Lecture 11 - Chapter 9 fourier series harm 8mg 2 best approximation Discrete Brier Transform Fast Fouriertunstorm aperiodic function Approximating

# Lecture 11 - Chapter 9 fourier series harm 8mg 2 best...

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Chapter 9 Thgonometwetpproximetrin fourier series best approximation 8mg harm 2 Discrete Brier Transform Fast Fouriertunstorm Approximating aperiodic function 4.1 periodic function f who assume f has period UT C If afunctur has period P Ffg ftp.uy can approximate f by first in term of arts fourier series r n 9.1 few 2 Lz got kcookxebiosinkxJCd 2gak tTTfo2FfcxicoskxdxikF9t.i n 9.3 KK fexjsinkx.de k't c n want to show 4 t is the best approximation to f in U norm by atigonometwepoynumial of degree n a trigonometric polynomial ofdgreen n H Sn Cx E ee eiko ki n
dis Jn Iif Sn HE Cfa Snow DX want to minimise yn Ab Jn If fun fiancee is 2dx CfcxD2d 2 fittfeae dx E nee nu ceffteikxeid.de use orthogonality of set El ei x e ein e ing i Kx e e ne pen kEk3 For KF L a 7 gjteikxeilxdx ffe.ie te if e e Yo o For K l as gouteikeikdx fo da 2T 4.6 becomes 49 Jn Jj Tax 2,1 info eiHdxt2I n9d eNotethetjnisquadratuo in terms of Ck to find minimum use critical parts of Jn as a function
of Cy's Alo nm 2J tfcaeim d t 212 7 C