--- Nikolai Golovchenko <golovchenko@MAIL.RU> wrote:
> -----Original Message-----

> >True, butt, if you incorporate the proper
> >interpolation along with your look up table, then
> the
> >jitter effects are mitigated. Without any
> >interpolation, the sinewave output from the look-up
> >table is a stair-stepped waveform. The higher the
> >update frequency, the smaller the steps and the
> closer
> >to a sine wave approximation. This 'stair-stepped'
>
>
> This means a biggg table. Interesting, what size of
> table will be sufficient
> to minimize jitter enough for DTMF application.

Actually, the table is not biggg. That's the beauty of
linear interpolation. See below.


>
> >So the next step is first order interpolation. For
> our
> >application, this is linear interpolation between
> >consecutive samples in the table. (For sampling
> >theory, there are some subtle but important
> >differences on the interpretation of a first-order
> >hold.) Which is to say, if you need a sample that
> is
> >not (exactly) at one of the sample points in your
> >table, then you approximate it by using linear
> >interpolation. For example, suppose you had a table
> >with 10 samples: f(i) is the function defined for i
> >=0..9 . Now suppose you need f(2.25)? Well, using
> >linear interpolation you'd approximate this:
> >
> >f(2.25) - f(2)    f(3)  - f(2)
> >-------------- = -------------
> >  2.25  -   2       3   -   2
> >
> >f(2.25) ~= f(2) + 0.25*(f(3) -f(2))
> >
>
>
> Let me compare two methods of sine generation for
> DTMF application:
> 1)Triangle generation with subsequent integration.
> 2)Phase accumalator&table with linear interpolation;
>
> The first method doesn't have table, instead,
> triangle waveform is generated
> using addition of a fixed step to the previous
> sample. No need to use
> interpolation means faster execution time. To
> produce sine waveform
> integration is used - some degradation in the
> waveform, which is acceptable
> in DTMF. As a result, the first method generates
> efficiently jitter free,
> sine waveform signal.

Actually "some degradation" may not be acceptable. A
symmetrical triangle wave has odd harmonics whose
strengthes vary inversely to the square of the
harmonic number (e.g. the third harmonic is 1/9'th the
strength of the fundamental). A low pass filter would
be of no use since to generate 440Hz, you'd need to
block 1320Hz which would also block a few of the
higher frequency DTMF tones as well. Ideally, you want
to have to only block some very high frequency
carrier. For example, if you were using PWM with a
20kHz carrier to generate DTMF then you'd need to
block the 20kHz and pass (a maximum of) ~1600Hz. A
relatively simple 2'nd order low pass filter with
perhaps a cascaded 2'nd order notch (or band-stop)
would be sufficient.

>
> The second method has table, therefore it requires
> more ROM; needs linear
> interpolation - more computing time because of
> multiplication. Result is the
> same.
>
>
> What do you think?

I just re-visited Scott's sine wave page:

http://www.interstice.com/~sdattalo/technical/software/pic/picsine.html

His table contains only 16 entries and (according to
the comments) can generate a new sample every 65
instruction cycles. I see a way to knock 10 cycles
off. So to generate the two tones you'd need about 110
cycles plus an additional overhead of perhaps 50 more
cycles. This'll give you a new sample at about a 30kHz
rate (for a 20Mhz pic). But you'd still need a way to
convert this to analog. So perhaps you'd could back
the generation frequency to 20kHz (or ~256 cycles) and
use an 8-bit pwm.

---------

Perhaps it's not obvious, but the triangle-to-sine
algorithm may also be viewed as a kind of a digital
filter, or more specifically the impulse response of a
digital filter. Consequently, you may wish to consider
other simple algorithms. (e.g. a 4'th order FIR filter
with binary coefficients or perhaps a 3'rd order IIR.)

.lo

=====

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