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Re: swept sine accuracy
On 5 Mar 2009 at 19:13, James W. Beauchamp wrote:
> 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
The sweep needs to be slow enough that the system response
does not change significantly (whatever is significant to
you) during the analysis time window. With modern FFT
methods the time window can be known exactly, but there's
more to it: You need to use a peak-hold sweep to only see
the response peaks, AND you need to use a Flat-Top spectral
window function to prevent spectral leakage (at signal
frequencies that give a non-integer number of cycles per
analysis sample set) from causing response bounce. (All of
the more usual window functions have lots of bounce, which
is simply a peak error at "wrong" frequencies.)
But there is another approach that works much better, IMHO:
Don't use a sweep, use a stepped frequency. Better yet, if
the same system is producing the driving signal and
analyzing the response, you can set the frequency steps to
fall exactly on spectral lines, such that you don't need
any window function. This gives a "perfect" spectrum in
the minimum amount of time.
The only caveat is that since you are stepping frequency,
the system under test must have time to respond to each
step before you make the measurement. In practice, since
the steps are small (only one spectral line apart), this
turns out to not be a problem.
I have Application Notes on Frequency Response Measurement
at <http://www.daqarta.com/dw_0a00.htm>. These are
specifically oriented toward my Daqarta software, but
should be generally applicable.
D A Q A R T A
Data AcQuisition And Real-Time Analysis
Scope, Spectrum, Spectrogram, Signal Generator
Science with your sound card!