HMM Study Guide Essay

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Hidden Markov Models (HMMs)
Joseph A. Giampapa
6 November 2014

Background of HMMs
• Best early tutorial:

Lawrence R. Rabiner, “A Tutorial on Hidden Markov Models and
Selected Applications in Speech Recognition,” in Proceedings of the
IEEE, Vol. 77, No. 2, February 1989. DOI: 0018-9219/89/020002,

• HMMs

– Introduced and studied in late 1960s and 1970s
– Became popular in the late 1980s

• Reasons for their popularity

– “Rich in mathematical structure” (Rabiner)
– They work well in practice for certain types of applications
– In particular, useful for characterizing signal models

Signal Model
• Consists of two parts:

– The observations, in a time-dependent sequence
• This is the signal
• Observation sequence can be discrete or continuous
– Discrete: alphabet, samples, sample intervals
– Continuous: speech, temperature, power

– The process that produces the observations

• Reasons for having a signal model:

– To understand and/or simulate the process
– To identify and recognize the signal
– To filter, transform, break-apart, componentize
(process) signals

Types of Signal Models
• Deterministic model

– E.g. sine wave, sum of exponentials
– The equation that describes it is known
– Just supply the parameters
• E.g. amplitude, frequency, phase

• Statistical model

– The sequence of observables is not easily characterized by a deterministic description
– You can hypothesize the variables and known quantities that influence the signal’s generation
– Underlying assumption: whatever produces the signal can be described by a parametric random process

• Question: How would you characterize the power consumption of