Fourier[list] InverseFourier[list] N1=256 Pure sin wave (note positive and negative frequency): data = Table[N[Sin[20 2 Pi k/N1]], {k, N1}]; ListLinePlot[data] Data=Fourier[data]; ListLinePlot[Abs[Data],PlotRange->All] sin wave + noise: see small amplitudes (Data) at all frequencies data = Table[N[Sin[20 2 Pi k/N1] + (RandomReal[] - 1/2)], {k, N1}]; ListLinePlot[data] Data=Fourier[data]; ListLinePlot[Abs[Data],PlotRange->All] sawtooth (has discontinuity -> lots of strong harmonics) data = Table[N[Mod[k,20]], {k, N1}]; ListLinePlot[data] Data=Fourier[data]; ListLinePlot[Abs[Data],PlotRange->All] Data[[1]] this is the zero^th harmonic, i.e, the DC signal to remove DC subtract average: md=Mean[data] data = Table[N[Mod[k,20]-md], {k, N1}]; ListLinePlot[data] Data=Fourier[data]; ListLinePlot[Abs[Data],PlotRange->All]; Data[[1]] triangular wave...no discontinuity so weaker harmonics data = Table[Abs[N[Mod[k,40]-20]]-10, {k, N1}]; ListLinePlot[data] Data=Fourier[data]; ListLinePlot[Abs[Data],PlotRange->All]; smooth the sawtooth with running average: data = Table[N[Mod[k,20]-md], {k, N1}]; data2=Table[Sum[data[[k1]],{k1,Max[1,k-5],k}]/5,{k,N1}]; ListLinePlot[data2]; Data2=Fourier[data2]; ListLinePlot[Abs[Data2],PlotRange->All]; smooth the sine wave+noise with running average data = Table[N[Sin[20 2 Pi k/N1] + (RandomReal[] - 1/2)], {k, N1}]; data2=Table[Sum[data[[k1]],{k1,Max[1,k-5],k}]/5,{k,N1}]; ListLinePlot[data2]; ListLinePlot[data]; Data2=Fourier[data2]; ListLinePlot[Abs[Data2],PlotRange->All]; Data=Fourier[data]; ListLinePlot[Abs[Data],PlotRange->All]