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Thread: Audio DAC Accuracy [Tech]
face BY : mike@bytethis.com.au

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

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...


Mike Cornelius                  Internet: mikeKILLspamspamspam_OUTbytethis.com.au
Byte This Interactive           Phone:    +61 2 9310-2157
PO Box 1342 Strawberry Hills    FAX:      +61 2 9319-3948
NSW 2012 Australia              URL:      http://www.bytethis.com.au

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