solderdude
Grand Contributor
Yep... but its the only reason I can think of to get a beneficial effect from upsampling... to bypass a poor reconstruction filter, or the total lack of one, and kind of 'fix' that DAC.
So, you don't understand the sampling theorem in other words...
Shannon Nyquist is not interpolation. It is exact reconstruction.
I understand that you can oversample and digitally interpolate to be able to use a simpler analogue reconstruction filter. This is not what I am getting at.. but likewise we, in a world not bound by the laws of causality, we use Whittaker-shannon interpolation to interpolate all missing values with the help of a sinc function. This is what reconstronction is, it is interpolation. Practically, it can be made good enough to be called a perfect reconstruction for the use cases we are interrested in here, but it is still interpolation.When upsampling there is always interpolation in order to get simpler post filtering and exact reconstruction.
When not upsampling and using a very steep analog filter (only 1st gen CDP) there is no interpolation but exact reconstruction.
Of course, not all filters are created equal and 'perfect' does not exist. Good enough does.
No see, here is where I do not agree. The interpolation is still happening, but in the analog electronics.The first gen (non Philips) CDP did not have any interpolation as there was no upsampling, instead this was done with a steep analog filter.
These were the ONLY DAC circuits (and DSD) that do not use interpolation.
A brick wall filter is a an ideal low pass filter. In the time domain that is a sinc function. The convolution of each discrete sample with the sinc will give you the values inbetween the samples. It is interpolation. This interpolation type even has it's own name and it's the Whittaker-Shannon's interpolation formula. You had only discrete data before, after you have data for all times in between these samples because you have interpolated those values. In this case with the help of a low pass filter.No that is simple low pass filtering.
Interpolation is calculating expected values between samples.
There is no calculation present in an analog filter.
The analog low pass filter operates in continuous time, therefore it does not "interpolate" as such. Its input "data" is continuous analog, in this case usually the output of a zero-order hold function of the sample values.In this case with the help of a low pass filter.
Yes, exactly. I mean, there are many different ways, but what we always try to achieve is to get as close to the sinc/brickwall interpolation as possible. Mathematically, in the end.A brickwall filter can also be done analog. It just means it is a steep filter.
It is easier to make it digitally and also more flexible (easy to shift the frequency).
There are many different ways to calculate the inbetween samples, hence the different filter types that exist.
Well it is made in two steps. First typically zero order hold or similar, then low pass filtering. Combined they are an approximation of sinc interpolation.The analog low pass filter operates in continuous time, therefore it does not "interpolate" as such. It's input data is analog, in this case usually the output of a zero-order hold of the sample values
In practice there are a few types filters one can select in a physical DAC. Some are not even close to ideal and are made that way on purpose.Yes, exactly. I mean, there are many different ways, but what we always try to achieve is to get as close to the sinc/brickwall interpolation as possible. Mathematically, in the end.
Not quite, as the analog low-pass is not linear-phase and thus the impulse response is not symmetrical.Well it is made in two steps. First typically zero order hold or similar, then low pass filtering. Combined they are an approximation of sinc interpolation.
Yes, a limit of practical implementation.Not quite, as the analog low-pass is not linear-phase and thus the impulse response is not symmetrical.
Impulse. One sample.Not quite, as the analog low-pass is not linear-phase and thus the impulse response is not symmetrical.
Seems like we are convergingIn practice there are a few types filters one can select in a physical DAC. Some are not even close to ideal and are made that way on purpose.
They all use interpolation but differ.
I tend to consider slow rolloff filters the "screw this, let's just have software upsampling do the heavy lifting and make sure the passband is fine" option.In practice there are a few types filters one can select in a physical DAC. Some are not even close to ideal and are made that way on purpose.
And not strictly just a limit either. While IIR filters exhibit group delay variation, their typical in-band group delay tends to be a lot lower than for an equivalent FIR filter (e.g. 19/fs --> 5/fs), which is why digital implementations have become fairly popular as a low-latency option now that computational accuracy tends to be high enough to eliminate the accumulated rounding error issues potentially associated with feedback-based filters. Their absence of pre-echo also means that periodic passband ripple is only associated with post-echo, which is masked far more easily, making substantially higher levels benign.Yes, a limit of practical implementation.