# Defining norm of a matrix of MFCC coefficients

Scenario Construction:

I have a MFCC generator block which gets the speech samples from the user and generates a rectangular matrix say $A$ of the order $m \times n$, whose elements are the Cesptral Coefficients(MFCC). Now, suppose I maintain a database which are previously stored containing the user speech signal. Through an LPC filter, I generate the speech sample and then direct it to the MFCC generator block, with a constraint that I don't give the entire set of samples from the database for the filter to generate the speech signal.

Rather, I give a part of the speech sample. Now this predicted speech signal will be now directed towards the MFCC generator block to generate the predicted signal's Cepstral coefficients which again turns out to be another rectangular matrix say $B$ of the same order $m \times n$. Then I use a matrix norm along with a heuristically chosen threshold to compare two matrices(find the error) and authenticate the user. If it fails, the input speech samples for the prediction is linearly increased and again the constraint is checked.

An insight into matrix A,B as defined before.

The rows of the matrix represent the number of coefficients to be generated per speech frame. The columns are the concatenation of coefficients of all the frames for the entire speech sample. A and B have the same setting.

During MFCC generation we make use of a window of fixed size, operate on the samples under the window which yields coefficients for MFCC for that frame and then slide the window such that the slide steps are less than the window size, i.e.,: every successive window overlaps.

Question:

I have seen this https://stackoverflow.com/questions/6932096/matching-two-series-of-mfcc-coefficients link. I found it somewhat useful. Yet, I have a few concerns to raise in regards to the problem that I just defined. Even when an authenticated user speaks ( utters the exact word that is stored in the database) it is not necessary that the MFCC (positions of each element in the matrix) should be in exact match with the one that is generated during prediction.If both the rectangular matrix is converted into a vector, there may be a time delay between the samples. If so, the norms defined in the link I mentioned needn't work out even for an authenticated user. How do I fix it? Is there any other form of solving the above problem.

• It sounds like you need to do some time registering before calculating the MFCC matrices - i.e. making sure the start of the speech signals line up. The chi-squared distance should still be appropriate, although you'd need to set an appropriate threshold. – tdc Dec 9 '11 at 10:03
• What is the underlying speech task you are trying to solve? Is it speaker verification, or is it speaker recognition? Are you constrained to approach the problem in the manner you've described? – Richard Povinelli Dec 9 '11 at 22:17
• @Richard: My problem is to solve speaker recognition. Yes , I am constrained to solve as per the above decided method. Even then if you have any other good means of other solutions at hand I ll surely go through to attain beneficiary. My primary motive is to combine MFCC technique and LPC for improved recognition. – Dinesh Dec 13 '11 at 13:24
• @TDC : Yes I believe so. – Dinesh Dec 13 '11 at 13:29
• You may try using dynamic time warping (DTW). I am not sure why you are looking for norm calculation. – talk2speech Mar 2 '18 at 9:17