Joseph A. Giampapa

6 November 2014 garof@cs.cmu.edu www.cs.cmu.edu/~garof

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,

URL:

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=18626

• 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

the…