Audio, hi-fi and car audio - YOU MUST KNOW THIS MAN

In article , Don Pearce
wrote:
On Fri, 31 Mar 2006 17:07:23 +0100, Nick Gorham wrote:

What I notice a lot and Jim may be able to explain this, is the HiFi
mags seem to often do FR plots using what they describe as a convolved
inpulse analysis, I have a theory what this means, but it would be nice
to have some references (ok, so I guess I could just look it up).

TBH I am often not quite sure *what* magazine reviewers mean when they make
statements like the above. All to often their results, and their
interpretation of them, seem rather odd... :-)

e,.g in this context I am weary of 'spectra' of broadband noise that have
the vertical axis labled as a 'voltage' or a 'power' when it should be in
units like 'power/Hz', and they give no info on how many samples, etc, were
used to work out the spectrum. Thus making the plotted values
meaningless...

Its mainly through playing with RIAA stages that I have become aware of
the importance of maintaining phase as well as frequency response, but
maybe this is old hat for you pro's.

The thing about impulse analysis is that it results in something that is
visually very easy to understand.

The use of 'impulses' to excite systems is, conceptually, a neat one. The
snag is that it may require either very high peak powers, or 'infinite'
peak powers! As such, it can lead to problems with nonlinear systems since
the output then may not be what you'd have found using signals with a much
lower peak level. Hence you may find that a frequency response obtained
this way isn't the same as you'd got from a swept sinewave, or quasi-random
'wideband noise'. IIRC for this reason, although adopted enthusiastically
at first for loudspeaker analysis, it is now used with care. Ditto for
MLSSA which can give similar problems if not used with due care.

The key point is that the 'impulse' has a predefined spectrum. i.e. it can
be used to inject, 'symultaneously' a range of frequencies with a defined
set of amplitudes and phases. You can then use the result to determine the
entire spectral response.

Convolution is just a mathematical trick for subjecting a signal to some
sort of fequency-dependent transformation. Roughly speaking, convolution
of a signal and a response in the time domain is equivalent to FFTing
them both into the frequency domain, multiplying them together
point-by-point and then re-FFTing them back to the time domain.

More generally, convolution means 'scanning' one pattern across another and
working out the result as a function of the 'offet' between them. The
resulting pattern is the 'convolution' of the two which have been
'convolved'.

The snag here is that people often want to do the 'inverse convolution' and
try to work out what one of the 'original patterns' was from knowing the
convolution and one of the inputs patterns. This is sometimes formally
impossible. An area where astronomers and others sometimes rely on
'inspired guesswork'... :-)

It is useful in this context for working out power spectra or correlations.
The basaic details of all this and FT's, etc are IIRC all in the original
Blackman & Tukey (spelling?) papers that were published in the Bell System
Tech J. ages ago, then published as a book (Dover?). Used by many IT and
analysis engineers as the foundation of work in this general area of
analysis. Alas, the emphasis of the above book is pretty mathematical, and
doesn't really explain examples that would be relevant here. I'm not sure
what source I'd recommend for this.

Slainte,

Jim

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