Hello! Are there theoretical considerations on how much information can be packed into a bitstream signal? If the bitstream is a serially transmitted PCM-signal, then it�s clear. But can this be topped by a 1- bit delta-sigma signal (independent from known noise-shaping methods)? Oliver
limits of bitstream coding
Started by ●February 27, 2008
Reply by ●February 27, 20082008-02-27
Oliver Glassl <oliver.glassl@t-online.de> writes:> Hello! > > Are there theoretical considerations on how much information can be > packed into a bitstream signal? If the bitstream is a serially > transmitted PCM-signal, then it�s clear. But can this be topped by a 1- > bit delta-sigma signal (independent from known noise-shaping methods)? > > > OliverHi Oliver, I'm not sure what you mean by the terms "bitstream signal" and "serially transmitted PCM-signal." Shannon's well-known capacity theorem gives an upper bound on the information capacity of a signal based on the SNR and bandwidth, but without understanding your terms, I don't know if this realy addresses your questions. Also, a delta-sigma signal by definition involves noise-shaping - that is what a delta-sigma modulator does. So your last question contains an apparent contradiction and, again, I'm not certain what it is you're asking. -- % Randy Yates % "With time with what you've learned, %% Fuquay-Varina, NC % they'll kiss the ground you walk %%% 919-577-9882 % upon." %%%% <yates@ieee.org> % '21st Century Man', *Time*, ELO http://www.digitalsignallabs.com
Reply by ●February 27, 20082008-02-27
On 27 Feb., 10:05, Randy Yates <ya...@ieee.org> wrote:> Oliver Glassl <oliver.gla...@t-online.de> writes: > > Hello! > > > Are there theoretical considerations on how much information can be > > packed into a bitstream signal? If the bitstream is a serially > > transmitted PCM-signal, then it�s clear. But can this be topped by a 1- > > bit delta-sigma signal (independent from known noise-shaping methods)? > > > Oliver > > Hi Oliver, > > I'm not sure what you mean by the terms "bitstream signal" and "serially > transmitted PCM-signal." > > Shannon's well-known capacity theorem gives an upper bound on the > information capacity of a signal based on the SNR and bandwidth, but > without understanding your terms, I don't know if this realy addresses > your questions. > > Also, a delta-sigma signal by definition involves noise-shaping - that > is what a delta-sigma modulator does. So your last question contains an > apparent contradiction and, again, I'm not certain what it is you're asking.I mean the comparison of a PCM signal and a 1-bit delta-sigma signal with the same data rate. And at least all noise-shaping methods I know employ feedback loops containing integrators, the highest order I know about that provides good stability is order seven. Easily implemented, even analog, low calculation cost if done digitally. I wanted to explore the limits with a method that is way too complicated to be done in realtime, but if it is already done theoretically, my plan is obsolete, of course.
Reply by ●February 27, 20082008-02-27
Oliver Glassl <oliver.glassl@t-online.de> writes:> On 27 Feb., 10:05, Randy Yates <ya...@ieee.org> wrote: >> Oliver Glassl <oliver.gla...@t-online.de> writes: >> > Hello! >> >> > Are there theoretical considerations on how much information can be >> > packed into a bitstream signal? If the bitstream is a serially >> > transmitted PCM-signal, then it�s clear. But can this be topped by a 1- >> > bit delta-sigma signal (independent from known noise-shaping methods)? >> >> > Oliver >> >> Hi Oliver, >> >> I'm not sure what you mean by the terms "bitstream signal" and "serially >> transmitted PCM-signal." >> >> Shannon's well-known capacity theorem gives an upper bound on the >> information capacity of a signal based on the SNR and bandwidth, but >> without understanding your terms, I don't know if this realy addresses >> your questions. >> >> Also, a delta-sigma signal by definition involves noise-shaping - that >> is what a delta-sigma modulator does. So your last question contains an >> apparent contradiction and, again, I'm not certain what it is you're asking. > > > > I mean the comparison of a PCM signal and a 1-bit delta-sigma signal > with the same data rate.So you want to compare a linear, N-bit PCM signal at Fs N-bit samples per second with a 1-bit delta sigma signal at Fs bits per second? If so, then you're comparing apples to oranges. A linear PCM signal at Fs samples per second always has a bandwidth of Fs/2 Hz; a 1-bit delta sigma signal at Fs bits per second always has a bandwidth << Fs/2 Hz. -- % Randy Yates % "Maybe one day I'll feel her cold embrace, %% Fuquay-Varina, NC % and kiss her interface, %%% 919-577-9882 % til then, I'll leave her alone." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
Reply by ●February 27, 20082008-02-27
> If so, then you're comparing apples to oranges. A linear PCM signal at > Fs samples per second always has a bandwidth of Fs/2 Hz; a 1-bit delta > sigma signal at Fs bits per second always has a bandwidth << Fs/2 Hz.So can you tell me the bandwidth of the highest theoretically possible order noise shaping 1-bit delta-sigma signal without stability problems, including all unknown noise shaping methods?
