"Jerry Avins" <jya@ieee.org> wrote in message news:_LCdnWcTNJg7ZvDZnZ2dnUVZ_sGdnZ2d@rcn.net...> Thomas Magma wrote: > >> I'm not sure if I exactly agree with the statement of not being able to >> get >> closer to the original signal then simply satisfying Nyquist. It seems to >> me >> that if you sampled (lets say) a 100 Hz perfect sinusoidal wave form at >> 200 >> Hz or so, that during playback (DAC process), this will appear as a very >> chunky square wave that contains tons of harmonics. It you oversampled >> that >> same 100 Hz sine wave at 44kHz then you have better represented the >> original >> sine wave and playback would contain vary little harmonic content. The >> two >> methods will sound different. > > The output of the DAC is not what you need to be thinking about. You > ignored the role of the reconstruction filter. If the sampling frequency > is 200 Hz, everything above 100 Hz must be removed from the analog > output. What harmonics did you mean? > > The sampling frequency must be greater that twice the highest signal > component. When sampling at 200 Hz, 100 Hz can't be reliably > reconstructed. 200.001 Hz is sufficient, but only if the sampling lasts > a good part of 1000 seconds and the signal remains unchanged for that > time. The bit of oversampling that is always needed to allow practical > anti-alias and reconstruction filters also assures reasonable resolution > times, but in theoretical cases that don't call for filters, resolution > time has to be accounted for. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������Thinking in the time domain, as you lower the sample rate you increase the digitization (Your sampled sine wave will start to look like a square wave). Clocking that data through a DAC at the same rate will produce strong harmonics (3rd 5th 7th etc). You can't regenerate the original sine wave out of a DAC no matter what digital reconstruction filtering you use if the playback rate is too slow. The output of a DAC will always start digitizing and producing harmonics as you lower the sample/playback rate, unless you have exceeded the full power bandwidth of the DAC or have analog filtering after the DAC. Thomas
Is higher oversampling ratio better in signal fidelity in digital world?
Started by ●May 18, 2006
Reply by ●May 19, 20062006-05-19
Reply by ●May 19, 20062006-05-19
> > Thinking in the time domain, as you lower the sample rate you increase the > digitization (Your sampled sine wave will start to look like a square > wave). Clocking that data through a DAC at the same rate will produce > strong harmonics (3rd 5th 7th etc). You can't regenerate the original sine > wave out of a DAC no matter what digital reconstruction filtering you use > if the playback rate is too slow. The output of a DAC will always start > digitizing and producing harmonics as you lower the sample/playback rate, > unless you have exceeded the full power bandwidth of the DAC or have > analog filtering after the DAC. > > Thomas >Just to debate a little with myself (slow day). A soundcards playback and recording rates are typically independent of each other. Playback being much higher. So reconstruction filtering is possible. If the playback rate equaled the recording rate you would notice the effects I was trying to explain.
Reply by ●May 19, 20062006-05-19
Thomas Magma said the following on 19/05/2006 19:21:> "Jerry Avins" <jya@ieee.org> wrote in message > news:_LCdnWcTNJg7ZvDZnZ2dnUVZ_sGdnZ2d@rcn.net... >> Thomas Magma wrote: >> >>> I'm not sure if I exactly agree with the statement of not being able to >>> get >>> closer to the original signal then simply satisfying Nyquist. It seems to >>> me >>> that if you sampled (lets say) a 100 Hz perfect sinusoidal wave form at >>> 200 >>> Hz or so, that during playback (DAC process), this will appear as a very >>> chunky square wave that contains tons of harmonics. It you oversampled >>> that >>> same 100 Hz sine wave at 44kHz then you have better represented the >>> original >>> sine wave and playback would contain vary little harmonic content. The >>> two >>> methods will sound different. >> The output of the DAC is not what you need to be thinking about. You >> ignored the role of the reconstruction filter. If the sampling frequency >> is 200 Hz, everything above 100 Hz must be removed from the analog >> output. What harmonics did you mean? >> >> The sampling frequency must be greater that twice the highest signal >> component. When sampling at 200 Hz, 100 Hz can't be reliably >> reconstructed. 200.001 Hz is sufficient, but only if the sampling lasts >> a good part of 1000 seconds and the signal remains unchanged for that >> time. The bit of oversampling that is always needed to allow practical >> anti-alias and reconstruction filters also assures reasonable resolution >> times, but in theoretical cases that don't call for filters, resolution >> time has to be accounted for. >> > > Thinking in the time domain, as you lower the sample rate you increase the > digitization (Your sampled sine wave will start to look like a square wave). > Clocking that data through a DAC at the same rate will produce strong > harmonics (3rd 5th 7th etc).Harmonics? Aliasing frequencies are not harmonically related (except in degenerate cases).> You can't regenerate the original sine wave out > of a DAC no matter what digital reconstruction filtering you use if the > playback rate is too slow.If you mean without using an analogue filter, then you can't reconstruct the original sine wave 100% at *any* sample rate (except infinity!).> The output of a DAC will always start digitizing"Digitising" is probably the wrong word here. What you're describing (the staircase-like waveform) is actually an artifact of the impulse-response of a zero-order hold, which itself is just a filter. -- Oli
