| Phase Alignment Algorithm In order for our music to have good sound quality, there is one last step to our algorithm. As it is now, if our signals were added together, their beats would not necessarily occur at the same time even though their tempos are the same. To fix this problem, we need to align the songs beats such that they occurr simultaneously. This phase alignment process is simply an extension of the beat matching algorithm. We begin by running one of our signals through all the steps of the beat-matching algorithm prior to the comb filtering. This gives a signal with strong peaks where the beats occur. Since we know the frequency at which these beats occur, we know which comb filter corresponds to this tempo. This comb filter is then convolved with the signal for one period. This is implemented by multiplication of the FFT's of the comb filter and the modified signal. We take the energy of this output and find the location in time of the maximum energy value. This process is repeated for the other signal, resulting in two locations in time -- where the first beat occurs in each signal. The signal whose beat occurs first is simply zero-padded until the two beats occur simultaneously. Now the two songs are phase-aligned. Matlab Code - phasealign.m - takes a time domain signal and returns the location of % the sample where its first beat occurs.
Matlab Plots Before Phase Alignment:  After Phase Alignment:  | 
