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Mathematics Math21b Spring 2009

Linear Algebra and Differential Equations

Exhibit: Linear algebra: autotune

Course Head: Oliver Knill

Office: SciCtr 434

Email: knill@math.harvard.edu

Youtube Demo of Autotune I |
Youtube Demo of Autotune II | Autotune is also called the "photoshop of Music". Instead of looking better", one can "sound better". In the mathematica project, you get a bit insight into the mechanism, but it does things only in a very primitive way: the bad frequencies are filtered out. The real autotune shifts the frequencies to the right place. |

Here is a very primitive Mathematica version of autotune in Mathematica:
A=Import["test.wav"]; M=8000; S=A[[1,1,1]]; n=Length[S]; tunes=Floor[Table[440*2^(k/12),{k,-36,55}]]; filter=Table[If[MemberQ[tunes,k],1,0],{k,M}]; S1[l_]:=Table[S[[l*M+k]],{k,M}]; S2[l_]:=FourierDCT[filter*FourierDCT[S1[l],2],3]; S3=Flatten[Table[S2[l],{l,0,Floor[n/M]-1}]]; U=Sound[SampledSoundList[{S3,S3},44100]]; Export["s.wav",U,"Wav"]; |

Please send questions and comments to math21b@fas.harvard.edu

Math21b (Exam Group 1)| Oliver Knill | Spring 2009 |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University