Reply by ●May 19, 20062006-05-19
Thomas Magma wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:_LCdnWcTNJg7ZvDZnZ2dnUVZ_sGdnZ2d@rcn.net... > >>Thomas Magma wrote: >> >> >>>I'm not sure if I exactly agree with the statement of not being able to >>>get >>>closer to the original signal then simply satisfying Nyquist. It seems to >>>me >>>that if you sampled (lets say) a 100 Hz perfect sinusoidal wave form at >>>200 >>>Hz or so, that during playback (DAC process), this will appear as a very >>>chunky square wave that contains tons of harmonics. It you oversampled >>>that >>>same 100 Hz sine wave at 44kHz then you have better represented the >>>original >>>sine wave and playback would contain vary little harmonic content. The >>>two >>>methods will sound different. >> >>The output of the DAC is not what you need to be thinking about. You >>ignored the role of the reconstruction filter. If the sampling frequency >>is 200 Hz, everything above 100 Hz must be removed from the analog >>output. What harmonics did you mean? >> >>The sampling frequency must be greater that twice the highest signal >>component. When sampling at 200 Hz, 100 Hz can't be reliably >>reconstructed. 200.001 Hz is sufficient, but only if the sampling lasts >>a good part of 1000 seconds and the signal remains unchanged for that >>time. The bit of oversampling that is always needed to allow practical >>anti-alias and reconstruction filters also assures reasonable resolution >>times, but in theoretical cases that don't call for filters, resolution >>time has to be accounted for. >> >>Jerry >>-- >>Engineering is the art of making what you want from things you can get. >>����������������������������������������������������������������������� > > > > Thinking in the time domain, as you lower the sample rate you increase the > digitization (Your sampled sine wave will start to look like a square wave). > Clocking that data through a DAC at the same rate will produce strong > harmonics (3rd 5th 7th etc). You can't regenerate the original sine wave out > of a DAC no matter what digital reconstruction filtering you use if the > playback rate is too slow. The output of a DAC will always start digitizing > and producing harmonics as you lower the sample/playback rate, unless you > have exceeded the full power bandwidth of the DAC or have analog filtering > after the DAC.Of course there is analog filtering after the DAC. It's called a reconstruction filter. Without one, no sample rate is high enough. With good one, a reasonable (small) oversampling suffices. With a sloppy one, more oversampling is needed. With analog-to-digital conversion, an analog anti-alias filter before the sampler is assumed. In the other direction, an analog reconstruction filter after the DAC is assumed. There's no practical other way. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 19, 20062006-05-19
Thomas Magma wrote:>>Thinking in the time domain, as you lower the sample rate you increase the >>digitization (Your sampled sine wave will start to look like a square >>wave). Clocking that data through a DAC at the same rate will produce >>strong harmonics (3rd 5th 7th etc). You can't regenerate the original sine >>wave out of a DAC no matter what digital reconstruction filtering you use >>if the playback rate is too slow. The output of a DAC will always start >>digitizing and producing harmonics as you lower the sample/playback rate, >>unless you have exceeded the full power bandwidth of the DAC or have >>analog filtering after the DAC. >> >>Thomas >> > > > Just to debate a little with myself (slow day). A soundcards playback and > recording rates are typically independent of each other. Playback being much > higher. So reconstruction filtering is possible. If the playback rate > equaled the recording rate you would notice the effects I was trying to > explain.Wrong again. How do you change the playback rate without changing the playback duration? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 19, 20062006-05-19
> > Wrong again. How do you change the playback rate without changing the > playback duration? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������By resampling at a much higher rate (playback). Then you can apply a digital reconstruction filter to remove quantization noise power on harmonics frequencies.
