Image Processing Reference
In-Depth Information
Note that for a running simulator, if the data is provided continuously through an output
port or pipe, then a suitably fast FFT can report a context switching metric in real time. This
is useful for diagnostics, for example correlating the detection of errors with high
complexity regimes.
2.3 Example of use
We evaluated hypothetical systems with 15 concurrent tasks. One system featured
asynchronous events. The other system had tasks cyclically scheduled at different periods.
The asynchronous system always had higher switching entropy. The context switching
metric distinguishes complicated but synchronized architectures from those with complex
temporal behaviour
For this metric, by computing the entropy of the phase spectrum in addition to the
amplitude may help in discriminating between complexity and noise. That would be
straightforward to include because right now we discard the phase information. Any
stationary signal that shows asymmetry must have some peculiar phase relationships going
on. So it might be easier to discount randomness in favour of more complex phase
relationships if we were to include both the amplitude spectrum and the phase spectrum in
the final metric.
Another simple alternative that works on the timing alone is the
gzip
program. This looks at
the distribution complexity in times and calculates the entropy metric. The usage of this
application is trivial. Take the output file, if a sequence of discrete inputs (zeros and number
of values), run it through
gzip
and record the size (Benedetto, et al, 2003). Comparisons of
two different sequences of identical length will suggest that the less complex program is the
one of the smaller zipped size.
3. Complementary approach - the multi-scale entropy measure
An alternate approach to measuring the temporal complexity involves the application of the
multi-scale entropy metric suggested by (Costa, 2005). This differs from the just described
context-witching metric in that it measures the complexity of a temporal behaviour or signal
over a wide range of fundamental periods. Whereas the single-scale metric works best over
a single-decade frequency spectrum scale, a multi-scale metric offers up the possibility of
looking at complexities at a variety of time scales, ranging over potentially orders of
magnitude. This is definitely useful but it can't be boiled down into a single complexity
metric; instead we will need to depict this graphically over what amounts to a logarithmic
frequency scale.
The basis for the multi-scale entropy metric is that many real-world behaviours often occur
over time scales of varying dynamic ranges. Costa originally applied this to a biomedical
application, trying to extract the temporal complexities of cardiac-driven circulatory
systems. When such a pulsed cardiac signal is multi-scale, it is actually composed of a
fundamental pulse and various arrhythmias, leading to a complicated spectrum of events.
The signal actually appears buried amongst competing behavioural periodicities at different
time scales and so it becomes that much harder to extract the information.
At first glance, we would imagine that a Fourier transform would work well to extract the
periods but in fact a typical FFT algorithm actually works best over a limited dynamic
range. By expanding the scope to a multi-scale level, Costa showed that this complexity
measure has use in a real-world application and we contend that it may also prove useful
