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'Audio DAC Accuracy [Tech]'
2000\04\04@214738 by Brandon, Tom

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I am looking at a project where I would like to synthesise various audio
waveforms. Looking at sine, square etc 20Hz-24kHz.etc. My question is in
regards to the accuracy of DAC needed. Now, typically Audio applications use
16+ bit at 44.1 and up. I have no problems with the sample rate, it has to
be at least double the highest  frequency of interest and close to double
will produce very low quality sine waves (e.g. CD audio, 20kHZ sine @
44.1kHz = ~2.2 samples\cycle) hence most audio converters use 8 to 16x
oversampling so you're looking at about 350kHz (44.1 @ 8x).

But what effect will bit depth have on the reproduction? Obviously it will
introduce larger step sizes and thus less smooth curves. If you're
reproducing complex signals I could see it effecting the
reproduction\capture of appropriate sines. Slight nonlinearities may not be
able to be filtered out as easily due to the complex source. But, Ig all
you're producing is single oscillators then what sort of accuracy would be
needed?

Also, for the same project I'd like to use 1 DAC to drive a few SHAs to do
mutlichannel. I've seen one SHA capable of >12bit (an Analog devices 16bit
SHA) based on DNL and this was only single channel. Does anyone know of a
multi channel SHA with a DNL suitable for 14+ bits ideally with settling
time to suit 1-2MHz. Also, I'm still looking for a DAC capable of 14+ bits @
>1MHz at a reasonable price.

Thanks,
Tom.

2000\04\04@230533 by Don Hyde

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The relationship between DAC bits and SNR (signal-to-noise ratio) is
actually pretty simple.  SNR is normally expressed in dB, doubling the
voltage of a signal increases its level by 6 dB (approximately).  The SNR of
a signal produced by a DAC is the ratio of the maximum signal output to the
step size.  Adding a bit to a DAC doubles the ratio of full-scale output to
minimum step size, therefor it increases the SNR by 6 dB.  An 8-bit DAC has
an SNR of 48 dB, which sounds pretty good (telephones use 8 bits at 8K
samples/second), but not as good as your stereo.  On a good day, FM radio
can give you 70 or 80 dB SNR (equivalent to around 12 bits at 30K samples or
so), which is not as good as a CD which, with 16 bits can give you 96 dB
SNR, which is better than almost anyone's ears.

120 dBA (absolute sound pressure) is often considered the threshold of pain
(I think mine is lower, but I guess it's pretty subjective).  A quiet room
might get as low as 40 dBA, so you probably have never experienced more than
about 80 dB SNR in real life, which is the reasoning behind the choice of 16
bits for CD's -- more than you get in real life, with some to spare.

> {Original Message removed}

2000\04\06@035916 by mike

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Hi Tom,

I'm not really (infact not at all)a DSP expert but as I understand it the
answer to your question actually has more to do with the filter at the
output of your DAC and sampling rate than anything else. Additional bits in
your D-A do not as I understand it buy you a better reconstructed output but
greater dynamic range.

An over-sampling D-A converter interpolates it's output between sucessive
samples based upon a particular filter function (it doesn't just output the
same voltage 8/16 sample times). The idea is to offload some (most) of the
filtering from the analog output.

Sampling theory says that ANY complex waveform with spectral components up
to 1/2Fs (half the sampling frequency) can be re-constructed using by a
number of independant sinusoids. The important thing to note is that these
sinusoids must always be lower than the nyquist frequency (obviously
otherwise there would be spectral components higher than the nyquist
frquency which we've already dis-allowed).

Essentially so long as your filter can re-create a sinusoid at the nyquist
frequency and below you can build any waveform  you like as long as it
doesn't contain spectral components above that frequency.

If you just want to produce a single sinusoid at a single output level then
1 bit resolution is plenty.
Think of it like this, if you had more bits and you were sampling an
(exactly) 20Khz sinusiod at (exactly) 40K samples/sec what would your data
look like ? It would consist of 2 different values dependent upon where in
the waveform the sample was taken but they would always be the same 2 values
(just like a 1 and a 0).

The very least you should expect your filter to do is get rid of any "steps"
in the output. If you picture such a waveform it should be fairly noticable
that the steps themselves must introduce some unwanted high frequencies into
your output (think of each step as half a square wave, not really accurate
but you get the idea, that rising or falling edge is pretty nasty spectrum
wise).

Conceptually the filter on an D-A is not just there to filter out the high
frequency components introduced by the D-A steps but also to re-build the
sampled data.

Your real problem as far as I can see is that you need to re-produce some
waveforms (such as a square wave or sawtooth wave with a fundamental of
20Khz) that have spectral components in excess of 20Khz.
A square wave or triangle for example is theoretically comprised of an
infinite set of odd harmonic sines' STARTING at the fundamental frequency.
In order to re-construct a decent looking square wave you might choose to
sample up to the 7th harmonic meaning you'll need around 300Khz bandwidth or
600K samples/sec.

If however you change the impulse response of your filter to corespond to
your desired waveshape you could probably build your tone generator a lot
more easily.

An alternative might be to look at a DDS synthesizer...

As I say I am not a DSP expert by any stretch of the imagination, if there's
something I've missed hopefully some body can fill in the gaps...

Regards,

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