non-understanding oversampling

[Bernhard]

Hi,

oversampling produces inbetween values.

Playing a 20kHz CD gives 9 stairs for a 4x os dac and 18 stairs for a 8x os dac.
Non-os has only 2,25 stairs.

Are those interpolated inbetween values absolutely correct ?

[Charles Hansen]

The interpolated values are "absolutely correct" if three things are true:

1) The input signal is a steady-state sine wave.

2) The combined reconstruction filter (analog + digital) is a perfect brickwall filter.

3) Any digital filtering is carried out to the degree of precision sufficient to satisfy your abitrary definition of "absolutely correct".

[poobah]

Bernhard,

Oversampling is done to relieve filtering requirements... digital processing is cheaper than analog filtering. Samples from a linear interpolation are not "perfect" but they don't need to be.

You can make them "perfect" through more (a LOT more) digital processing, fitting a curve over 4 points or more to derive your "stairs". It is a balancing with diminishing returns though. This is a MASSIVE increase in computing for a dmall decrease in filtering.

[Francis_Vaughan]

You also need to define "perfect". It is a slippery issue. If you define perfect to be samples that introduce no new energy into the audio band (or at least any energy is less than the noise floor) then the answer is most likely - yes.

[Bernhard]

thanks,

so a digital filter does not just do linear interpolation but something better ?

Obviously linear interpolation introduces errors to a sine wave, linearity errors increase with decreasing nr. of samples per full wave.

I just tested a Yamaha CDX-1110 which claims to have 18bit but only uses one 16bit PCM56 per channel.
It has HiBit and there is a chip marked dith ( = dither ) on the pcb.

Noise floor is very good, goes down to -70dB with -60dB signal, which is a few dBs better than other players.
Distortion is also very low with preselected chips but not better than in other players.
Just because of lower noise floor it is better visible so this will be my new player for PCM56 selection.

Still have to recheck those two chips in another player to make sure spectrum is the same.

[davidsrsb]

The early 14 bit DACs from Philips used linear interpolation. Modern chips use DSP IIR filtering to compute internediate values as 44.1 KS/s reconstruction of a 20KHz sinewave would become triangular with simple linear interpolation

[TDA1540]

The early 14 bit DACs from Philips used linear interpolation

?????????

[Francis_Vaughan]

It is very very unlikely any chipset ever did linear interpolation. This stuff is much older than digital audio - people knew what they were doing right at the start - although more than a few others didn't listen.

[ash_dac]

Originally posted by Francis_Vaughan
It is very very unlikely any chipset ever did linear interpolation. This stuff is much older than digital audio - people knew what they were doing right at the start - although more than a few others didn't listen.

Didn't they chuck in a load of zero's instead of intepolating ?


Cheers,

Ashley.

[Charles Hansen]

Originally posted by Bernhard
so a digital filter does not just do linear interpolation but something better ?

Pretty much all digital oversampling filters used for audio calculate the intermediate points in the following manner:

a) The desired number of intermediate points are created by inserting values of zero.

b) The resulting data stream is sent to a low-pass digital filter which is a fancy way of averaging the data points. If you think about it, you will realize that going from a finite value at one (original) sample to zero at the next (inserted) sample represents a very rapid (high-frequency) change. Going through the low-pass filter will lower the value original data points (as they are averaged with zeros) and increase the value of the inserted zeros (as they are averaged with the non-zero signal). If a brickwall filter is used, the new (interpolated) data points will exactly reconstruct the original steady-state signal.

NB! - This is no different (in the amplitude domain) than if a brickwall analog filter had been used. In either case the original steady-state signal will be exactly reconstructed.

Averaging two adjacent data points would be linear interpolation, and would give a very gradual frequency response rolloff. Creating a brickwall filter would require averaging an infinite number of samples. Most audio filters average around 100 data points (give or take a factor of two) and area a very good approximation to a brickwall filter.

c) The data is renormalized to the correct amplitude. This needs to be done because if you average the original signal with zeros, the result is lower than the original value.