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

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

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

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

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

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

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

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