Reply by ●May 19, 20062006-05-19
Thomas Magma wrote:>>Wrong again. How do you change the playback rate without changing the >>playback duration? >> >>Jerry >>-- >>Engineering is the art of making what you want from things you can get. >>����������������������������������������������������������������������� > > > By resampling at a much higher rate (playback).Then you are not playing back the same signal that was originally recorded. What conclusions can you draw from such a circumstance? One lesson is that there exists at least one technique that allows good reproduction of a signal captured without much oversampling. (There are in fact many.) The reconstruction filter removes aliases, not harmonics.> Then you can apply a digital > reconstruction filter to remove quantization noise power on harmonics > frequencies.The reconstruction filter removes aliases, not harmonics. If the signal was properly sampled (Nyquist and all that) there are no harmonics. Quantization noise, once assimilated into the signal (there are ways when capturing the signal to minimize it) can't later be removed. Sometimes intuition is useful. You need to abandon it when it leads you astray. Have you read a good book like Rick's or Smith's? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 19, 20062006-05-19
Thomas Magma wrote:>>Wrong again. How do you change the playback rate without changing the >>playback duration? >> >>Jerry >>-- >>Engineering is the art of making what you want from things you can get. >>����������������������������������������������������������������������� > > > By resampling at a much higher rate (playback).Then you are not playing back the same signal that was originally recorded. What conclusions can you draw from such a circumstance? One lesson is that there exists at least one technique that allows good reproduction of a signal captured without much oversampling. (There are in fact many.)> Then you can apply a digital > reconstruction filter to remove quantization noise power on harmonics > frequencies.The reconstruction filter removes aliases, not harmonics. If the signal was properly sampled (Nyquist and all that) there are no harmonics. Quantization noise, once assimilated into the signal (there are ways when capturing the signal to minimize it) can't later be removed. Sometimes intuition is useful. You need to abandon it when it leads you astray. Have you read a good book like Rick's or Smith's? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 19, 20062006-05-19
> Then you are not playing back the same signal that was originally > recorded. What conclusions can you draw from such a circumstance? >Ask the engineers at Creative. They resample at 48 kHz during playback regardless of the input sample rate.> The reconstruction filter removes aliases, not harmonics. If the signal > was properly sampled (Nyquist and all that) there are no harmonics. > Quantization noise, once assimilated into the signal (there are ways > when capturing the signal to minimize it) can't later be removed.Any distortion of a sine wave will cause harmonics. Lower sample rates cause quantization noise which is a form of distortion. Then resampling at a higher rate increases bandwidth, allowing you to see those harmonics. A low pass at the original fs/2 helps remove these.>Have you read a good book like Rick's or Smith's?Yes. Thomas
Reply by ●May 19, 20062006-05-19
Thomas Magma wrote:>>Then you are not playing back the same signal that was originally >>recorded. What conclusions can you draw from such a circumstance? >> > > > Ask the engineers at Creative. They resample at 48 kHz during playback > regardless of the input sample rate. > > >>The reconstruction filter removes aliases, not harmonics. If the signal >>was properly sampled (Nyquist and all that) there are no harmonics. >>Quantization noise, once assimilated into the signal (there are ways >>when capturing the signal to minimize it) can't later be removed. > > > Any distortion of a sine wave will cause harmonics. Lower sample rates cause > quantization noise which is a form of distortion. Then resampling at a > higher rate increases bandwidth, allowing you to see those harmonics. A low > pass at the original fs/2 helps remove these. > > >>Have you read a good book like Rick's or Smith's? > > > Yes.Have it your way then. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
