cutoff and sampling frequency

> Yes, I didn't explain it very well.  It is usual in CD players
> to use digital filters to generate a signal with a much higher
> sampling rate, and use analog filters on the result.
> Described in terms of the original sample rate, fs, the
> filter cutoff will be much higher.  I don't know what the
> current state-of-the-art is for CD players, though.
>
> -- glen

	In 1985 silicon was expensive so the state of the art was to take the 16  
bit signal, oversample it 4x with a 120 tap symmetrical filter using 12  
bit quantification of the coefficients, a 16x12 multiplier, a 16 bit  
accumulator, violently truncate the LSBs, and feed that without dithering  
to a 16-bit DAC.
	Some people tended to prefer Vinyl.

	Nowadays silicon is much cheaper but the budget constraints on the filter  
implementation still live (ie. get it as cheap as you can) so you can find  
all the spectrum between "getting it right" and "getting it cheap".

	=> some chips still use 16 bit undithered arithmetic (rare) see philips  
CD723 and I can tell you it's easy to hear
	=> some die hard fanatics will use DSPs or FPGAs to have high precision  
math and low rounding errors

	=> the vast majority of the chips are 24 bits and sigma delta with  
digital processing on-chip. They take 16 or 24 bits as input, oversample  
with a digital polyphase FIR , usually built with a cascade of 2x  
interpolators, to be able to easily take various input sample rates  
(48k,96k,192k etc), then massively oversample to generally about 2-6 MHz,  
run the thing through a sigma-delta noise shaper, and output it on an  
assortment of low-bit DACs.

	Implementation depends on cost, brand, etc, and not all details are  
mentioned in the datasheet.
	Usually the datasheets mention : number of taps, number of cascaded  
oversampling steps, number of bits in the output dacs (between 1 bit for  
really cheap and multiple 5 bit dacs for high end), number of output dacs  
(usually 2 since in balanced configuration), output symbol frequency,  
dynamic element matching, etc.
	Usually the following are not mentioned : bits of quantization in the tap  
coefficients, accumulator bits, rounding strategy, and lots of details  
that inquiring minds would want to know...

glen herrmannsfeldt wrote:
> John Monro wrote:
> (snip)
> 
>>> For a digital filter, it is only the ratio of the filter frequencies
>>> to the sample rate that matters.  For analog filters, the filter
>>> complexity (order) depends on the ratio of the cutoff rate to the
>>> frequency.   Since most CD players use oversampling and digital
>>> filters, it is more likely 16fc and 8fs.  (Or whatever the
>>> current numbers are.)
> 
>> Glen,I can't grasp the point you are making here.  It appears that you 
>> are saying that the filter order is 16fc and 8fs, which is clearly not 
>> correct.
> 
> Yes, I didn't explain it very well.  It is usual in CD players
> to use digital filters to generate a signal with a much higher
> sampling rate, and use analog filters on the result.
> Described in terms of the original sample rate, fs, the
> filter cutoff will be much higher.  I don't know what the
> current state-of-the-art is for CD players, though.

Is there an A-to-D in the loop somewhere? How can one use an analog 
filter on the signal with the much higher sampling rate?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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glen herrmannsfeldt wrote:
> John Monro wrote:
> (snip)
> 
>>> For a digital filter, it is only the ratio of the filter frequencies
>>> to the sample rate that matters.  For analog filters, the filter
>>> complexity (order) depends on the ratio of the cutoff rate to the
>>> frequency.   Since most CD players use oversampling and digital
>>> filters, it is more likely 16fc and 8fs.  (Or whatever the
>>> current numbers are.)
> 
>> Glen,I can't grasp the point you are making here.  It appears that you 
>> are saying that the filter order is 16fc and 8fs, which is clearly not 
>> correct.
> 
> Yes, I didn't explain it very well.  It is usual in CD players
> to use digital filters to generate a signal with a much higher
> sampling rate, and use analog filters on the result.
> Described in terms of the original sample rate, fs, the
> filter cutoff will be much higher.  I don't know what the
> current state-of-the-art is for CD players, though.
> 
> -- glen
> 
In my first posting I was pointing out a typo in Ron's posting, in which 
he referred to a 'gap' (attenuation) between 2fc and fs.  I was pretty 
sure he meant to say "fc and fs/2."  Up to that point the discussion 
seemed to be around systems in which the sampling rate was only somewhat 
above the max. signal frequency, and not to oversampled systems.

However, you have referred to CD systems where the output to the D/A is 
oversampled.  I don't think you are correct when you say:
"Described in terms of the original sample rate, fs, the filter cutoff 
will be much higher."

Having a very high output sample rate certainly eases the restrictions 
on the anti-alias filter, and one of the things a designer will do is to 
raise the cut-off frequency, as this allows a simpler anti-alias filter 
is to be used for a given amount of ripple in the audible pass-band. 
There is no point though in making the cut-off frequency very much 
higher than the highest-frequency component in the audio signal, and 
certainly there is no point in making the cut-off frequency "much 
higher" than the original sample rate.

