By Constance Reid

"It provides a delicate portrait of an outstanding individual. It describes correctly and intelligibly on a nontechnical point the realm of mathematical rules during which Hilbert created his masterpieces. And it illuminates the history of German social heritage opposed to which the drama of Hilberts existence was once performed. past this, it's a poem in compliment of mathematics." -SCIENCE

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**Example text**

29 A. 1. Implementation of the Hermite polynomial Implemented in Mathematica. 2. Implementation of the Fourier series Implemented in Mathematica. 3. Implementation of the Fourier transform Implemented in Mathematica. n:=n; k:=k; M=10; Freq=2; f=Cos[2*Pi/M*n*Freq]; F=Sum[f*E ^(-I*2*Pi*k*n/M),fn,0,M-1g]; Hf=2/M*Sum[F*Sin[(2*Pi*k*n)/M],fk,1,M/2-1g]; Plot[Abs[F],fk,-M/2,M/2g,AxesLabel -> f"w","F(w)"g]; Plot[ff,Hfg],fn,-2*M/Pi,2*M/Pig,AxesLabel -> f"t","f(t),Hf(t)"g]; 32 References [1] Aniansson J. et al, Fouriermetoder, KTH, Stockholm, 1989.

3. Implementation of the Fourier transform Implemented in Mathematica. n:=n; k:=k; M=10; Freq=2; f=Cos[2*Pi/M*n*Freq]; F=Sum[f*E ^(-I*2*Pi*k*n/M),fn,0,M-1g]; Hf=2/M*Sum[F*Sin[(2*Pi*k*n)/M],fk,1,M/2-1g]; Plot[Abs[F],fk,-M/2,M/2g,AxesLabel -> f"w","F(w)"g]; Plot[ff,Hfg],fn,-2*M/Pi,2*M/Pig,AxesLabel -> f"t","f(t),Hf(t)"g]; 32 References [1] Aniansson J. et al, Fouriermetoder, KTH, Stockholm, 1989. [2] Goldberg R. , Fourier transforms, Cambrige university press, Cambridge. , Boston, 1996. [4] Lennart HellstrÄom, LinjÄar analys, HÄogskolan i VÄaxjÄo, 1995.

If we instead subtract fmc and fbmc we get an upper AM-SSB signal. 1 has the same delay as the Hilbert ¯lter. The delay is needed in real applications to synchronize the two signals fm (t) and fbm (t). 29 A. 1. Implementation of the Hermite polynomial Implemented in Mathematica. 2. Implementation of the Fourier series Implemented in Mathematica. 3. Implementation of the Fourier transform Implemented in Mathematica. n:=n; k:=k; M=10; Freq=2; f=Cos[2*Pi/M*n*Freq]; F=Sum[f*E ^(-I*2*Pi*k*n/M),fn,0,M-1g]; Hf=2/M*Sum[F*Sin[(2*Pi*k*n)/M],fk,1,M/2-1g]; Plot[Abs[F],fk,-M/2,M/2g,AxesLabel -> f"w","F(w)"g]; Plot[ff,Hfg],fn,-2*M/Pi,2*M/Pig,AxesLabel -> f"t","f(t),Hf(t)"g]; 32 References [1] Aniansson J.