Image Processing Reference
In-Depth Information
Signal
Entropy
FT(Signal)
Entropy
2
2
Periodic Impulse
Train
(−)
low
low
+
Disordered
Autocorrelation
with Mean
1+ln()
~ 2+ln()
Maximum
entropy over
frequency
range
Table 1. Mapping of signal entropies to their corresponding frequency domain entropies.
The trend of increasing entropies with increasing disorder is maintained through the
transformation process.
Maximum
entropy
over time
interval
Random
in frequency domain
Random(u(t))
Noise
Time
Time
Low Entropy
Context Switching
High Entropy
Context Switching
Fig. 1. Example of context-switching waveforms with low entropy (left) and high entropy
(right). The low entropy signals are more regular.
In practice using a discrete Fourier transform such as the Fast Fourier Transform (FFT)
(Brigham & Morrow, 1967) allows us to then use the summation variant of the entropy,
where N is the order of the FFT.
=−∑ ( )∙ln( )
(5)
Search WWH ::




Custom Search