Regards,
John

John Monro wrote:
(snip)

> Having a very high output sample rate certainly eases the restrictions 
> on the anti-alias filter, and one of the things a designer will do is to 
> raise the cut-off frequency, as this allows a simpler anti-alias filter 
> is to be used for a given amount of ripple in the audible pass-band. 
> There is no point though in making the cut-off frequency very much 
> higher than the highest-frequency component in the audio signal, and 
> certainly there is no point in making the cut-off frequency "much 
> higher" than the original sample rate.

Someone else posted more details about current CD players
than I knew.  I won't argue about how much higher it has
to be to be "very much higher" or "much higher."  It also
depends on your reference.

With Fs/2 at 22.05kHz, compared to a cutoff that might be
20kHz without oversampling I might say that 30kHz is
much higher.  Others will disagree.

-- glen

>> Having a very high output sample rate certainly eases the restrictions  
>> on the anti-alias filter, and one of the things a designer will do is  
>> to raise the cut-off frequency, as this allows a simpler anti-alias  
>> filter is to be used for a given amount of ripple in the audible  
>> pass-band. There is no point though in making the cut-off frequency  
>> very much higher than the highest-frequency component in the audio  
>> signal, and certainly there is no point in making the cut-off frequency  
>> "much higher" than the original sample rate.

	Certainly. You'd want to minimize the frequency response drop close to  
the cutoff, so some margin would be necessary, but not anything like  
100K... perhaps 30-40K or something. Also you want to keep the same analog  
filter for playing 24-192 and marketing wants to put "50 kHz bandwidth" on  
the brochure so why not.

> Someone else posted more details about current CD players
> than I knew.  I won't argue about how much higher it has
> to be to be "very much higher" or "much higher."  It also
> depends on your reference.
>
> With Fs/2 at 22.05kHz, compared to a cutoff that might be
> 20kHz without oversampling I might say that 30kHz is
> much higher.  Others will disagree.
>
> -- glen
>

	Well say you take good old 16/44 and you want to reconstruct it according  
to the Nyquist classics (ie pseudo brickwall with sin x/x impulse  
response), if you don't oversample at all you are going to need an  
extremely complicated analog filter with expensive, precision components.  
The first CD players used such filters, 9th order elliptic or something (I  
read an article about this recently).
	This is because the first image you want to eliminate is really close to  
the end of your band of interest...
	So your analog filter has to :

	- pass the signal up to 20k while being flat
	- attenuate sufficiently the first image which starts a 22k !

	Easy in DSP, but in analog... yikes !
	Also your analog filter has to compensate the sinx/x frequency character  
of the non-oversampled DAC output.

	-> lots of opamps
	-> lots of precision capacitors
	-> you can't put that in an IC
	-> very very expensive
	-> noise and other signal quality problems

	If you oversample, you might as well go all the way and at least  
oversample 8x, it will cost you the same as 2x, just a few cents in logic,  
but your analog filter will be much simpler since the requirements for the  
analog filter are :

	- pass the signal up to 20k
	- attenuate sufficiently the first image which is at 300 kHz

	Needless to say you can use something simple like a second order Bessel  
which is nearly free since you were going to need those opamps anyway.
	And it will sound better (provided you dont do anything stupid in the  
digital filter like skimp on the bits or forget to dither !)

	Multibit Sigma Deltas have other requirements, they output a high  
frequency (2-6 MHz) stream of low (1-6) bit samples and the quantization  
noise is shaped out of the audio band so the job of the analog filter is  
more to remove this quantization noise than to complete the job of the  
digital filter. This is important since there is more noise than signal at  
the output of a sigma delta converter unless you run it at full scale.  
Still, the analog filters are simple because they don't need to be super  
high order. The noise to remove is in high frequencies and, if the  
delta-sigma is well designed (which means multibit), this noise is  
UNCORRELATED with the signal unlike the images.

	The output of any modern current-output sigma delta DAC is essentially  
high frequency noise whose spectrum extends far past the 2-6 MHz symbol  
frequency. It is, in reality, not different from what you would find at  
the output of a 6 Msps DAC since that is exactly what it is.
	Then you use an opamp as a current-to-voltage converter.

	If there is on this list someone designing audio equipment, I will take  
the opportunity to mention an often neglected fact :

	Consider the classical opamp wired as a current to voltage converter with  
the - input as a virtual ground connected to the dac's current output.  
Since the opamp used in those is generally some variant of NE5532 with a  
low slew rate and GBW, a settling time that is about as fast as grass  
growing, and an output impedance that quickly becomes uncontrolled above  
the audio band, there is much more "virtual" than "ground" here so  
basically the input stage of the opamp, and perhaps the output stage of  
the DAC, spend some of their time in various unspecified nonlinear states  
which of course manifests itself as really sucky sound. If you are lucky  
you get muffled sound with a lack of detail, if you are not lucky you get  
a strident, harsh signature.

	The cure is simple, use a much faster opamp that will digest the high  
frequency noise and essentially design the stuff as if it was connected to  
a 10 Msps DAC (which it is). Google Hawksford. This should set you back $2  
per channel. If you're really on a tight budget you can use plan B which  
is a common base transistor followed by a RC lowpass and then the opamp  
filters.

	Oops, wandered off topic ;)