1. Stereo Mix Source Identification and Separation
Based on work done by
Carlos Avendano
By: Jeff England
EE 6820

2. How a Stereo Mix is Created
Each Source Recorded Independently
Sources are then mixed together with different panning indexes
αij is the amplitude-panning coefficient
i represents either the left or right channel
Left (i = 1)
Right (i = 2)
Mix is then convolved with reverberation impulse response

3. Similarity Function Let Xi(m,k) be the STFT of the signal xi(t)
Basic idea is to compare left and right channels in the frequency domain to identify the different sources based on the panning coefficients
Let Xi(m,k) be the STFT of the signal xi(t)
m is the time index
k is the frequency index
Similarity Function determines the similarities between left and right channels.
Equation is bounded between 0 and 1
Sources panned to center are equal to 1
Source panned completely to either side are equal to 0

4. Panning Index Equation
Subtract similarity functions of left and right channels to determine where in the left right plane the panning index is located.
Use the following resolving function to determine source location
Use Similarity function, difference equation and resolving function to determine the panning indices
If Δ(m,k) > 0
If Δ(m,k) = 0
If Δ(m,k) < 0

5. Signal to Interference Ratio
The panning index equation works best when the different sources in the mix do not overlap in the transform domain
Need to measure the error to determine the width of the panning window
Find panning index ψ0 with magnitude g0
Find interference panning index ψe with magnitude ge
SIR is used to define the panning index window size

6. Panning Index Window Select time-frequency bins equal to panning index
Selecting only these bins will separate the particular source
Use a window centered around the panning index will reduce distortion but may increase interference
Following equation is the Gaussian window equation which will be used to define the panning index window

7. End Result
Subtract windowed result from original signal to get new signal without the source.
Use inverse STFT to get back to spatial domain

8. Goals & References 1) Duplicate Carlos Avendano’s work
2) Find the number of sources (tracks) in the mix
3) Identify the different instruments in the mix
References:
“Frequency-Domain Source Identification and Manipulation in Stereo Mixes for Enhancement, Suppression and Re-Panning Applications”
Carlos Avendano
October 2003