... Vector to waveform conversion Lecture 4 17Example of projecting signals to an orthonormal signal space),()()()(),()()()(),()()()( 323 1 323 21313 22 2 122 221 2 12 121 1 121 21111aatatatsaatatatsaatatats=⇔+==⇔+==⇔+=sssψψψψψψ)(1tψ)( 2 tψ),( 121 11aa=s),( 22 2 12 aa=s),( 323 13aa=sTransmitted ... ==><=∫∞∞− 2 )()(),()()()( txatax =)()(,tytxdyx−== “length”of x(t) Lecture 4 12 Example of distances in signal space)(1tψ)( 2 tψ),( 121 11aa=s),( 22 2 12 aa=s),( 323 13aa=s),( 21 zz=zzsd,1zsd, 2 zsd,3The ... space)(1tψ)( 2 tψ),( 121 11aa=s),( 22 2 12 aa=s),( 323 13aa=s),( 21 zz=zzsd,1zsd, 2 zsd,3The Euclidean distance between signals z(t) and s(t):3 ,2, 1)()()()( 2 22 211,=−+−=−=izazatztsdiiizsi1E3E 2 E Lecture 4 13Orthogonal signal...