# What does the output of Gaussian Mixture Model (GMM) represents in a HMM-GMM based speech recognition application?

Till now I know that- first the speech is converted frames and feature vectors are calculated for each frame using MFCC. And while training the Acoustic model- HMM model is generate for each phoneme and each such HMM model has 3 states representing starting, middle and ending of context dependent phonemes. Also each of these states gives the likelihood probability for a given observation sequence using GMM.

My question is:

What is this observation sequence taken in GMM, is it the feature vector of a single MFCC frame or a sequence of MFCC frames ? If not then what exactly are these observation sequences and how are they related to MFCC feature vectors.

• Indeed, observation sequence is simply a N-dimmensional (usually 13) vector of MFCC's. So for each frame of audio, MFCC's are being calculated and passed into HMM. HMM on the other hand, calculates the likelihood score given the model and input vector. – jojek Apr 14 '16 at 7:36
• So, does this means each HMM state corresponds to each MFCC frames ? – user2530619 Apr 14 '16 at 8:03
• Not really. Each HMM state contains GMM, which models that state. Imagine that you are trying to model a tri-phone. Each state would have a GMM that models a single phoneme. – jojek Apr 14 '16 at 8:09
• @user2530619, each HMM state is scored against each MFCC frame. "corresponds" is not the right word here, it does not make much sense. – Nikolay Shmyrev Apr 14 '16 at 22:05
• I understand that each HMM state is scored against each MFCC frame, but my doubt is how is this relation buildup i.e. how are the HMM states restricted to score against a single MFCC frames, why can't it be multiple frames or is it that while HMM states are formed we somehow specify that each state will represent each frame. – user2530619 Apr 15 '16 at 9:43