isr@rodan.acs.syr.edu (Michael S. Schechter - ISR group account) (01/10/90)
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
bryanh@hplsla.HP.COM (Bryan Hoog) (01/10/90)
> >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