1. Sustained Phones (/aa/, /ae/, /eh/, /sh/, /z/, /f/, /m/, /n/)
Second Order Kolmogorov Entropy Estimation of speech data – The setup
Speech data, sampled at 22.5 KHz
Sustained Phones (/aa/, /ae/, /eh/, /sh/, /z/, /f/, /m/, /n/)
Short (single utterance) phones (/aa/, /ae/, /eh/, /sh/, /z/, /f/, /m/, /n/)
CVC words (bat, beat, boat, boy)
Output – Second order Kolmogorov Entropy
Using these, we wish to analyze:
The presence or absence of chaos in any time series.
Their discrimination characteristics across different attractors for classification

2. The analysis setup
Currently, this analysis includes estimates of K2 for different embedding dimensions
Variation in entropy estimates with the neighborhood radius, epsilon was studied
Variation in entropy estimates with SNR of the signal was studied
Currently, the analysis was performed on 3 vowels, 2 nasals and 2 fricatives
Results show that vowels and nasals have a much smaller entropy, as compared to fricatives
Further, k2 consistently decreases with embedding dimension for vowles and nasals, while for fricatives, it consistently increases

3. The analysis setup (in progress / coming soon)…
Data size (length of the time series):
This is crucial for our purpose, since we wish to extract information from short time series (sample data from utterances).
Speaker variation:
We wish to study variations in the Kolmogorov entropy of phone or word level attractors
across different speakers.
across different phones/words
across different broad phone classes

4. Correlation Entropy vs. Embedding Dimension – various epsilons

5. Correlation Entropy vs. Embedding Dimension – various epsilons

6. Correlation Entropy vs. Embedding Dimension – various epsilons

7. Correlation Entropy vs. Embedding Dimension – various SNRs

8. Correlation Entropy vs. Embedding Dimension – various SNRs

9. Correlation Entropy vs. Embedding Dimension – various SNRs