Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!ucbvax!hplabs!hp-pcd!hplsla!bryanh
From: bryanh@hplsla.HP.COM (Bryan Hoog)
Newsgroups: comp.dsp
Subject: Re: Sine Waves & Harmonic Dist-Help
Message-ID: <9360004@hplsla.HP.COM>
Date: 10 Jan 90 06:57:54 GMT
References: <1701@rodan.acs.syr.edu>
Organization: HP Lake Stevens, WA
Lines: 29

>
>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