Second Order Kolmogorov Entropy estimates from speech data

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

Second Order Kolmogorov Entropy estimates from speech data

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

Second Order Kolmogorov Entropy estimates from speech data

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

Second Order Kolmogorov Entropy estimates from speech data

Correlation Entropy vs. Embedding Dimension – various epsilons

Second Order Kolmogorov Entropy estimates from speech data

Correlation Entropy vs. Embedding Dimension – various epsilons

Second Order Kolmogorov Entropy estimates from speech data

Correlation Entropy vs. Embedding Dimension – various epsilons

Second Order Kolmogorov Entropy estimates from speech data

Correlation Entropy vs. Embedding Dimension – various SNRs

Second Order Kolmogorov Entropy estimates from speech data

Correlation Entropy vs. Embedding Dimension – various SNRs

Second Order Kolmogorov Entropy estimates from speech data

Correlation Entropy vs. Embedding Dimension – various SNRs