rfbrw said:
But that's not what you're doing when you map 16-bit quantized data into 24-bits. The "required distance" was initially established by the original analgue waveform. Once you've quantized that waveform to a given bit width, your error is then fixed and subsequently increasing the number of bits doesn't reduce the error.
Let's say you've got a line drawing made up of nice smooth curves. You're told to reproduce that drawing but you can only do it with fixed 1" straight line segments which we'll say represents 16-bit quantization. Now we have a drawing which is an approximation of the original and it has a fixed amount of error built-in.
If we were to have reproduced that drawing using 24-bit quantization, we could use line segments of 1/256 inch and get a much closer approximation.
But given the 16-bit drawing, mapping that into 24-bits, all we're doing is increasing the length of the line segments. Instead of their representing 1", they now represent 256 inches. So really all you're doing is making the drawing bigger. And the error scales along with it. So you haven't added any resolution at all. The resolution's the same and it's just as close an approximation as it was when it was represented with 1" lines.
se
Steve Eddy said:
Long sigh. Shoulders slump. Considers the maximium loading of the door frame.
It is about mathematics.Given the same full scale value increasing the wordlength increases resolution by which I mean resolution in numerical terms.
In the context of oversampling digital filters it is about moving the bulk of the filtering into the digital domain. Having decided to use the oversampling digital filter(e.g. SM5843 or DSP chip etc.) we are where we are. We have more bits than we started out with. This new value is the object of the excercise. From then on its about dealing with the increased wordlength.
ray
Peace guys,
I think you both mean the same thing, we are not going to gain any more information then what is already on the CD. The point of oversampling is to be able to relax the analog filters after the DAC. In the process the bit-depth increases as a side effect of the filtering, and then it makes no sense to truncate again to 16-bits before sending to the DAC, we'll just send the entire 24-bit word.
Do ya'll agree with this?
I think you both mean the same thing, we are not going to gain any more information then what is already on the CD. The point of oversampling is to be able to relax the analog filters after the DAC. In the process the bit-depth increases as a side effect of the filtering, and then it makes no sense to truncate again to 16-bits before sending to the DAC, we'll just send the entire 24-bit word.
Do ya'll agree with this?
ojg said:Peace guys,
I think you both mean the same thing, we are not going to gain any more information then what is already on the CD. The point of oversampling is to be able to relax the analog filters after the DAC. In the process the bit-depth increases as a side effect of the filtering, and then it makes no sense to truncate again to 16-bits before sending to the DAC, we'll just send the entire 24-bit word.
Do ya'll agree with this?
Yes say I.
ray
I have to say I never envisaged this much of a response when starting this thread - since the original post I have bought a book on DSP techniques and it all seems much clearer now.
The question on whether or not the resolution increases is a strange one, but one I feel I can answer quite comprehensively now.
Sampling theory tells us that the highest (theoretical) frequency will be half of the sampling frequency so therefore one individual sample can hold half of one full wavelength (at the highest recordable frequency). A single sample is a square wave, so therefore is composed of the fundamental frequency and all of the additional harmonics (which would usually be removed in the analogue domain), but the only useful information it holds is the fundamental.
Oversampling techniques do not add information, but do increase resolution by interpolating intermediate samples - for instance if one were to record half a wavelength of a 22.05kHz signal at a sampling rate of 44.1kHz the result would be one square sample with the fundamental frequency and all of the harmonics (which would then be removed in the analogue domain after the DAC).
Oversampling (with the use of a digital FIR filter) of the single sample would create a curve that approximates a sine wave (half of one wavelength) that would then be converted to an analogue signal. The new curve holds no more information than the original square sample - it just has much less of the harmonics associated with a square wave.
The advantage is that a lower order filter can be used in the analogue stage - which most would say is a good thing.
Does everyone agree???
Please let me know if I've said something that is not correct.
The question on whether or not the resolution increases is a strange one, but one I feel I can answer quite comprehensively now.
Sampling theory tells us that the highest (theoretical) frequency will be half of the sampling frequency so therefore one individual sample can hold half of one full wavelength (at the highest recordable frequency). A single sample is a square wave, so therefore is composed of the fundamental frequency and all of the additional harmonics (which would usually be removed in the analogue domain), but the only useful information it holds is the fundamental.
Oversampling techniques do not add information, but do increase resolution by interpolating intermediate samples - for instance if one were to record half a wavelength of a 22.05kHz signal at a sampling rate of 44.1kHz the result would be one square sample with the fundamental frequency and all of the harmonics (which would then be removed in the analogue domain after the DAC).
Oversampling (with the use of a digital FIR filter) of the single sample would create a curve that approximates a sine wave (half of one wavelength) that would then be converted to an analogue signal. The new curve holds no more information than the original square sample - it just has much less of the harmonics associated with a square wave.
The advantage is that a lower order filter can be used in the analogue stage - which most would say is a good thing.
Does everyone agree???
Please let me know if I've said something that is not correct.
ojg said:I think you both mean the same thing, we are not going to gain any more information then what is already on the CD. The point of oversampling is to be able to relax the analog filters after the DAC. In the process the bit-depth increases as a side effect of the filtering, and then it makes no sense to truncate again to 16-bits before sending to the DAC, we'll just send the entire 24-bit word.
Do ya'll agree with this?
Fair 'nuff.
Though while I see that it requires greater than 16 bits to do the mathematics, the end result of the process is still 16 bit words, yes?
se
Steve Eddy said:
Yes it does, but I am afraid that the steep analog filter will do more harm to the signal then the digital filters will. And I also believe that if you let the non-OS signal go unfiltered into the amplifier this will not be good either. If you have any examples/proof to the contrary then I am all ears
ojg said:Yes it does, but I am afraid that the steep analog filter will do more harm to the signal then the digital filters will. And I also believe that if you let the non-OS signal go unfiltered into the amplifier this will not be good either. If you have any examples/proof to the contrary then I am all ears
You don't necessarily have to let it through completely unfiltered. A simple 20kHz second-order Bessel filter could be effective and not produce any phase distortion.
