# MLSP 2007 Data Analysis Competition

Convolutive Blind Source Separation
**Submission Deadline April 13, 2007**

### Prepared by

Biomagnetic Imaging Laboratory

University of California at San Francisco, CA 94122

Email, Homepage

## Background

Blind source separation (BSS) is used to separate a set of unknown signals given only a set of observations that result from an unknown mixture of the signals. The simplest form of BSS occurs if the mixing is linear, instantaneous, and there are at least as many sensors as sources. Instantaneous mixing is an appropriate model for, e.g., EEG, MEG, EKG, and MKG data, for which the measured signals are electromagnetic potentials or fields. However, the instantaneous mixing model is inappropriate for mixtures of audio, for which the mixing is convolutive in nature.

## Goal

To separate the (convolutive) mixture of two sources of real audio data given two observations.

## Data Set

Two microphones were used to collect the data, which consist of two audio sources. The first source is speech from a male speaker and the second source is a short segment of music. The data is in Matlab format (version 7). The two variables contained in this file include`x`and

`fs`. Each of the two rows of

`x`corresponds to the data collected at a single sensor and fs contains the sampling frequency in Hz.

Download data set [MATLAB version 7]

## Deliverables

A Matlab file (described below) and a brief description of the method should be emailed to Deniz Erdogmus by April 13, 2007.
For **linear systems**:
The Matlab data file should contain a (global) feedforward flag, `flg`,
and a cell variable, `W`, that designates the demixing
coefficients. The variable `flg` should be 1 if the local demixing
filters are combined into a global feedforward system and should be 0 if
they are combined into a global feedback system. The *i*'th element of
the cell variable, `W{i}`, should contain the (2 x 2) demixing
matrix for lag *i-1*, where `W{i}(j,k)` is the transfer
function between the *j*'th source estimate and the *k*'th
observation. The variables described above will be
used to generate estimates of the separated sources, `y`, using
the following code:

Notice that this code assumes the use of FIR filters. If AR or ARMA filters are desired then please include in the submission the Matlab code required to generate the source estimates from the supplied coefficients.(flg = 1)

y = zeros(2,30000);

for i = 1:length(W)

y = y + W{i}*filter([zeros(1,i-1) 1],1,x,[],2);

end

(flg = 0)

Lw = length(W);

y = zeros(2,30000);

z = zeros(2,Lw);

for n = 1:30000

net = zeros(2,1);

for i = 1:Lw

net = net + W{i}*z(:,Lw+1-i);

end

y(:,n) = x(:,n) + net;

z(:,1:Lw-1) = z(:,2:Lw);

z(:,Lw) = y(:,n);

end

For **nonlinear systems**: The Matlab data file should contain a
data matrix,

## Winner

Only the mixture of the sources is provided to the contestants; however, the data were originally collected one source at a time. Consequently, we can use the one-at-a-time SIR [1], [2] to provide an unambiguous measure of separation performance for the linear demixing systems. The figure of merit used for nonlinear demixing systems will be based on a subjective listening test, which will be performed in a double-blind fashion. The listening test will include two equally-weighted aspects: the quality of the separation and the sound quality of the source estimates (e.g., if the separated sources are corrupted by distracting whistling artifacts).The overall winner will also be based on a double-blind listening test, which will be performed between the best linear and the best nonlinear systems.

The winners will be invited to submit a paper describing their solution to the conference and the follow-up journal special issue.

- [1] Daniel Schobben, Kari Torkkola and Paris Smaragdis, "Evaluation of blind signal separation methods," Intl. Workshop on Independent Component Analysis and Signal Separation (ICA '99), Aussois, France, pp. 261-266, Jan. 1999. [PDF]
- [2] Kenneth E. Hild II, Deniz Erdogmus, and Jose C. Principe, "Experimental upper bound for the performance of convolutive source separation methods," IEEE Trans. on Signal Processing, Vol. 54, No. 2, pp. 627-635, Feb. 2006. [HTML]