On Jan 24, 12:31 am, spflanze <
art...@wavenet.org> wrote:
> On Jan 23, 11:51 am,BillSloman<
bill.slo...@ieee.org> wrote:
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> > On Jan 23, 6:20 pm, spflanze <
art...@wavenet.org> wrote:
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> > > On Jan 21, 11:09 pm, miso <
m...@sushi.com> wrote:
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> > > > If we did a mental exercise and reduced the bits in the DDS, eventually
> > > > it would be a square wave. So wouldn't the first noise appear at 3x the
> > > > modulation frequency if the modulation frequency and clock rate have an
> > > > integer relationship. If so, then your post filter is substantially
> > > > easier to build.
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> > > That would be true if it were a perfect DAC with infinite bandwidth.
> > > But there is a finite bandwidth and finite slew rate so its output is
> > > other than a succession of perfect squares. Triangular elements are
> > > involved and those have even harmonics.
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> > A triangular wave is just the integral of a square wave, and has the
> > same - odd only - harmonics, but with the amplitude dropoing in
> > proportion to the square of the harmonic number.
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> > But yes, the output from a DDS is potentially messier than the output
> > from simpler switching circuit.
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> > Have you thought about a delay-line filter? You clock your square wave
> > through a shift register, hook up a suitable resistor to each stage,
> > and sum the outputs. IIRR a sinc function tapered with a Hamming
> > window to kills the Gibbs oscillation can give you a very clean sine
> > wave; you've got residual high-frequency harmonics, but the resistors
> > can be 0.1% parts (with a bit of padding to get the exact values) and
> > the lower harmonics can be held to better than 60dB down.
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> > <snip>
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> It is the sawtooth that has the even harmonics. You are right that the
> triangular wave can be considered the result of a square wave with its
> higher harmonics being attenuated by an integrating filter.
>
> I can see how an array of resistor values on a shift register can be
> chosen to replicate the impulse response of a filter. I do not follow
> how a sync function can be implemented with this. A reference would be
> appreciated.
It's not a synchronising function but sinc - sine(x)/x which gives the
resistor value at each tap.
Google wasn't too helpful, until I remembered that the structure is
also known as a transversal filter
http://www.rane.com/note122.html
shows one at Fig 25
http://www-sigproc.eng.cam.ac.uk/~op205/3F3_5_Design_of_FIR_Filters.pdf
goes into the theory.
> What advantage would a delay line filter have over a Sallen-Key filter
> with many poles?
It's more compact, and you can get 0.1% tolerance resistors, while 1%
tolerance capacitors are as good as you can buy. It's also a finite
impulse response filter, with a linear phase shift.
--
Bill Sloman, Nijmegen