thesis
Aspects of real-time digital spectral analysis
- Publication date
- Publisher
Abstract
In the field of control engineering there is
a need
to
study
the dynamic behaviour
of systems which are subjected
to
random
disturbances. A technique
which
is
of great practical use
is to
describe the dynamic
properties as a
function
of
frequency. This
involves determining the frequency content, or spectrum, of
the
disturbances,
and
the frequency
response
function
of
the
system.
There
are many analogue and digital techniques which are designed for this
type
of spectral analysis.
However, digital computer
techniques
are
often avoided because they
are slow, and data must
be
collected
'off-line'.
A
recently
discovered
computational method,
termed the fast-
Fourier-transform (FFT),
enables
digital
spectral analysis
to be
carried-
out in
a much shorter
time than
was previously possible.
In
view of
this discovery it
was
decided to develop digital computer programmes
which would overcome
the disadvantages
of conventional
digital
spectral
analysis. Using these
programmes a computer would
be
connected, via
an analogue
to digital interface, to the
signal source, and would process
the data
as
it
entered
the
computer.
In the jargon
of computing,
the
computer would
be 'on-line'
and analyzing
the
spectra
in 'real-time'.
The first
part of
the
project consisted of an
investigation
of
the FFP
when programmed
for an on-line
digital
computer.
The
results of
this investigation
showed
that
a rapid, accurate, and compact
FFT
could be
programmed
by
using
fixed-point
arithmetic, and coding
in
an assembly language. The
speed of
the transform
was sufficient
to
allow spectral analysis over a
frequency
range useful
in
control
applications.
Two
on-line computer programmes
based upon
the YPP were
then
written; one
for 'real-time'
spectral analysis of a single record, and
another
for the 'real-time'
estimation of
the frequency
response
function
relating
two
signals.
In
order
that the
results of
these
programmes could
be
sensibly
interpreted, a statistical study was made
of
the
spectral estimators used
in the
programmes.
Arising from this
study, several contributions
to the field of
digital
spectra. analysis
were made.
These
were : -
1) A
more general covariance relationship
for cross-spectral
estimators.
2) An
examination of aliasing
in digital
spectral estimators.
3) Some theoretical
results concerning spectral estimators
for
closed loop
systems with random
disturbances inside the loop,
Some
experimental work was conducted with
the
real-time'
spectral analysis programmes, and it
was concluded
that the tec:
inique
is
more powerful
than
conventional
digital.
methods
because it is on-
line,
and can provide estimates with
improved
resolution and
statistical stability. Real-time digital
spectral analysis methods also
have the
advantage
that they
may
be
simply and quickly modified
to suit
specific applications
