create new samples at a higher sampling frequency (and almost always higher resolution), but can anyone tell me the system used to interpolate these new samples?

I have been toying with some ideas of my own, but fear they have already been used.

Are the new samples based on statistical functions from adjacent samples or, more complexly, on FFT analysis - windowing many adjacent samples and using the frequency content?

I would be intreagued to know what techniques are currently in use - I hope someone out there knows how the big guns do this.

[bocka]

Upsampling and oversampling is completely different in description.

Well, oversampling is well known and quite easy. Look at some given data maybe the output volate of a DAC

0.3, 0.7, 0.1, -0.9, ...

A non-os DAC will exactly hold the output voltage until the next sampling data comes. And now, we are spreading the time a little bit lets say 4 times:

0.3 0.3 0.3 0.3 0.7 0.7. 0.7 0.7 0.1 0.1 0.1 0.1 -0.9 -0.9 -0.9 -0.9

This is exactly the same as before only the time resolution in this example is 4 times higher so there are more numbers in.

The oversampling filter is very easy, it only takes the first samples and throw the next 3 ones away. Our oversampled data looks now like

0.3 0 0 0 0.7 0 0 0 0.1 0 0 0 -0.9 0 0 0

Unfortunately the energy of the is 4 the signal is 4-times lower as before, so multiply it with 4:

1.2 0 0 0 2.8 0 0 0 0.4 0 0 0 -3.6 0 0 0

Thats it, our oversampling filter is ready. Now you need only a simple low-pass filter, to get rid of the side-bands (they are mirrored at the sampling rate and if you have a 4-times oversampling filter the side bands are much more away). A simple FIR filter with about 100 taps is doing some mathematical filtering (only multiply, add and time shifting a little bit), the coefficents you can find nearly everywhere on the web and so you get rid of the zeros in our example and the high frequency pulses.

I think programming a DSP will take some hours (or days?) to implement this oversampling feature if you have the correct coefficents.

Upsampling is very much more complicated, it uses a (digital) PLL to syncronise two clocks, it filters data in much more behavior, and so on.

Look on the Analog Devices datasheed AD1896, there is a very simplified description (and this is over some pages...) of the theory. But upsamling as well as oversampling contains no FFT or statistical analysis.

[annex666]

Originally posted by bocka
...but upsamling as well as oversampling contains no FFT or statistical analysis. [/B]

Contains no FFT?

How does a digital low-pass filter work if not by FFT related techniques?


I'm confused

[ojg]

Originally posted by bocka

Upsampling is very much more complicated, it uses a (digital) PLL to syncronise two clocks, it filters data in much more behavior, and so on.

Not necessarily, what you are describing is asynchronous sample rate conversion where the incoming and outgoing sample rates are not synchronized, this is what the AD1896 does.

Upsampling is the correct term when the output sample rate is synchronous too (and usually an integer multiple of) the incoming sample rate, and in this case a simple FIR filter is sufficient as you showed in your example above.

To annex666: Here http://www.dspguide.com/ is a good free book that describes basic DSP without going into too much heavy math. Here you can read how to do FIR filters in the time-domain using convolution.

[Steve Eddy]

Originally posted by annex666
I understand the theory behind the system - interpolate between real samples to create new samples at a higher sampling frequency (and almost always higher resolution), but can anyone tell me the system used to interpolate these new samples?

How can you get any higher resolution?

se

[Peter Daniel]

You might check this link as well
http://www.sakurasystems.com/articles/Kusunoki.html

[ojg]

Originally posted by Steve Eddy

How can you get any higher resolution?

Well, the filter is usually executed on a processor with higher resolution (32bit) than that of the incoming signal (16bit), so the output signal will have more resolution and then dither can be applied to produce a final 24bit dithered signal.

However the SNR will not increase, it is limited by the input signal. So there is always this never-ending discussion about what the point is of increasing the bit-depth when the signal already is limited by the 16 bits on CD. Maybe this is what you had in mind?

Originally posted by Peter Daniel
You might check this link as well
http://www.sakurasystems.com/articles/Kusunoki.html

Thanks for the link Peter, I just read this paper and I don't know whether to laugh or cry. All I want to say is that I am always sceptical of technical papers coming from equipment makers. You have to think consider if the conclusion was reached first, and then the rest of the paper was written to back it up.

[Steve Eddy]

Originally posted by ojg
Well, the filter is usually executed on a processor with higher resolution (32bit) than that of the incoming signal (16bit), so the output signal will have more resolution and then dither can be applied to produce a final 24bit dithered signal.

I still don't see how you get any more resolution when the original signal has already been quantized at 16-bits. To me, more resolution implies more information. And you've already fixed the amount of information when you did the original 16-bit quantization.

However the SNR will not increase, it is limited by the input signal. So there is always this never-ending discussion about what the point is of increasing the bit-depth when the signal already is limited by the 16 bits on CD. Maybe this is what you had in mind?

Yes. Again, I fail to see how one achieves any greater resolution when the the resolution has already been established by the 16-bit quantization of the original signal.

se

[Peter Daniel]

Originally posted by ojg







Thanks for the link Peter, I just read this paper and I don't know whether to laugh or cry. All I want to say is that I am always sceptical of technical papers coming from equipment makers. You have to think consider if the conclusion was reached first, and then the rest of the paper was written to back it up.

Unfortunately I can't comment, because I didn't read it.

[rfbrw]

Originally posted by Steve Eddy


How can you get any higher resolution?

se

It goes something like this. For whatever reason a digital is required. A desired specification for said filter is laid down. From the desired specification flow the coefficients for the filter. These coefficients are unlikely to be nice round numbers, so in order to remain close to the calculated value, these coefficients need to be as long as is practically possible. Assume a bunch of cheapskates with a job lot of 16 bit DSP chips. This chip will implement the filter using its multipliers. If you multiply a x-bit number by a y-bit number you get a x+y-bit number. So the 16-bit input is multiplied the 16-bit coefficients and produces a 32bit result which is dithered down to 24 bits. The data has now been requantized and its resolution increased but the full scale value originally represented by 16-bits has not changed.It is analogous to going from a 30cm ruler to a 300mm ruler. They are both the same length but the later has finer increments or greater resolution.

ray