You can calculate the theoretical value of the average noise, but not the actual value for a particular sample.Can quantisation error ever be determined per sample of the quantised signal?
You are right, because even if it were to be possible to determine quantisation error per sample, it would take an infinite number of bits in the fractional part to completely elimimate it.It is not possible to completely eliminate quantization errors.
Please kindly state the major reason why it cannot be determined per sample.You can calculate the theoretical value of the average noise, but not the actual value for a particular sample.
Averaging samples can reduce the error but not eliminate it.
I'd like to start off with ADC and DAC which should be easy to consider. I would prefer the fixed-point representation.Hi,
are you talking about ADC / DAC?
Or generally in digital signal processing? what data format?
Klaus
Because it's an unknown depending upon the accuracy of the converter at that particular sample.Please kindly state the major reason why it cannot be determined per sample.
Quantisation noise is inherent and you can only reduce it by either having extra bits or oversampling of a bandlimited signal. As to measuring quantisation error per sample... what for?Hi,
Can quantisation error ever be determined per sample of the quantised signal? Viewing quantisation noise as random noise does not seem to truly solve the problem with quantisation noise.
All responses are welcome , please.
If you oversample, that automatically results to additional bits. That is in line with the theory of the day. My aim is to reduce quantisation noise without increasing bit resolution or by even decreasing bit resolution, which is what the sigma-delta modulator does.Quantisation noise is inherent and you can only reduce it by either having extra bits or oversampling of a bandlimited signal. As to measuring quantisation error per sample... what for?
This informs the use of the probability density function and random noise to tackle it. But that is a blackbox approach.Quantization errors if perfectly linear will always be 1/2 of the quanta level maximum but could be near 0. It is always measured over a number of bits either as Mean Squared Error or SNR..
True! However, sigma-delta modulators have limitations as to how much they can improve the SQNR. I understand that the sigma-delta modulator shapes quantisation noise by modulation, but they are designed by some kind of blackbox approach. I believe I can achieve more if I can follow an approach that is not blackbox based.Sigma Delta quantization technique offers smaller errors with better linearity.
I am interested in this. Please suggest articles or other documentation I can look at.There are also other methods of sampling using tertiary encoding with redundancy to reduce quantization errors are UHF speeds.
Sure, it is an unknown at this time. I don't know how many people believe with me that it can be known. Finding a way to get it known is my primary target right now.Because it's an unknown depending upon the accuracy of the converter at that particular sample.
I would say very few besides yourself believe that, so it seems like a waste of time to explore this further, but it's your time to have fun.Sure, it is an unknown at this time. I don't know how many people believe with me that it can be known. Finding a way to get it known is my primary target right now.
Tricks like sigma-delta modulation start with a sample (charge, current) and apply multiple steps to create a number.If you oversample, that automatically results to additional bits. That is in line with the theory of the day. My aim is to reduce quantisation noise without increasing bit resolution or by even decreasing bit resolution, which is what the sigma-delta modulator does.
...
Sure, it is an unknown at this time. I don't know how many people believe with me that it can be known. Finding a way to get it known is my primary target right now.
I know errors due to differential and integral nonlinearities exist. But I'd like to set those to zero for the purpose of what I am doing.Hi,
so basically there is quantisation noise in ADC and DAC systems.
* The quantisation error ideally is +/- 0.5 LSB.
* there is an additional error by DNL
* and nonlinearities
Now quantisation noise is the frequency spectrum caused by quantisation error over a number over of consecutive samples.
This noise also depends on the true input signal.
Example:
A 12 bit ADC surely has quantisation errors. But when it samples a rather low noise DC signal, there is a good chance that the digital value is constant for let´s say a period of 256 samples.
So now if you perform an FFT over these 256 samples you get a signal at the first bin (DC) but no siganl at all other bins. So no noise at all.
If you do the same on slowly rising (triangle signal) low noise signal you get a clean staircase on the digital side ... maybe with many samples being the same value, followed by several samples with the next higher digital value.
So in the FFT you will see the DC, then (in best case) no noise until the fundamental (digital_value_rise) frequency .. and then agaon nothing than the overtones of the fundamental.
If the input is a clean sine, then I expect DC, the sine as fundamental and overtones to the sine.
This all was for ideal ADC.
On a real ADC you have DNL and nonlinearitiies.
If you do the same tests as above .. you get almost identical FFT results but with increased noise floor.
**
So my answer how to decrease quantisation noise is: (while not increasing bit number, non oversampling, no post noise filtering)
* reduce DNL
* improve linearity
* reduce input frequency (often not possible)
* reduce input signal amplitude (often not possible)
* Or increase input signal amplitude if you want to decrease: signal / quantisation_noise ratio
Klaus
Don't agree about blackbox approach. There's a detailed theory behind delta-sigma modulators.I understand that the sigma-delta modulator shapes quantisation noise by modulation, but they are designed by some kind of blackbox approach. I believe I can achieve more if I can follow an approach that is not blackbox based.
Yes, I agree that the sigma-delta modulator applies multiple steps to create a number. With the digital sigma-delta modulator, the signal is upsampled to a higher frequency and then interpolated. Then it is quantized to a much lower bit resolution and sampling frequency by downsampling. With feedback, the sigma-delta modulator modulates (i.e. uses multiple step to creat a number, just like you pointed out) at the oversampled frequency. When this numbers are further filtered, we get the noise-shaped signal.Tricks like sigma-delta modulation start with a sample (charge, current) and apply multiple steps to create a number.
The sample, of course, is quantized (has a number of electrons captured on a capacitor, for instance); that is already
a statistically variable quantity, since you cannot capture half an electron.
Thermodynamics means that voltages, currents, and power measurements are always varying. No amount of postprocessing
of a sample will exceed thermal noise limitations on voltages any more than it will exceed quantization limitations on charge.
"Theory of the day" is actually a century or so of theoretical development that is not susceptible to simple suspicions; only
a novel noncompliant observation would challenge those theories.
Yes, there is a detailed theory behind sigma-delta modulators. However, there is a limit to what SQNR can be achieved. One can't just say I want to design for a SQNR of 300 dB (just to mention a number) and proceed to achieve it, no matter how hard the person tries.Don't agree about blackbox approach. There's a detailed theory behind delta-sigma modulators.
I agree.One can't just say I want to design for a SQNR of 300 dB (just to mention a number) and proceed to achieve it, no matter how hard the person tries.
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