From a Manufacturers' Comment by "The MSB Team" in the April 2003 Stereophile regarding the review of MSB's Platinum DAC:
We filter most DACs because some poor-quality amplifiers may alias some of the high frequency content back into the audio range. Although this is a very rare occurrence that we have never seen in 10 years of producing DACs without output filters, it is possible, so the mass-producers of DAC chips always specify a low-pass filter.
se
"Bits is Bits" - not true!
People make many mistakes when talking about the resolution of digital information - often trying to relate directly the number of bits two "words" have.
Take for example the information in a digital filter - the input is an integer number (-1, 0, 1, 2, 3 etc) i.e can be represented as a range of 2^n levels, where n is the size of the input word in bits.
The processing is done using floating point numbers which do not follow the same rule - i.e. a 32bit floating number does not have a range of 2^32 integer numbers. Instead it is broken into two parts the exponent and mantissa (strangely enough called exponent-mantissa form) to represent non-integer numbers (1.234, 2343.12 etc) - all processing is done while the data is in this form, then it is requantised (often applying dithering or other noise shaping techniques) into 24bit (integer) "words" that the DACs turn to analogue voltages.
Does this make sence?
Hope it helps
People make many mistakes when talking about the resolution of digital information - often trying to relate directly the number of bits two "words" have.
Take for example the information in a digital filter - the input is an integer number (-1, 0, 1, 2, 3 etc) i.e can be represented as a range of 2^n levels, where n is the size of the input word in bits.
The processing is done using floating point numbers which do not follow the same rule - i.e. a 32bit floating number does not have a range of 2^32 integer numbers. Instead it is broken into two parts the exponent and mantissa (strangely enough called exponent-mantissa form) to represent non-integer numbers (1.234, 2343.12 etc) - all processing is done while the data is in this form, then it is requantised (often applying dithering or other noise shaping techniques) into 24bit (integer) "words" that the DACs turn to analogue voltages.
Does this make sence?
Hope it helps
ojg said:Peace guys,
I think you both mean the same thing, we are not going to gain any more information then what is already on the CD. The point of oversampling is to be able to relax the analog filters after the DAC. In the process the bit-depth increases as a side effect of the filtering, and then it makes no sense to truncate again to 16-bits before sending to the DAC, we'll just send the entire 24-bit word.
Do ya'll agree with this?
Spot on !
We do not gain information, we gain acuracy in describing a signal which does not need additional precision te be described......
Main feature is the analog filtering issue
One word that everyone seems to forget, ignore or whatever:
A huge advantage of taking away the digital filter, is the lower jitter being fed to the DAC chips. No need to be a genius to understand that sounds better.......
nice thread
regards
Right...
...The information on the disc is a series of samples - these are effectively square waves.
A square wave contains a lot of redundant "information" - we are essentially only interested in the primary harmonic and not all the other harmonics (which hold no additional "information" as they are merely multiples of the fundamental at lower amplitudes).
Conventionally the analogue filter after the DAC is designed to remove these harmonics by having a pass-band upper limit of that of a single samples primary harmonic frequency - therefore removing frequencies above this.
Upsampling/oversampling techniques work by increasing the frequency range of the signal (in the digital domain), but filling the frequencies above the original pass-band with no information. Therefore when the digital to analogue process is undertaken the filter can be simpler - the redundant "information" of the original square samples was been removed in the digital domain.
Does this help?
...The information on the disc is a series of samples - these are effectively square waves.
A square wave contains a lot of redundant "information" - we are essentially only interested in the primary harmonic and not all the other harmonics (which hold no additional "information" as they are merely multiples of the fundamental at lower amplitudes).
Conventionally the analogue filter after the DAC is designed to remove these harmonics by having a pass-band upper limit of that of a single samples primary harmonic frequency - therefore removing frequencies above this.
Upsampling/oversampling techniques work by increasing the frequency range of the signal (in the digital domain), but filling the frequencies above the original pass-band with no information. Therefore when the digital to analogue process is undertaken the filter can be simpler - the redundant "information" of the original square samples was been removed in the digital domain.
Does this help?
annex666 said:
They are not square waves, they are impulses, a snapshot of the amplitude of the waveform at an instant in time.
The point of the analogue filter is to remove the images of the sampled spectrum that repeat at multiples of Fs. Oversampling digital filters like the SAA7220,SM5843 etc. increase Fs and in so doing move the images further along the spectrum easing the analogue domain filtering requirements
The frequency range is not increased. Even though the sample rate is increased the samples still have be digitally filtered at the original sample rate divided by 2.
ray.
rfbrw said:
And what is an impulse if not a square wave of exactly one half wavelength? - This impulse contains a primary frequency (fs/2) and all the harmonics associated with a square wave.
Are these images not derived from the fact that the square wave (or impulse) contains not only the primary but also additional harmonics?
The images repeat at multiples of fs - possibly because they are harmonics of the impulse?
YES the frequency range is increased! - simple sampling theory tells us that the maximum frequency that can be stored is exactly half of the sampling frequency. I'd like to see you justify the fact that increasing the sampling frequency does not increase the frequency range - the fact that this frequency range has no information in it (due to the upper frequeny range of the original sampling rate) does not change the fact that the frequency range is increased!
It is the fact that the sampling frequency (and therefore highest recordable frequency) are higher that makes it possible to use a lower order analouge filter - the images related to the sampling frequency are now further above the highest needed frequency.
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