swept sine accuracy

["James W. Beauchamp" <jwbeauch@xxxxxxxxxxxxxxxxxxxxxx>]

Guys,

This is a not strictly an auditory question, but it could be
useful for people doing acoustic measurements. If you use a
swept sine wave to measure the frequency response of a linear
system, what is the limitation on the speed of the sweep in
terms of how accurate the result would be? I imagine it has
something to do with how smooth the actual frequency response 
is. If it has some pronounced bumps, they could be smoothed
out if the sweep is too fast.

In practice, you could sweep at some arbitrary rate, and then
slow it by a factor of two, and if the result is the same
(within an acceptable tolerance) you could say that you've
converged on the solution.

But I'd like to have a theoretical result.

Jim Beauchamp
Univ. of Illinois at Urbana-Champaign