On Sep 30, 1:04�pm, Richard Dobson <richarddob...@blueyonder.co.uk> wrote:> Clay wrote: > > .. > > > > > > > > >> "less than one sampling interval" is not meaningful if adding in some > >> other constant delay greater than a sampling interval. �so, if it's > >> real-time, i guess Sammy will need some real-fast A/D and D/A (simple > >> audio 1-bit codecs won't do) he can accomplish delay by less than a > >> simapling interval by linearly interpolating between the most current > >> two samples. > > >> � � y[n] = x[n]*(1-t0/T) + x[n-1]*(t0/T) > > >> oh crap! �the ZOH of the D/A will put in another 1/2 sample delay, so > >> Sammy, it would have to be greater than 1/2 sample in any case. > > >> but, if what you want is a precision delay, where the precision is > >> much less than a sampling interval, and you can tolerate a minimum > >> delay of a constant and integer value (say, 32 samples), then you can > >> have two versions of the same signal but one is delayed relative to > >> the other by much less than a sampling interval. > > I am totally confused by this thread. Is it discussing general > fractional delays, or (literally) what the subject line says? If this is > non-causal (offline, etc) you can do whatever you like. but if it is a > real-time stream, I would have thought such a delay is impossible, as > until the second sample arrives (one whole interval behind the first > one) you do not know what values to interpolate between. The minimum > latency will be longer than the target delay. > > Richard Dobson- Hide quoted text - > > - Show quoted text -Richard, Certainly you bring up a valid point about what the OP is really asking. I skipped ahead to actual causal cases. And in this situation many approaches exist to get the desired result as offered by various responders. Now if the antialias filter is designed to meet certain properties before the signal is sampled, then you can go a long ways towards an approximation to reconstruct the signal using only one sided interpolation. Clearly such filters will be not phase linear. This I believe can get you close to doing your delay, but the "rub" is the signal has a non standard digital form and using sinc reconstruction is not what you want to use. Unser describes non sync types of antialias and reconstruction filter kernals in his paper "Sampling -- 50 years after Shannon." The May 2009 issue of Signal Processing Magazine has an article "Beyond Bandlimited Sampling" by Eldar and Michaeli which explores other types of filters and signal representations which takes this idea furthur. Just more food for thought. Clay