Sine Waves & Harmonic Dist-Help

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2 total messages Started by Michael S. Schechter - ISR group... Tue, 09 Jan 1990 17:29

#2420

Author: Michael S. Schechter - ISR group...
Date: Tue, 09 Jan 1990 17:29

16 lines
1280 bytes

Thanks to those of you who responded about my question
concerning interpolation of sines. After thinking on the problem
further, I realized that one of those things from way way back in
school may be useful and looked at the Taylor series. It looks
like by using it to directly generate values, I can generate a
5-term x,x3,x5,x7,x9 series faster than I could interpolate, and
in any case, easily fast enough to get 16 samples/cycle at 20kHz.
(one of the specs).
This 5-term series has a worst-case error of 4e-6 from "correct"
values over the range 0->pi/2. 
**** New Question ****
  Does this error (4e-6) indicate a signal-to-harmonic ratio of
about 103 dB ?? (I'm trying to get >100 dB)
  or, is the relationship very complicated?

Thanks, Mike.    isr@rodan.acs.syr.edu

Re: Sine Waves & Harmonic Dist-Help

#2422

Author: Bryan Hoog
Date: Wed, 10 Jan 1990 06:57

29 lines
1482 bytes

>
>This 5-term series has a worst-case error of 4e-6 from "correct"
>values over the range 0->pi/2. 
>**** New Question ****
>  Does this error (4e-6) indicate a signal-to-harmonic ratio of
>about 103 dB ?? (I'm trying to get >100 dB)
>  or, is the relationship very complicated?
>

   Depends largely on the relationship between the sine frequency
 and the sampling frequency, and on the amplitude distribution of
 the errors.  Parseval's theorem can be used to bound the problem.
 If the sine frequency is a sub-harmonic of the sampling frequency,
 the errors will show up as harmonics in the frequency domain.  If
 the amplitude error distribution is two-valued (+-4.E-6), and the
 sine values range over -1 to +1, it appears that you still have
 better than 100 dB signal-to-total-harmonic ratio.  This should be
 worst case.

   Disclaimer:  All this is from a college DSP course, and it's been
 awhile.


 Bryan Hoog (bryanh@hplsla) (desk:Bryan Hoog/HPA100/UX)
 Hewlett-Packard
 Lake Stevens Instrument Division
 8600 Soper Hill Road
 Everett, Washington  98205
 206-335-2070

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