Reply by ●February 27, 20082008-02-27
Oliver Glassl <oliver.glassl@t-online.de> writes:>> If so, then you're comparing apples to oranges. A linear PCM signal at >> Fs samples per second always has a bandwidth of Fs/2 Hz; a 1-bit delta >> sigma signal at Fs bits per second always has a bandwidth << Fs/2 Hz. > > > So can you tell me the bandwidth of the highest theoretically possible > order noise shaping 1-bit delta-sigma signal without stability > problems, including all unknown noise shaping methods?Hi Oliver, The bandwidth of a delta sigma converter running at an oversampling rate of M*Fs is Fs / 2. You trade off oversampling rate for dynamic range. Perhaps Figure 9 in the following presentation on delta sigma converters will help: http://www.digitalsignallabs.com/presentation.pdf -- % Randy Yates % "I met someone who looks alot like you, %% Fuquay-Varina, NC % she does the things you do, %%% 919-577-9882 % but she is an IBM." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
Reply by ●February 27, 20082008-02-27
> The bandwidth of a delta sigma converter running at an oversampling rate > of M*Fs is Fs / 2. �You trade off oversampling rate for dynamic range.Thanks! If I understand it right the turning point at an oversampling rate of 2 for the different orders of noise shaping indicates a vast potential for improvements.
Reply by ●February 27, 20082008-02-27
Oliver Glassl <oliver.glassl@t-online.de> writes:>> The bandwidth of a delta sigma converter running at an oversampling rate >> of M*Fs is Fs / 2. �You trade off oversampling rate for dynamic range. > > Thanks! > If I understand it right the turning point at an oversampling rate of > 2 for the different orders of noise shaping indicates a vast potential > for improvements.I suppose it's possible. I've only designed low-order modulators (2nd or 3rd order), so I don't know what "gotcha's" exist when attempting very high-order modulators. -- % Randy Yates % "Ticket to the moon, flight leaves here today %% Fuquay-Varina, NC % from Satellite 2" %%% 919-577-9882 % 'Ticket To The Moon' %%%% <yates@ieee.org> % *Time*, Electric Light Orchestra http://www.digitalsignallabs.com
Reply by ●February 27, 20082008-02-27
Randy Yates wrote:> Oliver Glassl <oliver.glassl@t-online.de> writes: > >>> The bandwidth of a delta sigma converter running at an oversampling rate >>> of M*Fs is Fs / 2. You trade off oversampling rate for dynamic range. >> Thanks! >> If I understand it right the turning point at an oversampling rate of >> 2 for the different orders of noise shaping indicates a vast potential >> for improvements. > > I suppose it's possible. I've only designed low-order modulators (2nd or > 3rd order), so I don't know what "gotcha's" exist when attempting very > high-order modulators.Just keep going higher and higher order, until you get to 24 bits in the modulator, and then you can throw out all the noise shaping stuff. :-) Steve
Reply by ●February 27, 20082008-02-27
Oliver Glassl wrote:>> The bandwidth of a delta sigma converter running at an oversampling rate >> of M*Fs is Fs / 2. You trade off oversampling rate for dynamic range. > > Thanks! > If I understand it right the turning point at an oversampling rate of > 2 for the different orders of noise shaping indicates a vast potential > for improvements.An oversampling rate of 2 is not worth doing. You can see from Randy's graph that the higher the filter order, the worse the performance at OR = 2, and it never gets very good. I think that any practical design would oversample by at least four. Keep in mind that higher oversampling rates are easier to achieve (for audio) than higher noise-shaping orders. That probably explains the current trend in delta-sigma converters, and why you haven't seen your proposed approach embodied. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
