-----Original Message-----
From: Tracy Smith <dot_lo@YAHOO.COM>
To: PICLIST@MITVMA.MIT.EDU <PICLIST@MITVMA.MIT.EDU>
Date: Sunday, November 14, 1999 6:01 PM
Subject: Re: DTMF Tones? [Idea]How to produce sine wave


>1 out of 3 pieces of information distributed on the
>pic list is decent. :)

I would say 1 out of 10. ;)


>
>> I think that my method resembles phase accumulator
>> and table method except
>> there is no table. The table is generated on the run
>> and this is triangle.
>> In my case error of triangle generation is lower,
>> because there is no
>> restriction to use only table values. Finally, this
>> reduced error makes the
>> sine wave frequency more stable. Certainly, the
>> phase accumulator method is
>> more straight-forward and simple, at the cost of
>> frequency jitter. In case
>> of DTMF this is mainly the frequency what matters,
>> because DTMF frequencies
>> are very close.
>
>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.

>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.

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?

_

Nikolai Golovchenko, Electrical Engineering Student
National Mining University of Ukraine www.nmuu.dp.ua
Dnepropetrovsk, Ukraine
E-mail: golovchenko@mail.ru