On Nov 12, 7:16�pm, Robert Adams <robert.ad...@analog.com> wrote:> On Nov 12, 2:48�pm, John O'Flaherty <quias...@yeeha.com> wrote: > > > > > > > On Wed, 12 Nov 2008 11:13:54 -0800 (PST), HardySpicer > > > <gyansor...@gmail.com> wrote: > > >On Nov 13, 5:27 am, "lxx.helen" <lxx.he...@gmail.com> wrote: > > >> let's think of the noise shaping function for sigma-delta modulators. In > > >> frequency domain, we say quantization noise is pushed to higher frequency > > >> and then removed by lowpass filter. > > > >> what I wana do is to find a time domain understanding of this noise > > >> shaping function... > > > >> start from the white assumption of quantization noise. I can imagine this > > >> is because we assume the quantization error randomly distributed in the > > >> range from -delta/2 to delta/2. > > > >> Then after oversamping and negative feedback, what mechanism in time > > >> domain changes the noise's distribution? and what in time domain > > >> corresponds to the low/high probability of low/high frequency noise? > > > >> thank you very much~ > > > >Forget the time domain. I spend much of my time in the frequency > > >domain nowadays - much more peaceful and you can understand things > > >better. > > > I find that I frequent the time domain - it's much more eventful. > > -- > > John- Hide quoted text - > > > - Show quoted text - > > You can consider sigma-delta to be "waveform approximation" instead of > "sample approximation". If you have, say, a third-order feedback loop > then the first three integrals of the output bitstream will match the > first three integrals of the input waveform. > > Common misunderstanding; > > "If I am oversampling by 64X, then I just count the number of ones and > -1's in each 64-clock period and this is all the information that I > can get. So this is only a 6-bit system!" > > This is wrong. Firstly, the decimation filters used in these > converters are often thousands of taps long, so this means that- Hide quoted text - > > - Show quoted text -Sorry, hit the wrong button, continued here ... You can consider sigma-delta to be "waveform approximation" instead of "sample approximation". If you have, say, a third-order feedback loop then the first three integrals of the output bitstream will match the first three integrals of the input waveform. Common misunderstanding; "If I am oversampling by 64X, then I just count the number of ones and -1's in each 64-clock period and this is all the information that I can get. So this is only a 6-bit system!" This is wrong. Firstly, the decimation filters used in these converters are often thousands of taps long, so this means that EACH BIT CONTRIBUTES TO MANY OUTPUT SAMPLES. Secondly, THE ORDER OF THE BITS COUNT (A LOT). If you were only interested in the first integral, then it's true that the order would not matter too much, but once you go to higher order then there are complex correlations between all the bits and the order matters very much. So you need to analyze the error of these systems not in terms of single-sample input-to-output error, but rather in terms of waveform error between a discrete-time filtered version of the input, and the digitally-filtered version of the bit-stream (with the discrete-time filter matching the digital filter exactly); this way, you can start to think about the error waveform. However, note that since the filters have a lot of time dispersion, you can only talk about the RMS Waveform error, not an individual sample error. This is somewhat related to the concept of sub-radix-2 conversion; if you have a number system with a radix of less than two, than there are MANY ways that you can obtain an output value within a particular error tolerance. This means it is possible that a single bit can play a role in many different output samples; in some samples it will play a more "major" role than in others, depending on the alignment of the bit with that particular filter tap for that particular output time. Bob Adams