Editing Baum–Welch algorithm (section)

===Speech recognition===
Hidden Markov Models were first applied to speech recognition by [[James K. Baker]] in 1975.<ref>{{Cite journal |last1=Baker |first1=James K. |author-link1=James K. Baker |doi=10.1109/TASSP.1975.1162650 |title=The DRAGON system—An overview |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |volume=23 |pages=24–29 |year=1975 }}</ref> Continuous speech recognition occurs by the following steps, modeled by a HMM. Feature analysis is first undertaken on temporal and/or spectral features of the speech signal. This produces an observation vector. The feature is then compared to all sequences of the speech recognition units. These units could be [[phonemes]], syllables, or whole-word units. A lexicon decoding system is applied to constrain the paths investigated, so only words in the system's lexicon (word dictionary) are investigated. Similar to the lexicon decoding, the system path is further constrained by the rules of grammar and syntax. Finally, semantic analysis is applied and the system outputs the recognized utterance. A limitation of many HMM applications to speech recognition is that the current state only depends on the state at the previous time-step, which is unrealistic for speech as dependencies are often several time-steps in duration.<ref>{{cite journal |last=Rabiner |first=Lawrence |title=A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition |journal=Proceedings of the IEEE |date=February 1989 |volume=77 |issue=2 |pages=257–286 |doi=10.1109/5.18626 |citeseerx=10.1.1.381.3454 |s2cid=13618539 }}</ref> The Baum–Welch algorithm also has extensive applications in solving HMMs used in the field of speech synthesis.<ref>{{cite journal |last1=Tokuda |first1=Keiichi |first2=Takayoshi |last2=Yoshimura |first3=Takashi |last3=Masuko |first4=Takao |last4=Kobayashi |first5=Tadashi |last5=Kitamura |title=Speech Parameter Generation Algorithms for HMM-Based Speech Synthesis |journal=IEEE International Conference on Acoustics, Speech, and Signal Processing |year=2000 |volume=3 }}</ref>